Sherpa 3.0.0 Manual

Welcome to the Sherpa manual. The manual for versions prior to 3.0.0 can be found here.

1. Introduction

Sherpa is a Monte Carlo event generator for the Simulation of High-Energy Reactions of Particles in lepton-lepton, lepton-photon, photon-photon, lepton-hadron and hadron-hadron collisions. This document provides information to help users understand and apply Sherpa for their physics studies. The event generator is introduced, in broad terms, and the installation and running of the program are outlined. The various options and parameters specifying the program are compiled, and their meanings are explained. This document does not aim at giving a complete description of the physics content of Sherpa. To this end, the authors refer the reader to the original publications, [GHK+09] and [B+19].

1.1. Introduction to Sherpa

Sherpa [B+19] is a Monte Carlo event generator that provides complete hadronic final states in simulations of high-energy particle collisions. The produced events may be passed into detector simulations used by the various experiments. The entire code has been written in C++, like its competitors Herwig 7 [B+08, B+16] and Pythia 8 [B+22].

Sherpa simulations can be achieved for the following types of collisions:

• for lepton–lepton collisions, as explored by the CERN LEP experiments,

• for lepton–photon collisions,

• for photon–photon collisions with both photons either resolved or unresolved,

• for deep-inelastic lepton-hadron scattering, as investigated by the HERA experiments at DESY, and,

• in particular, for hadronic interactions as studied at the Fermilab Tevatron or the CERN LHC.

The list of physics processes that can be simulated with Sherpa covers all reactions in the Standard Model. Other models can be implemented either using Sherpa’s own model syntax, or by using the generic interface [HKSS15] to the UFO output [Darme+23, DDF+12] of FeynRules [CdAD+11, CD09]. The Sherpa program owes this versatility to the two inbuilt matrix-element generators, AMEGIC++ and Comix, and to it’s phase-space generator Phasic [KKS02], which automatically calculate and integrate tree-level amplitudes for the implemented models. This feature enables Sherpa to be used as a cross-section integrator and parton-level event generator as well. This aspect has been extensively tested, see e.g. [GKP+04, H+06].

As a second key feature of Sherpa the program provides an implementation of the merging approaches of [HKSS09] and [GHK+13, HKSS13]. These algorithms yield improved descriptions of multijet production processes, which copiously appear at lepton-hadron colliders like HERA [CGH10], or hadron-hadron colliders like the Tevatron and the LHC, [GKS+05, HSS10, KSSS04, KSSS05]. An older approach, implemented in previous versions of Sherpa and known as the CKKW technique [CKKW01, Kra02], has been compared in great detail in [A+08] with other approaches, such as the MLM merging prescription [MMP02] as implemented in Alpgen [MMP+03], Madevent [MS03, SL94], or Helac [KP00, PW07] and the CKKW-L prescription [LL05, Lon02] of Ariadne [Lon92].

This manual contains all information necessary to get started with Sherpa as quickly as possible. It lists options and switches of interest for steering the simulation of various physics aspects of the collision. It does not describe the physics simulated by Sherpa or the underlying structure of the program. Many external codes can be linked with Sherpa. This manual explains how to do this, but it does not contain a description of the external programs. You are encouraged to read their corresponding documentations, which are referenced in the text. If you use external programs with Sherpa, you are encouraged to cite them accordingly.

The MCnet Guidelines apply to Sherpa. You are kindly asked to cite [B+19] if you have used the program in your work. Should your application of Sherpa furthermore involve specific non-trivial aspects of the simulation chain we urge you to also cite the relevant publications explicitly.

The Sherpa authors strongly recommend the study of the manuals and many excellent publications on different aspects of event generation and physics at collider experiments written by other event generator authors.

This manual is organized as follows: in Basic structure the modular structure intrinsic to Sherpa is introduced. Getting started contains information about and instructions for the installation of the package. There is also a description of the steps that are needed to run Sherpa and generate events. The Input structure is then discussed, and the ways in which Sherpa can be steered are explained. All parameters and options are discussed in Parameters. Advanced Tips and tricks are detailed, and some options for Customization are outlined for those more familiar with Sherpa. There is also a short description of the different Examples provided with Sherpa.

The construction of Monte Carlo programs requires several assumptions, approximations and simplifications of complicated physics aspects. The results of event generators should therefore always be verified and cross-checked with results obtained by other programs, and they should be interpreted with care and common sense.

1.2. Basic structure

Sherpa is a modular program. This reflects the paradigm of Monte Carlo event generation, with the full simulation split into well defined event phases, based on QCD factorization theorems. Accordingly, each module encapsulates a different aspect of event generation for high-energy particle reactions. It resides within its own namespace and is located in its own subdirectory of the same name. The main module called SHERPA steers the interplay of all modules—or phases—and the actual generation of the events. Altogether, the following modules are currently distributed with the Sherpa framework:

ATOOLS

This is the general toolbox for all other modules. It contains classes with mathematical tools like vectors and matrices, organization tools such as read-in or write-out devices, and physics tools like particle data or classes for the event record.

METOOLS

In this module some general methods for the evaluation of helicity amplitudes have been accumulated. They are used in AMEGIC++, the EXTRA_XS module, and the matrix-element generator Comix. This module also contains helicity amplitudes for some generic matrix elements, that are, e.g., used by HADRONS++. Further, METOOLS also contains a simple library of tensor integrals which are used in the PHOTONS++ QED matrix element corrections.

BEAM

This module manages the treatment of the initial beam spectra for different colliders. The three options which are currently available include a monochromatic beam, which requires no extra treatment, photon emission in the Equivalent Photon Approximation (EPA) and—for the case of an electron collider—laser backscattering off the electrons, leading to photonic initial states.

PDF

The PDF module provides access to various parton density functions (PDFs) for the proton and the photon. In addition, it hosts an interface to the LHAPDF package, which makes a full wealth of PDFs available. An (analytical) electron structure function is supplied in the PDF module as well.

MODEL

This module sets up the physics model for the simulation. It initializes particle properties, basic physics parameters (coupling constants, mixing angles, etc.) and the set of available interaction vertices (Feynman rules). By now, there exist explicit implementations of the Standard Model (SM), its Minimal Supersymmetric extension (MSSM), the ADD model of large extra dimensions, and a comprehensive set of operators parameterising anomalous triple and quartic electroweak gauge boson couplings. An interface to FeynRules, i.e. the UFO model input is also available.

EXTRA_XS

In this module a (limited) collection of analytic expressions for simple \(2 \rightarrow 2\) processes within the SM are provided together with classes embedding them into the Sherpa framework. This also includes methods used for the definition of the starting conditions for parton-shower evolution, such as colour connections and the hard scale of the process.

AMEGIC++

AMEGIC++ [KKS02] is Sherpa’s original matrix-element generator. It employs the method of helicity amplitudes [KS85], [BMM94] and works as a generator, which generates generators: During the initialization run the matrix elements for a given set of processes, as well as their specific phase-space mappings are created by AMEGIC++. Corresponding C++ sourcecode is written to disk and compiled by the user using the makelibs script. The produced libraries are linked to the main program automatically in the next run and used to calculate cross sections and to generate weighted or unweighted events. AMEGIC++ has been tested for multi-particle production in the Standard Model [GKP+04]. Its MSSM implementation has been validated in [H+06]. An extensive validation for models invoked via FeynRules package has been presented in [CdAD+11].

COMIX

Comix is a multi-leg tree-level matrix element generator, based on the colour dressed Berends-Giele recursive relations [DHM06]. It employs a new algorithm to recursively compute phase-space weights. The module is a useful supplement to older matrix element generators like AMEGIC++ in the high multiplicity regime. Due to the usage of colour sampling it is particularly suited for an interface with parton shower simulations and can hence be easily employed for the ME-PS merging within Sherpa. It is Sherpa’s default large multiplicity matrix element generator for Standard Model production processes.

PHASIC++

All base classes dealing with the Monte Carlo phase-space integration are located in this module. For the evaluation of the initial-state (laser backscattering, initial-state radiation) and final-state integrals, the adaptive multi-channel method of [KP94], [BPK94] is used by default together with a Vegas optimization [Lep] of the single channels. In addition, final-state integration accomplished by Rambo [KSE86], Sarge [DvHK00] and HAAG [vHP02] is supported.

CSSHOWER++

This is the module hosting Sherpa’s default parton shower, which was published in [SK08b]. The corresponding shower model was originally proposed in [NS05], [NS]. It relies on the factorisation of real-emission matrix elements in the Catani–Seymour (CS) subtraction framework [CS97], [CDST02]. There exist four general types of CS dipole terms that capture the complete infrared singularity structure of next-to-leading order QCD amplitudes. In the large-\(N_C\) limit, the corresponding splitter and spectator partons are always adjacent in colour space. The dipole functions for the various cases, taken in four dimensions and averaged over spins, are used as shower splitting kernels.

DIRE

This is the module hosting Sherpa’s alternative parton shower [HP]. In the Dire model, the ordering variable exhibits a symmetry in emitter and spectator momenta, such that the dipole-like picture of the evolution can be re-interpreted as a dipole picture in the soft limit. At the same time, the splitting functions are regularized in the soft anti-collinear region using partial fractioning of the soft eikonal in the Catani–Seymour approach [CS97], [CDST02]. They are then modified to satisfy the sum rules in the collinear limit. This leads to an invariant formulation of the parton-shower algorithm, which is in complete analogy to the standard DGLAP case, but generates the correct soft anomalous dimension at one-loop order.

AMISIC++

AMISIC++ contains classes for the simulation of multiple parton interactions according to [SvZ87]. In Sherpa the treatment of multiple interactions has been extended by allowing for the simultaneous evolution of an independent parton shower in each of the subsequent (semi-)hard collisions.

REMNANTS

REMNANTS contains classes for the simulation of the beam remnants, including in particular the spatial form of the matter distribution which is relevant for the underlying event, and the treatment of the intrinsic transverse momentum.

RECONNECTIONS

RECONNECTIONS handles the colour reconnections preceding the hadronisation. This module will experience future refinements.

AHADIC++

AHADIC++ is Sherpa’s hadronisation package, for translating the partons (quarks and gluons) into primordial hadrons, to be further decayed in HADRONS++. The algorithm bases on the cluster fragmentation ideas presented in [Got83], [Got84], [Web84], [GM87] and implemented in the Herwig family of event generators. The actual Sherpa implementation is based on [CK22].

HADRONS++

HADRONS++ is the module for simulating hadron and tau-lepton decays. The resulting decay products respect full spin correlations (if desired). Several matrix elements and form-factor models have been implemented, such as the Kühn-Santamaría model, form-factor parameterisation from Resonance Chiral Theory for the tau and form factors from heavy quark effective theory or light cone sum rules for hadron decays.

PHOTONS++

The PHOTONS++ module holds routines to add QED radiation to hadron and tau-lepton decays. This has been achieved by an implementation of the YFS algorithm [YFS61], described in [SK08a], [KLLSchonherr19] and [FS23]. The structure of PHOTONS++ is such that the formalism can be extended to scattering processes and to a systematic improvement to higher orders of perturbation theory [SK08a]. The application of PHOTONS++ therefore accounts for corrections that usually are added by the application of PHOTOS [Ba94] to the final state.

SHERPA

Finally, SHERPA is the steering module that initializes, controls and evaluates the different phases during the entire process of event generation. All routines for the combination of truncated showers and matrix elements, which are independent of the specific matrix element and parton shower generator are found in this module.

The actual executable of the Sherpa generator can be found in the subdirectory <prefix>/bin/ after installation and is called Sherpa. To run the program, input files have to be provided in the current working directory or elsewhere by specifying the corresponding path, see Input structure. All output files are then written to this directory as well.

2. Getting started

2.1. Installation

Sherpa is distributed as a tarred and gzipped file named sherpa-<VERSION>.tar.gz, and can be unpacked in the current working directory with

$ tar -zxf sherpa-<VERSION>.tar.gz

Alternatively, it can also be accessed via Git through the location specified on the download page.

To guarantee successful installation, the following tools should be available on the system:

• C++ compiler

• cmake

• make or ninja

Recommended:

• Fortran compiler

• LHAPDF (including devel packages). If not available, use the -DSHERPA_ENABLE_INSTALL_LHAPDF=ON cmake option to install LHAPDF on-the-fly during the Sherpa installation (internet connection required).

• libzip (including devel packages). If not available, use the -DSHERPA_ENABLE_INSTALL_LIBZIP=ON cmake option to install libzip on-the-fly during the Sherpa installation (internet connection required).

Compilation and installation proceed through the following commands if you use the distribution tarball:

$ cd sherpa-<VERSION>/
$ cmake -S . -B <builddir> [+ optional configuration options described below]
$ cmake --build <builddir> [other build options, e.g. -j 8]
$ cmake --install <builddir>

where <builddir> has to be replaced with the (temporary) directory in which intermediate files are stored during the build process. You can simply use the current working directory, i.e. cmake -S . -B . to compile in-source if you want to keep everything Sherpa-related in one directory.

Note that re-running cmake with different configuration options is not the same as running it in a fresh working directory. Use ccmake . instead to check/change the current configuration. To start afresh, e.g. to pick up a different version of a dependency, you can use the cmake --fresh [...] option in recent versions of cmake, or just delete the cache (rm -rf CMakeCache.txt CMakeFiles).

If not specified differently, the directory structure after installation is organized as follows

$(prefix)/bin

Sherpa executable and scripts

$(prefix)/include

headers for process library compilation

$(prefix)/lib

basic libraries

$(prefix)/share

PDFs, Decaydata, fallback run cards

The installation directory $(prefix) can be specified by using the -DCMAKE_INSTALL_PREFIX=/path/to/installation/target directive and defaults to the current working directory (.).

If Sherpa has to be moved to a different directory after the installation, one has to set the following environment variables for each run:

• SHERPA_INCLUDE_PATH=$newprefix/include/SHERPA-MC

• SHERPA_SHARE_PATH=$newprefix/share/SHERPA-MC

• SHERPA_LIBRARY_PATH=$newprefix/lib/SHERPA-MC

• LD_LIBRARY_PATH=$SHERPA_LIBRARY_PATH:$LD_LIBRARY_PATH

Sherpa can be interfaced with various external packages, e.g. HepMC for event output, LHAPDF for PDF sets, or Rivet for analysis. For this to work, the user has to add the corresponding options to the cmake configuration, e.g. for Rivet:

$  cmake [...] -DSHERPA_ENABLE_RIVET=ON

If your Rivet installation is not in a standard directory, you instead have to point cmake to the path where Rivet is installed:

$  cmake [...] -DRIVET_DIR=/my/rivet/install/dir

The provided path has to point to the top level installation directory of the external package, i.e. the one containing the lib/, share/, … subdirectories.

Other external packages are activated using equivalent configuration options, i.e. either using -DSHERPA_ENABLE_<PACKAGENAME>=ON or using -D<PackageName>_DIR=/my/package/install/dir (or both, but enabling a package is already implied if its directory is given). Note that the package name in the SHERPA_ENABLE_<PACKAGENAME> is always capitalised, while the capitalisation can differ in <PackageName>_DIR, as defined by the third-party package. For a complete list of possible configuration options (and their correct capitalisation), run cmake -LA.

The Sherpa package has successfully been compiled, installed and tested on various Linux distributions (Arch Linux, SUSE Linux, RHEL, Scientific Linux, Debian, Ubuntu) and on macOS, using the GNU Compiler Collection (GCC), Clang and Intel OneAPI 2022.

If you have multiple compilers installed on your system, you can use shell environment variables to specify which of these are to be used. A list of the available variables is printed with

$ -DCMAKE_CXX_COMPILER=myc++compiler

in the Sherpa top level directory and looking at the last lines. Depending on the shell you are using, you can set these variables e.g. with export (bash) or setenv (csh). For example, to use a specific versioned GCC installation, you could run before calling cmake:

export CXX=g++-13
export CC=gcc-13
export CPP=cpp-13

2.1.1. Installation on Cray XE6 / XK7

Sherpa has been installed successfully on Cray XE6 and Cray XK7. The following configure command should be used:

$ cmake -DSHERPA_ENABLE_MPI=ON <your options>

Sherpa can then be run with

$ aprun -n <nofcores> <prefix>/bin/Sherpa -lrun.log

The modularity of the code requires setting the environment variable CRAY_ROOTFS, cf. the Cray system documentation.

2.1.2. Installation on IBM BlueGene/Q

Sherpa has been installed successfully on an IBM BlueGene/Q system. The following cmake command should be used

$ cmake <your options> -DSHERPA_ENABLE_MPI=ON -DCMAKE_C_COMPILER=mpicc -DCMAKE_CXX_COMPILER=mpic++ -DCMAKE_Fortran_COMPILER=mpif90

Sherpa can then be run with

$ qsub -A <account> -n <nofcores> -t 60 --mode c16 <prefix>/bin/Sherpa -lrun.log

2.1.3. macOS Installation

The installation on macOS works analogously to an installation on a GNU/Linux system. You might need to ensure first that the Xcode Command Line Tools are installed. Other missing command line tools can be installed through a package manager like Homebrew or MacPorts.

2.2. Running Sherpa

The Sherpa executable resides in the directory <prefix>/bin/ where <prefix> denotes the path to the Sherpa installation directory. The way a particular simulation will be accomplished is defined by several parameters, which can all be listed in a common file, or data card (Parameters can be alternatively specified on the command line; more details are given in Input structure). This steering file is called Sherpa.yaml and some example setups (i.e. Sherpa.yaml files) are distributed with Sherpa. They can be found in the directory <prefix>/share/SHERPA-MC/Examples/, and descriptions of some of their key features can be found in the section Examples.

Note

It is not in general possible to reuse steering files from previous Sherpa versions. Often there are small changes in the parameter syntax of the files from one version to the next. These changes are documented in our manuals. In addition, update any custom Decaydata directories you may have used (and reapply any changes which you might have applied to the old ones), see Hadron decays.

The very first step in running Sherpa is therefore to adjust all parameters to the needs of the desired simulation. The details for doing this properly are given in Parameters. In this section, the focus is on the main issues for a successful operation of Sherpa. This is illustrated by discussing and referring to the parameter settings that come in the example steering file ./Examples/V_plus_Jets/LHC_ZJets/Sherpa.LO.yaml, cf. Z production. This is a simple configuration created to show the basics of how to operate Sherpa. It should be stressed that this steering file relies on many of Sherpa’s default settings, and, as such, you should understand those settings before using it to look at physics. For more information on the settings and parameters in Sherpa, see Parameters, and for more examples see the Examples section.

2.2.1. Process selection and initialization

Central to any Monte Carlo simulation is the choice of the hard processes that initiate the events. These hard processes are described by matrix elements. In Sherpa, the selection of processes happens in the PROCESSES part of the steering file. Only a few 2->2 reactions have been hard-coded. They are available in the EXTRA_XS module. The more usual way to compute matrix elements is to employ one of Sherpa’s automated tree-level generators, AMEGIC++ and Comix, see Basic structure. If no matrix-element generator is selected, using the ME_GENERATORS tag, then Sherpa will use whichever generator is capable of calculating the process, checking Comix first, then AMEGIC++ and then EXTRA_XS. Therefore, for some processes, several of the options are used. In this example, however, all processes will be calculated by Comix.

To begin with the example, the Sherpa run has to be started by changing into the <prefix>/share/SHERPA-MC/Examples/V_plus_Jets/LHC_ZJets/ directory and executing

$ <prefix>/bin/Sherpa

You may also run from an arbitrary directory, employing <prefix>/bin/Sherpa --path=<prefix>/share/SHERPA-MC/Examples/V_plus_Jets/LHC_ZJets. In the example, an absolute path is passed to the optional argument –path. It may also be specified relative to the current working directory. If it is not specified at all, the current working directory is understood.

For good book-keeping, it is highly recommended to reserve different subdirectories for different simulations as is demonstrated with the example setups.

If AMEGIC++ is used, Sherpa requires an initialization run, where C++ source code is written to disk. This code must be compiled into dynamic libraries by the user by running the makelibs script in the working directory. After this step Sherpa is run again for the actual cross section integrations and event generation. For more information on and examples of how to run Sherpa using AMEGIC++, see Running Sherpa with AMEGIC++.

If the internal hard-coded matrix elements or Comix are used, and AMEGIC++ is not, an initialization run is not needed, and Sherpa will calculate the cross sections and generate events during the first run already.

As the cross sections get integrated, the integration over phase space is optimized to arrive at an efficient event generation. Subsequently events are generated if a number of events is passed to the optional argument --events or set in the Sherpa.yaml file with the EVENTS parameters.

The generated events are not stored into a file by default; for details on how to store the events see Event output formats. Note that the computational effort to go through this procedure of generating, compiling and integrating the matrix elements of the hard processes depends on the complexity of the parton-level final states. For low multiplicities (2->2,3,4), of course, it can be followed instantly.

Usually more than one generation run is wanted. As long as the parameters that affect the matrix-element integration are not changed, it is advantageous to store the cross sections obtained during the generation run for later use. This saves CPU time especially for large final-state multiplicities of the matrix elements. Per default, Sherpa stores these integration results in a directory called Results/. The name of the output directory can be customised via Results directory

<prefix>/bin/Sherpa -r <result>/

or with RESULT_DIRECTORY: <result>/ in the steering file, see RESULT_DIRECTORY. The storage of the integration results can be prevented by either using

<prefix>/bin/Sherpa -g

or by specifying GENERATE_RESULT_DIRECTORY: false in the steering file.

If physics parameters change, the cross sections have to be recomputed. The new results should either be stored in a new directory or the <result> directory may be re-used once it has been emptied. Parameters which require a recomputation are any parameters affecting the Models, Matrix elements or Selectors. Standard examples are changing the magnitude of couplings, renormalisation or factorisation scales, changing the PDF or centre-of-mass energy, or, applying different cuts at the parton level. If unsure whether a recomputation is required, a simple test is to temporarily use a different value for the RESULT_DIRECTORY option and check whether the new integration numbers (statistically) comply with the stored ones.

A warning on the validity of the process libraries is in order here: it is absolutely mandatory to generate new library files, whenever the physics model is altered, i.e. particles are added or removed and hence new or existing diagrams may or may not anymore contribute to the same final states. Also, when particle masses are switched on or off, new library files must be generated (however, masses may be changed between non-zero values keeping the same process libraries). The best recipe is to create a new and separate setup directory in such cases. Otherwise the Process and Results directories have to be erased:

$ rm -rf Process/ Results/

In either case one has to start over with the whole initialization procedure to prepare for the generation of events.

2.2.2. The example set-up: Z+Jets at the LHC

The setup file (Sherpa.yaml) provided in ./Examples/V_plus_Jets/LHC_ZJets/ can be considered as a standard example to illustrate the generation of fully hadronised events in Sherpa, cf. Z production. Such events will include effects from parton showering, hadronisation into primary hadrons and their subsequent decays into stable hadrons. Moreover, the example chosen here nicely demonstrates how Sherpa is used in the context of merging matrix elements and parton showers [HKSS09]. In addition to the aforementioned corrections, this simulation of inclusive Drell-Yan production (electron-positron channel) will then include higher-order jet corrections at the tree level. As a result the transverse-momentum distribution of the Drell-Yan pair and the individual jet multiplicities as measured by the ATLAS and CMS collaborations at the LHC can be well described.

Before event generation, the initialization procedure as described in Process selection and initialization has to be completed. The matrix-element processes included in the setup are the following:

proton proton -> parton parton -> electron positron + up to five partons

In the PROCESSES list of the steering file this translates into

PROCESSES:
- 93 93 -> 11 -11 93{5}:
    Order: {QCD: 0, EW: 2}
    CKKW: 20
  [...]

Fixing the order of electroweak couplings to 2, matrix elements of all partonic subprocesses for Drell-Yan production without any and with up to five extra QCD parton emissions will be generated. Proton–proton collisions are considered at beam energies of 6.5 TeV. Model parameters and couplings can all be defined in the Sherpa.yaml file as you will see in the rest of this manual.

The QCD radiation matrix elements have to be regularised to obtain meaningful cross sections. This is achieved by specifying CKKW: 20 when defining the process in Sherpa.yaml. Simultaneously, this tag initiates the ME-PS merging procedure. To eventually obtain fully hadronised events, the FRAGMENTATION setting has been left on it’s default value Ahadic (and therefore been omitted from the steering file), which will run Sherpa’s cluster hadronisation, and the DECAYMODEL setting has it’s default value Hadrons, which will run Sherpa’s hadron decays. Additionally corrections owing to photon emissions are taken into account.

For a first example run with this setup, we suggest to simplify the run card significantly and only later, for physics studies, going back to the full-featured run card. So replace the full process listing with a short and simple

PROCESSES:
- 93 93 -> 11 -11 93{1}:
    Order: {QCD: 0, EW: 2}
    CKKW: 20

for now. In addition, remove the ASSOCIATED_CONTRIBUTIONS_VARIATIONS listing, since these can no longer be calculated after modifying PROCESSES. You might also need to remove (or install) PDFs that are not available on your system from the PDF_VARIATIONS listing. Then you can go ahead and start Sherpa for the first time by running the

$ <prefix>/bin/Sherpa

command as described in Running Sherpa. Sherpa displays some output as it runs. At the start of the run, Sherpa initializes the relevant model, and displays a table of particles, with their PDG codes and some properties. It also displays the Particle containers, and their contents. The other relevant parts of Sherpa are initialized, including the matrix element generator(s). The Sherpa output will look like:

Welcome to Sherpa, <user name> on <host name>.
Initialization of framework underway ...
[...]
Seed: 1234
[...]
Initializing beam spectra ...
  Type: Collider Setup
  Beam 1: P+ (enabled = 0, momentum = (6500,0,0,6500))
  Beam 2: P+ (enabled = 0, momentum = (6500,0,0,-6500))
Initializing PDFs ...
  Hard scattering:    PDF4LHC21_40_pdfas + PDF4LHC21_40_pdfas
  MPI:                PDF4LHC21_40_pdfas + PDF4LHC21_40_pdfas
[...]
Fixed electroweak parameters
  Input scheme: alpha(mZ)-mZ-sin(theta_W) scheme, input: 1/\alphaQED(m_Z), sin^2(theta_W), m_Z, m_h, widths
  Ren. scheme:  alphamZsW
  Parameters:   sin^2(\theta_W) = 0.23113
                vev              = 246.16 - 3.36725 i
Set \alpha according to EW scheme
  1/\alpha(0)   = 128.802
  1/\alpha(def) = 128.802
Particle data:
[...]
Initializing showers ...
Initializing matrix elements for the hard processes ...
Building processes (3 ME generators, 1 process blocks) ...
Setting up processes ........ done (59 MB, 0s/0s)
Performing tests ........ done (60 MB, 0s/0s)
[...]
Initializing hadron particle information ...
Initialized fragmentation
Initialized hadron decays (model = HADRONS++)
Initialized soft photons
[...]

Then Sherpa will start to integrate the cross sections. The output will look like:

Calculating xs for '2_2__j__j__e-__e+' (Comix) ...
Integration parameters: n_{min} = 5000, N_{opt} = 10, N_{max} = 1, exponent = 0.5
Starting the calculation at 09:43:52. Lean back and enjoy ... .
1630.48 pb +- ( 54.9451 pb = 3.36988 % ) 5000 ( 5029 -> 99.4 % )
full optimization:  ( 0s elapsed / 5s left ) [09:43:52]
1692.37 pb +- ( 46.7001 pb = 2.75945 % ) 12071 ( 12133 -> 99.5 % )
full optimization:  ( 0s elapsed / 5s left ) [09:43:52]
[...]

The first line here displays the process which is being calculated. In this example, the integration is for the \(2 \to 2\) process, parton, parton \(\to\) electron, positron. The matrix element generator used is displayed after the process. As the integration progresses, summary lines are displayed, like the ones shown above. The current estimate of the cross section is displayed, along with its statistical error estimate. The number of phase space points calculated is displayed after this, and the efficiency is displayed after that. On the line below, the time elapsed is shown, and an estimate of the total time till the optimisation is complete. In square brackets is an output of the system clock.

When the integration is complete, the output will look like:

[...]
1677.75 pb +- ( 1.74538 pb = 0.104031 % ) 374118 ( 374198 -> 100 % )
full optimization:  ( 4s elapsed / 1s left ) [09:43:56]
1677.01 pb +- ( 1.36991 pb = 0.0816873 % ) 534076 ( 534157 -> 99.9 % )
integration time:   ( 5s elapsed / 0s left ) [09:43:58]
2_2__j__j__e-__e+ : 1677.01 pb +- ( 1.36991 pb = 0.0816873 % )  exp. eff: 20.6675 %
  reduce max for 2_2__j__j__e-__e+ to 1 ( eps = 0.001 -> exp. eff 0.206675 )

with the final cross section result and its statistical error displayed.

Sherpa will then move on to integrate the other processes specified in the run card.

When the integration is complete, the event generation will start. As the events are being generated, Sherpa will display a summary line stating how many events have been generated, and an estimate of how long it will take. When the event generation is complete, Sherpa’s output looks like:

[...]
  Event 100 ( 1 s total ) = 1.12208e+07 evts/day
Summarizing the run may take some time ...
+----------------------------------------------------------------------------+
| Nominal or variation name     XS [pb]      RelDev  AbsErr [pb]      RelErr |
+----------------------------------------------------------------------------+
| Nominal                       1739.79         0 %      171.304      9.84 % |
| ME & PS: MUR=0.5 MUF=0.5      1635.61     -5.98 %      187.894     11.48 % |
| ME & PS: MUR=2 MUF=2          2261.57     29.99 %      387.031     17.11 % |
| [<results for other variations>]                                           |
+----------------------------------------------------------------------------+

A summary of the number of events generated is displayed, with the total cross section for the process and possible systematic variations [BSS16] and Input structure.

The generated events are not stored into a file by default; for details on how to store the events see Event output formats.

2.2.3. Parton-level event generation with Sherpa

Sherpa has its own tree-level matrix-element generators called AMEGIC++ and Comix. Furthermore, with the module PHASIC++, sophisticated and robust tools for phase-space integration are provided. Therefore Sherpa obviously can be used as a cross-section integrator. Because of the way Monte Carlo integration is accomplished, this immediately allows for parton-level event generation. Taking the LHC_ZJets setup, users have to modify just a few settings in Sherpa.yaml and would arrive at a parton-level generation for the process gluon down-quark to electron positron and down-quark, to name an example. When, for instance, the options “EVENTS: 0” and “OUTPUT: 2” are added to the steering file, a pure cross-section integration for that process would be obtained with the results plus integration errors written to the screen.

For the example, the process definition in PROCESSES simplifies to

- 21 1 -> 11 -11 1:
    Order: {QCD: 1, EW: 2}

with all other settings in the process block removed. And under the assumption to start afresh, the initialization procedure has to be followed as before. Picking the same collider environment as in the previous example there are only two more changes before the Sherpa.yaml file is ready for the calculation of the hadronic cross section of the process g d to e- e+ d at LHC and subsequent parton-level event generation with Sherpa. These changes read SHOWER_GENERATOR: None, to switch off parton showering, FRAGMENTATION: None, to do so for the hadronisation effects, MI_HANDLER: None, to switch off multiparton interactions, and ME_QED: {ENABLED: false}, to switch off resummed QED corrections onto the \(Z \rightarrow e^- e^+\) decay. Additionally, the non-perturbative intrinsic transverse momentum may be wished to not be taken into account, therefore set BEAM_REMNANTS: false.

2.2.4. Multijet merged event generation with Sherpa

For a large fraction of LHC final states, the application of reconstruction algorithms leads to the identification of several hard jets. Calculations therefore need to describe as accurately as possible both the hard jet production as well as the subsequent evolution and the interplay of multiple such topologies. Several scales determine the evolution of the event.

Various such merging schemes have been proposed: [CKKW01], [Lon02], [MMP02], [Kra02], [MMPT07], [LL08], [HKSS09], [HRT09], [HN10], [HKSS11], [LP12], [HKSS13], [GHK+13], [LPb], [LPa]. Comparisons of the older approaches can be found e.g. in [H+], [A+08]. The currently most advanced treatment at tree-level, detailed in [HKSS09], [HSS10], [CGH10], is implemented in Sherpa.

How to setup a multijet merged calculation is detailed in most Examples, e.g. W+jets production, Z production or Top quark (pair) + jets production.

2.2.5. Running Sherpa with AMEGIC++

When Sherpa is run using the matrix element generator AMEGIC++, it is necessary to run it twice. During the first run (the initialization run) Feynman diagrams for the hard processes are constructed and translated into helicity amplitudes. Furthermore suitable phase-space mappings are produced. The amplitudes and corresponding integration channels are written to disk as C++ source code, placed in a subdirectory called Process. The initialization run is started using the standard Sherpa executable, as described in Running Sherpa. The relevant command is

$ <prefix>/bin/Sherpa

The initialization run stops with the message “New libraries created. Please compile.”, which is nothing but the request to carry out the compilation and linking procedure for the generated matrix-element libraries. The makelibs script, provided for this purpose and created in the working directory, must be invoked by the user (see ./makelibs -h for help):

$ ./makelibs

Note that the cmake tool has to be available for this step

Another option is ./makelibs -m, which creates one library per subprocess. This can be useful for very complex processes, in particular if the default combined library generation fails due to a limit on the number of command line arguments. Note that this option requires that Sherpa is run with AMEGIC_LIBRARY_MODE: 0 (default: 1).

Afterwards Sherpa can be restarted using the same command as before. In this run (the generation run) the cross sections of the hard processes are evaluated. Simultaneously the integration over phase space is optimized to arrive at an efficient event generation.

2.3. Cross section determination

To determine the total cross section, in particular in the context of multijet merging with Sherpa, the final output of the event generation run should be used, e.g.

+----------------------------------------------------------------------------+
| Nominal or variation name     XS [pb]      RelDev  AbsErr [pb]      RelErr |
+----------------------------------------------------------------------------+
| Nominal                       1739.79         0 %      171.304      9.84 % |
| ME & PS: MUR=0.5 MUF=0.5      1635.61     -5.98 %      187.894     11.48 % |
| ME & PS: MUR=2 MUF=2          2261.57     29.99 %      387.031     17.11 % |
| [<results for other variations>]                                           |
+----------------------------------------------------------------------------+

Note that the Monte Carlo error quoted for the total cross section is determined during event generation. It, therefore, might differ substantially from the errors quoted during the integration step, and it can be reduced simply by generating more events.

In contrast to plain fixed order results, Sherpa’s total cross section in multijet merging setups (MEPS, MENLOPS, MEPS@NLO) is composed of values from various fixed order processes, namely those which are combined by applying the multijet merging, see Multijet merged event generation with Sherpa. In this context, it is important to note:

The higher multiplicity tree-level cross sections determined during the integration step are meaningless by themselves, only the inclusive cross section printed at the end of the event generation run is to be used.

Sherpa total cross sections have leading order accuracy when the generator is run in LO merging mode (MEPS), in NLO merging (MENLOPS, MEPS@NLO) mode they have NLO accuracy.

2.3.1. Differential cross sections from single events

To calculate the expectation value of an observable defined through a series of cuts and requirements each event produced by Sherpa has to be evaluated whether it meets the required criteria. The expectation value is then given by

\[\langle O\rangle = \frac{1}{N_\text{trial}} \cdot \sum_i^n {w_i(\Phi_i) O(\Phi_i)}.\]

Therein the \(w_i(\Phi_i)\) are the weight of the event with the phase space configuration \(\Phi_i\) and \(O(\Phi_i)\) is the value of the observable at this point. \(N_\text{trial} = \sum_i^n n_{\text{trial,i}}\) is the sum of number of trials \(n_\text{trial,i}\) of all events. A good cross check is to reproduce the inclusive cross section as quoted by Sherpa (see above).

In case of unweighted events one might want to rescale the uniform event weight to unity using w_norm. The above equation then reads

\[\langle O \rangle = \frac{w_\text{norm}}{N_\text{trial}} \cdot \sum_i^n{\frac{w_i(\Phi_i)}{w_\text{norm} O(\Phi_i)}}\]

wherein \(\frac{w_i(\Phi_i)}{w_\text{norm}} = 1\), i.e. the sum simply counts how many events pass the selection criteria of the observable. If however, PartiallyUnweighted event weights or Enhance_Factor or Enhance_Observable are used, this is no longer the case and the full form needs to be used.

All required quantities, \(w_i\), \(w_\text{norm}\) and \(n_{\text{trial},i}\), accompany each event and are written e.g. into the HepMC output (cf. Event output formats).

3. Command Line Options

The available command line options for Sherpa (given either in long form (starting with two hyphen) or, alternatively in a short-hand form) include:

--run-data, -f <file>

Read settings from input file <file>, see Input structure. This is deprecated, use positional arguments to specify input files instead, see Input structure.

--path, -p <path>

Read input file from path <path>, see Input structure.

--sherpa-lib-path, -L <path>

Set Sherpa library path to <path>, see SHERPA_CPP_PATH.

--events, -e <N_events>

Set number of events to generate <N_events>, see EVENTS.

--event-type, -t <event_type>

Set the event type to <event_type>, see EVENT_TYPE.

--result-directory, -r <path>

Set the result directory to <path>, see RESULT_DIRECTORY.

--random-seed, -R <seed>

Set the seed of the random number generator to <seed>, see RANDOM_SEED.

--me-generators, -m <generators>

Set the matrix element generator list to <generators>, see ME_GENERATORS. If you specify more than one generator, use the YAML sequence syntax, e.g. -m '[Amegic, Comix]'.

--mi-handler, -M <handler>

Set multiple interaction handler to <handler>, see MI_HANDLER.

--event-generation-mode, -w <mode>

Set the event generation mode to <mode>, see EVENT_GENERATION_MODE.

--shower-generator, -s <generator>

Set the parton shower generator to <generator>, see SHOWER_GENERATOR.

--fragmentation, -F <module>

Set the fragmentation module to <module>, see Fragmentation.

--decay, -D <module>

Set the hadron decay module to <module>, see Hadron decays.

--analysis, -a <analyses>

Set the analysis handler list to <analyses>, see ANALYSIS. If you specify more than one analysis handler, use the YAML sequence syntax, e.g. -a '[Rivet, Internal]'.

--analysis-output, -A <path>

Set the analysis output path to <path>, see ANALYSIS_OUTPUT.

--output, -O <level>

Set general output level <level>, see OUTPUT.

--event-output, -o <level>

Set output level used during event generation <level>, see OUTPUT.

--log-file, -l <logfile>

Set log file name <logfile>, see LOG_FILE.

--disable-result-directory-generation, -g

Do not create result directory, see RESULT_DIRECTORY.

--disable-batch-mode, -b

Switch to non-batch mode, see BATCH_MODE.

--enable-init-only, -I

Only initialize the run, i.e. writes out the Process directory, if necessary writes out the libraries for AMEGIC++ and quits the run, see Running Sherpa and INIT_ONLY.

--print-version-info, -V

Print extended version information at startup.

--version, -v

Print versioning information.

--help, -h

Print a help message.

'PARAMETER: Value'

Set the value of a parameter, see Parameters. Equivalent input forms are PARAMETER:Value (without a space) and PARAMETER=Value; these forms can normally be used without quotation marks. Just as for any other command line option, the setting takes precedence over corresponding settings defined in runcards. You can also set nested settings or settings that expect lists of values; see Input structure for more details.

'Tags: {TAG: Value}'

Set the value of a tag, see Tags. More than one tag can be specified using 'Tags: {TAG1: Value1, TAG2: Value2, ...}'.

4. Input structure

A Sherpa setup is steered by various parameters, associated with the different components of event generation.

These have to be specified in a configuration file which by default is named Sherpa.yaml residing in the current working directory. If you want to use a different setup directory for your Sherpa run, you have to specify it on the command line as -p <dir> or 'PATH: <dir>' (including the quotes).

To read parameters from a configuration file with a different name, you may give the file name as a positional argument on the command line like this: Sherpa <file>. Note that you can also pass more than one file like this: Sherpa <file1> <file2> ... In this case, settings in files to the right take precedence. This can be useful to reduce duplication in the case that you have several setups that share a common set of settings.

Note that you can also pass filenames using the legacy syntax -f <file> or 'RUNDATA: [<file1>, <file2>]'. However, this is deprecated. Use positional arguments instead. Mixing this legacy syntax and positional arguments for specifying configuration files yields undefined behaviour.

Sherpa’s configuration files are written in the YAML format. Most settings are just written as the settings’ name followed by its value, like this:

EVENTS: 100M
BEAMS: 2212
BEAM_ENERGIES: 7000
...

In other words, they are key-value pairs of the top-level mapping. For some settings, the value is itself a mapping. Hence, we get a nested structure, for example:

HARD_DECAYS:
  Enabled: true
  Apply_Branching_Ratios: false

where Enabled and Apply_Branching_Ratios are sub-settings of the top-level HARD_DECAYS setting. The hierarchy is denoted by indentation here. In YAML, this is called block style and relies on proper formatting (i.e. each element must be on a separate line, and indentation must be consistent). Alternatively, one can use flow style, using indicators such as braces instead of whitespace to indicate structure. For the previous example, the inner mapping can be written with curly braces and commas:

HARD_DECAYS: { Enabled: true, Apply_Branching_Ratios: false }

Other settings are sequences of elements. An example would be a sequence of two scale variations:

SCALE_VARIATIONS:
- 0.25
- 4.00

In block style, each sequential item is prepended with a single dash. Equivalently, the snippet can be rewritten in flow style using square brackets (line breaks are completely optional then, and are omitted here):

SCALE_VARIATIONS: [0.25, 4.00]

Each SCALE_VARIATIONS item can itself be a sequence (to specify different variations for the factorisation and renormalisation scale). Block and flow style can be freely mixed in the different levels:

SCALE_VARIATIONS:
- 0.25
- [0.25, 1.00]
- [1.00, 0.25]

The different settings and their structure are described in detail in another chapter of this manual, see Parameters.

All parameters can be overwritten on the command line, i.e. command-line input has the highest priority. Each argument is parsed as a single YAML line. This usually means that you have to quote each argument:

$ <prefix>/bin/Sherpa 'KEYWORD1: value1' 'KEYWORD2: value2' ...

Because each argument is parsed as YAML, you can also specify nested settings, e.g. to disable hard decays (even if it is enabled in the config file) you can write:

$ <prefix>/bin/Sherpa 'HARD_DECAYS: {Enabled: false}'

Or you can specify the list of matrix-element generators writing:

$ <prefix>/bin/Sherpa 'ME_GENERATORS: [Comix, Amegic]'

Note that we have used flow style here, because block style would require line breaks, which are difficult to deal with on the command line.

For scalar (i.e. single-valued) settings, you can use a more convenient syntax on the command line, where the levels are separated with a colon:

$ <prefix>/bin/Sherpa KEYWORD1:value1 KEYWORD2:value2 ...
$ <prefix>/bin/Sherpa HARD_DECAYS:Enabled:false

As this syntax needs no space after the colon, you can normally suppress quotation marks as we did here. For non-nested scalar settings, there is yet another possibility, using an equal sign instead of a colon:

$ <prefix>/bin/Sherpa KEYWORD1=value1 KEYWORD2=value2 ...

All over Sherpa, particles are defined by the particle code proposed by the PDG. These codes and the particle properties will be listed during each run with OUTPUT: 2 for the elementary particles and OUTPUT: 4 for the hadrons. In both cases, antiparticles are characterized by a minus sign in front of their code, e.g. a mu- has code 13, while a mu+ has -13.

All dimensionful quantities need to be specified in units of GeV and millimeter. The same units apply to all numbers in the event output (momenta, vertex positions). Scattering cross sections are quoted in pico-barn in the output.

There are a few extra features for an easier handling of the parameter file(s), namely global tag replacement, see Tags, and algebra interpretation, see Interpreter.

4.1. Interpreter

Sherpa has a built-in interpreter for algebraic expressions, like cos(5/180*M_PI). This interpreter is employed when reading integer and floating point numbers from input files, such that certain parameters can be written in a more convenient fashion. For example it is possible to specify the factorisation scale as sqr(91.188).

There are predefined tags to alleviate the handling

M_PI

Ludolph’s Number to a precision of 12 digits.

M_C

The speed of light in the vacuum.

E_CMS

The total centre of mass energy of the collision.

The expression syntax is in general C-like, except for the extra function sqr, which gives the square of its argument. Operator precedence is the same as in C. The interpreter can handle functions with an arbitrary list of parameters, such as min and max.

The interpreter can be employed to construct arbitrary variables from four momenta, like e.g. in the context of a parton level selector, see Selectors. The corresponding functions are

Mass(v)

The invariant mass of v in GeV.

Abs2(v)

The invariant mass squared of v in GeV^2.

PPerp(v)

The transverse momentum of v in GeV.

PPerp2(v)

The transverse momentum squared of v in GeV^2.

MPerp(v)

The transverse mass of v in GeV.

MPerp2(v)

The transverse mass squared of v in GeV^2.

Theta(v)

The polar angle of v in radians.

Eta(v)

The pseudorapidity of v.

Y(v)

The rapidity of v.

Phi(v)

The azimuthal angle of v in radians.

Comp(v,i) The i’th component of the vector

v. i = 0 is the energy/time component, i = 1, 2, and 3 are the x, y, and z components.

PPerpR(v1,v2)

The relative transverse momentum between v1 and v2 in GeV.

ThetaR(v1,v2)

The relative angle between v1 and v2 in radians.

DEta(v1,v2)

The pseudo-rapidity difference between v1 and v2.

DY(v1,v2)

The rapidity difference between v1 and v2.

DPhi(v1,v2)

The relative polar angle between v1 and v2 in radians.

4.2. Tags

Tag replacement in Sherpa is performed through the data reading routines, which means that it can be performed for virtually all inputs. Specifying a tag on the command line or in the configuration file using the syntax TAGS: {<Tag>: <Value>} will replace every occurrence of $(<Tag>) in all files during read-in. An example tag definition could read

$ <prefix>/bin/Sherpa 'TAGS: {QCUT: 20, NJET: 3}'

and then be used in the configuration file like:

RESULT_DIRECTORY: Result_$(QCUT)
PROCESSES:
- 93 93 -> 11 -11 93{$(NJET)}:
    Order: {QCD: 0, EW: 2}
    CKKW: $(QCUT)

5. Parameters

A Sherpa run is steered by various parameters, associated with the different components of event generation. These are set in Sherpa’s configuration file, see Input structure for more details. Tag replacements may be performed in all inputs, see Tags.

5.1. General parameters

The following parameters describe general run information. See Input structure for how to use them in a configuration file or on the command line.

5.1.1. EVENTS

This parameter specifies the number of events to be generated.

It can alternatively be set on the command line through option -e, see Command Line Options.

5.1.2. EVENT_TYPE

This parameter specifies the kind of events to be generated. It can alternatively be set on the command line through option -t, see Command Line Options.

• The default event type is StandardPerturbative, which will generate a hard event through exact matrix elements matched and/or merged with the parton shower, eventually including hadronisation, hadron decays, etc..

Alternatively there are two more specialised modes, namely:

• MinimumBias, which generates minimum bias events through the SHRIMPS model implemented in Sherpa, see Minimum bias events

• HadronDecay, which allows to simulate the decays of a specific hadron.

5.1.3. SHERPA_VERSION

This parameter ties a config file to a specific Sherpa version, e.g. SHERPA_VERSION: 2.2.0. If two parameters are given they are interpreted as a range of Sherpa versions: SHERPA_VERSION: [2.2.0, 2.2.5] specifies that this config file can be used with any Sherpa version between (and including) 2.2.0 and 2.2.5.

5.1.4. TUNE

Warning

This parameter is currently not supported.

5.1.5. OUTPUT

This parameter specifies the screen output level (verbosity) of the program. If you are looking for event file output options please refer to section Event output formats.

It can alternatively be set on the command line through option -O, see Command Line Options. A different output level can be specified for the event generation step through EVT_OUTPUT or command line option -o, see Command Line Options

The value can be any sum of the following:

• 0: Error messages (-> always displayed).

• 1: Event display.

• 2: Informational messages during the run.

• 4: Tracking messages (lots of output).

• 8: Debugging messages (even more output).

E.g. OUTPUT=3 would display information, events and errors. Use OUTPUT_PRECISION to set the default output precision (default 6). Note: this may be overridden in specific functions’ output.

For expert users: The output level can be overridden for individual functions, e.g. like this

FUNCTION_OUTPUT:
  "void SHERPA::Matrix_Element_Handler::BuildProcesses()": 8
  ...

where the function signature is given by the value of __PRETTY_FUNCTION__ in the function block. Another expert parameter is EVT_OUTPUT_START, with which the first event affected by EVT_OUTPUT can be specified. This can be useful to generate debugging output only for events affected by a certain issue.

5.1.6. LOG_FILE

This parameter specifies the log file. If set, the standard output from Sherpa is written to the specified file, but output from child processes is not redirected. This option is particularly useful to produce clean log files when running the code in MPI mode, see MPI parallelization. A file name can alternatively be specified on the command line through option -l, see Command Line Options.

5.1.7. RANDOM_SEED

Sherpa uses different random-number generators. The default is the Ran3 generator described in [PTVF07]. Alternatively, a combination of George Marsaglias KISS and SWB [MZ91] can be employed, see this website. The integer-valued seeds of the generators are specified by RANDOM_SEED: [A, .., D]. They can also be set individually using RANDOM_SEED1: A through RANDOM_SEED4: D. The Ran3 generator takes only one argument (in this case, you can simply use RANDOM_SEED: A). This value can also be set using the command line option -R, see Command Line Options.

5.1.8. EVENT_SEED_MODE

The tag EVENT_SEED_MODE can be used to enforce the same seeds in different runs of the generator. When set to 1, existing random seed files are read and the seed is set to the next available value in the file before each event. When set to 2, seed files are written to disk. These files are gzip compressed, if Sherpa was compiled with option -DSHERPA_ENABLE_GZIP=ON. When set to 3, Sherpa uses an internal bookkeeping mechanism to advance to the next predefined seed. No seed files are written out or read in.

5.1.9. ANALYSIS

Analysis routines can be switched on or off using the ANALYSIS parameter. The default is no analysis. This parameter can also be specified on the command line using option -a, see Command Line Options.

The following analysis handlers are currently available

Internal

Sherpa’s internal analysis handler.

To use this option, the package must be configured with option

-DSHERPA_ENABLE_ANALYSIS=ON. An output directory can

be specified using ANALYSIS_OUTPUT.

Rivet

The Rivet package, see Rivet Website.

To enable it, Rivet and HepMC have to be installed and Sherpa must be configured

as described in Rivet analyses.

Multiple options can also be specified, e.g. ANALYSIS: [Internal, Rivet].

5.1.10. ANALYSIS_OUTPUT

Name of the directory for histogram files when using the internal analysis and name of the Yoda file when using Rivet, see ANALYSIS. The directory/file will be created w.r.t. the working directory. The default value is Analysis/. This parameter can also be specified on the command line using option -A, see Command Line Options.

5.1.11. TIMEOUT

A run time limitation can be given in user CPU seconds through TIMEOUT. This option is of some relevance when running SHERPA on a batch system. Since in many cases jobs are just terminated, this allows to interrupt a run, to store all relevant information and to restart it without any loss. This is particularly useful when carrying out long integrations. Alternatively, setting the TIMEOUT variable to -1, which is the default setting, translates into having no run time limitation at all. The unit is seconds.

5.1.12. RLIMIT_AS

A memory limitation can be given to prevent Sherpa to crash the system it is running on as it continues to build up matrix elements and loads additional libraries at run time. Per default the maximum RAM of the system is determined and set as the memory limit. This can be changed by giving RLIMIT_AS: where the size is given as e.g. 500 MB, 4 GB, or 10 %. When running with MPI parallelization it might be necessary to divide the total maximum by the number of cores. This can be done by setting RLIMIT_BY_CPU: true.

Sherpa checks for memory leaks during integration and event generation. If the allocated memory after start of integration or event generation exceeds the parameter MEMLEAK_WARNING_THRESHOLD, a warning is printed. Like RLIMIT_AS, MEMLEAK_WARNING_THRESHOLD can be set using units. The warning threshold defaults to 16MB.

5.1.13. BATCH_MODE

Whether or not to run Sherpa in batch mode. The default is 1, meaning Sherpa does not attempt to save runtime information when catching a signal or an exception. On the contrary, if option 0 is used, Sherpa will store potential integration information and analysis results, once the run is terminated abnormally. All possible settings are:

0

Sherpa attempts to write out integration and analysis results when catching an exception.

1

Sherpa does not attempt to write out integration and analysis results when catching an exception.

2

Sherpa outputs the event counter continuously, instead of overwriting the previous one (default when using LOG_FILE).

4

Sherpa increases the on-screen event counter in constant steps of 100 instead of an increase relative to the current event number. The interval length can be adjusted with EVENT_DISPLAY_INTERVAL.

8

Sherpa prints the name of the hard process for the last event at each print out.

16

Sherpa prints the elapsed time and time left in seconds only.

The settings are additive such that multiple settings can be employed at the same time.

Note

When running the code on a cluster or in a grid environment, BATCH_MODE should always contain setting 1 (i.e. BATCH_MODE: 1 or 3 or 5 etc.).

The command line option -b should therefore not be used in this case, see Command Line Options.

5.1.14. INIT_ONLY

This can be used to skip cross section integration and event generation phases. Note that these phases are always skipped if Sherpa detects that libraries are missing and need to be compiled first, see Running Sherpa. The following values can be used for INIT_ONLY:

0

The default. Sherpa will normally attempt to proceed after initialisation to integrate cross sections (or read in cached results) and generate events.

1

Sherpa will always exit after initialisation, skipping integration and event generation.

2

Sherpa skips cross section integration. This is useful when Sherpa is used to calculate specific matrix element values, see Calculating matrix element values for externally given configurations.

5.1.15. NUM_ACCURACY

The targeted numerical accuracy can be specified through NUM_ACCURACY, e.g. for comparing two numbers. This might have to be reduced if gauge tests fail for numerical reasons. The default is 1E-10.

5.1.16. SHERPA_CPP_PATH

The path in which Sherpa will eventually store dynamically created C++ source code. If not specified otherwise, sets SHERPA_LIB_PATH to $SHERPA_CPP_PATH/Process/lib. This value can also be set using the command line option -L, see Command Line Options. Both settings can also be set using environment variables.

5.1.17. SHERPA_LIB_PATH

The path in which Sherpa looks for dynamically linked libraries from previously created C++ source code, cf. SHERPA_CPP_PATH.

5.1.18. Event output formats

Sherpa provides the possibility to output events in various formats, e.g. the HepMC format. The authors of Sherpa assume that the user is sufficiently acquainted with these formats when selecting them.

If the events are to be written to file, the parameter EVENT_OUTPUT must be specified together with a file name. An example would be EVENT_OUTPUT: HepMC3[MyFile], where MyFile stands for the desired file base name. More than one output can also be specified:

EVENT_OUTPUT:
  - HepMC3[MyFile]
  - Root[MyFile]

The following formats are currently available:

HepMC3

Generates output using HepMC3 library. The format of the output is controlled with the HEPMC3_IO_TYPE setting. The default value is 0 and corresponds to ASCII GenEvent output. Other available options are: 1 (HepEvt output), 2 (HepMC2 ASCII output), 3 (ROOT file output with every event written as an object of class GenEvent), and 4 (ROOT file output with GenEvent objects written into TTree).

The HepMC::GenEvent::m_weights weight vector stores the following items: [0] event weight, [1] combined matrix element and PDF weight (missing only phase space weight information, thus directly suitable for evaluating the matrix element value of the given configuration), [2] event weight normalisation (in case of unweighted events event weights of ~ +/-1 can be obtained by (event weight)/(event weight normalisation)), and [3] number of trials. The total cross section of the simulated event sample can be computed as the sum of event weights divided by the sum of the number of trials. This value must agree with the total cross section quoted by Sherpa at the end of the event generation run, and it can serve as a cross-check on the consistency of the HepMC event file. Note that Sherpa conforms to the Les Houches 2013 suggestion (http://phystev.in2p3.fr/wiki/2013:groups:tools:hepmc) of indicating interaction types through the GenVertex type-flag. Multiple event weights can also be used, cf. On-the-fly event weight variations. The following additional customisations can be used.

HEPMC_USE_NAMED_WEIGHTS: <true|false> Enable filling weights with an associated name. The nominal event weight has the key Weight. MEWeight, WeightNormalisation and NTrials provide additional information for each event as described above. The default value is true.

HEPMC_EXTENDED_WEIGHTS: <false|true> Write additional event weight information needed for a posteriori reweighting into the WeightContainer, cf. A posteriori scale and PDF variations using the HepMC GenEvent Output. Necessitates the use of HEPMC_USE_NAMED_WEIGHTS. The default value is false.

HEPMC3_SHORT: <false|true> Generates output in HepMC::IO_GenEvent format, however, only incoming beams and outgoing particles are stored. Intermediate and decayed particles are not listed. The default value is false.

HEPMC_TREE_LIKE: <false|true> Force the event record to be strictly tree-like. Please note that this removes some information from the matrix-element-parton-shower interplay which would be otherwise stored. The default value is false. Has no effect if HEPMC3_SHORT is used.

Requires -DHepMC3_DIR=/path/to/hepmc3 (or -DSHERPA_ENABLE_HEPMC3=ON, if HepMC3 is installed in a standard location).

LHEF

Generates output in Les Houches Event File format. This output format is intended for output of matrix element configurations only. Since the format requires PDF information to be written out in the outdated PDFLIB/LHAGLUE enumeration format this is only available automatically if LHAPDF is used, the identification numbers otherwise have to be given explicitly via LHEF_PDF_NUMBER (LHEF_PDF_NUMBER_1 and LHEF_PDF_NUMBER_2 if both beams carry different structure functions). This format currently outputs matrix element information only, no information about the large-Nc colour flow is given as the LHEF output format is not suited to communicate enough information for meaningful parton showering on top of multiparton final states.

Root

Generates output in ROOT ntuple format for NLO event generation only. For details on the ntuple format, see A posteriori scale and PDF variations using the ROOT NTuple Output. ROOT ntuples can be read back into Sherpa and analyzed using the option EVENT_INPUT. This feature is described in Production of NTuples.

Requires -DROOT_DIR=/path/to/root (or -DSHERPA_ENABLE_ROOT=ON, if ROOT is installed in a standard location).

The output can be further customized using the following options:

FILE_SIZE

Number of events per file (default: unlimited).

EVENT_FILE_PATH

Directory where the files will be stored.

EVENT_OUTPUT_PRECISION

Steers the precision of all numbers written to file (default: 12).

For all output formats except ROOT, events can be written directly to gzipped files instead of plain text. The option -DSHERPA_ENABLE_GZIP=ON must be given during installation to enable this feature.

5.1.19. On-the-fly event weight variations

Sherpa can compute alternative event weights on-the-fly [BSS16], resulting in alternative weights for the generated event. An important example is the variation of QCD scales and input PDF. There are also on-the-fly variations for approximate electroweak corrections, this is discussed in its own section, Approximate Electroweak Corrections.

5.1.19.1. Specifying variations

There are two ways to specify scale and PDF variations. Either using the unified VARIATIONS list, and/or by using the specialised SCALE_VARIATIONS and PDF_VARIATIONS, and QCUT_VARIATIONS lists. Only the VARIATIONS list allows to specify correlated variations (i.e. varying both scales and PDFs at the same time), but it is more verbose and therefore harder to remember. Therefore, we suggest to use the more specialised variants whenever uncorrelated variations are required.

They are evoked using the following syntax:

SCALE_VARIATIONS:
- [<muF2-fac-1>, <muR2-fac-1>]
- [<muF2-fac-2>, <muR2-fac-2>]
- <mu2-fac-3>

PDF_VARIATIONS:
- <PDF-1>
- <PDF-2>

QCUT_VARIATIONS:
- <qcut-fac-1>
- <qcut-fac-2>

This example specifies a total of seven on-the-fly variations.

Scale factors in SCALE_VARIATIONS can be given as a list of two numbers, or as a single number. When two numbers are given, they are applied to the factorisation and the renormalisation scale, respectively. If only a single number is given, it is applied to both scales at the same time. The factors for the renormalisation and factorisation scales must be given in their quadratic form, i.e. a “4.0” in the settings means that the (unsquared) scale is to be multiplied by a factor of 2.0.

For the PDF_VARIATIONS, any set present in any of the PDF library interfaces loaded through PDF_LIBRARY can be used. If no PDF set is given it defaults to the nominal one. Specific PDF members can be specified by appending the PDF set name with /<member-id>.

It can be painful to write every variation explicitly, e.g. for 7-point scale factor variations or if one wants variations for all members of a PDF set. Therefore an asterisk can be appended to some values, which results in an expansion. For PDF sets, this means that the variation is repeated for each member of that set. For scale factors, 4.0* is expanded to itself, unity, and its inverse: 1.0/4.0, 1.0, 4.0. A special meaning is reserved for specifying a single number 4.0* as a SCALE_VARIATIONS list item, which expands to a 7-point scale variation:

SCALE_VARIATIONS:
- 4.0*

is therefore equivalent to

SCALE_VARIATIONS:
- [0.25, 0.25]
- [0.25, 1.00]
- [1.00, 0.25]
- [1.00, 1.00]
- [4.00, 1.00]
- [1.00, 4.00]
- [4.00, 4.00]

Equivalently, one can even just write SCALE_VARIATIONS: 4.0*, because a single scalar on the right-hand side will automatically be interpreted as the first item of a list when the setting expects a list.

Such expansions may include trivial scale variations and the central PDF set, resulting in the specification of a completely trivial variation, which would just repeat the nominal calculation. Per default, these trivial variations are automatically omitted during the calculation, since the nominal calculation is anyway included in the Sherpa output. If required (e.g. for debugging), this filtering can be explicitly disabled using VARIATIONS_INCLUDE_CV: true.

We now discuss the alternative VARIATIONS syntax. The following snippet specifies two on-the-fly variations, where scales and PDFs are varied simultaneously:

VARIATIONS:
- ScaleFactors:
    MuR2: <muR2-fac-1>
    MuF2: <muF2-fac-1>
    QCUT: <qcut-fac-1>
  PDF: <PDF-1>
- ScaleFactors:
    MuR2: <muR2-fac-2>
    MuF2: <muF2-fac-2>
    QCUT: <qcut-fac-2>
  PDF: <PDF-2>
...

The key word VARIATIONS takes a list of variations. Each variation is specified by a set of scale factors, and a PDF choice (or AlphaS(MZ) choice, see below).

Scale factors can be given for the renormalisation, factorisation and for the merging scale. The corresponding keys are MuR2, MuF2 and QCUT, respectively. The factors for the renormalisation and factorisation scales must be given in their quadratic form, i.e. a MUR2: 4.0 means that the (unsquared) renormalisation scale is to be multiplied by a factor of 2.0. All scale factors can be omitted (they default to 1.0). Instead of MuR2 and MuF2, one can also use the keyword Mu2. In this case, the given factor is applied to both the renormalisation and the factorisation scale.

Instead of using PDF: <PDF> (which consistently also varies the strong coupling if the PDF has a different specification of it!), one can also specify a pure AlphaS variation by giving its value at the Z mass scale: AlphaS(MZ): <alphas(mz)-value>. This can be useful e.g. for leptonic productions, and is currently exclusive to the VARIATIONS syntax.

Also VARIATIONS can expand values using the star syntax:

VARIATIONS:
  - ScaleFactors:
      Mu2: 4.0*

is therefore equivalent to

VARIATIONS:
  - ScaleFactors:
      MuF2: 0.25
      MuR2: 0.25
  - ScaleFactors:
      MuF2: 1.0
      MuR2: 0.25
  - ScaleFactors:
      MuF2: 0.25
      MuR2: 1.0
  - ScaleFactors:
      MuF2: 1.0
      MuR2: 1.0
  - ScaleFactors:
      MuF2: 4.0
      MuR2: 1.0
  - ScaleFactors:
      MuF2: 1.0
      MuR2: 4.0
  - ScaleFactors:
      MuF2: 4.0
      MuR2: 4.0

As another example, a complete variation using the PDF4LHC convention would read

VARIATIONS:
  - ScaleFactors:
      Mu2: 4.0*
  - PDF: CT10nlo*
  - PDF: MMHT2014nlo68cl*
  - PDF: NNPDF30_nlo_as_0118*

Please note, this syntax will create \(6+52+50+100=208\) additional weights for each event. Even though reweighting is used to reduce the amount of additional calculation as far as possible, this can still necessitate a considerable amount of additional CPU hours, in particular when parton-shower reweighting is enabled (see below).

The rest of this section applies to both the combined VARIATIONS and the individual SCALE_VARIATIONS etc. syntaxes.

5.1.19.2. Variation output

The total cross section for all variations along with the nominal cross section are written to the standard output after the event generation has finalized. Additionally, some event output (see Event output formats) and analysis methods (see ANALYSIS) are able to process alternate event weights. Currently, the only supported event output method is HepMC3 (requires configuration with HepMC version 3 or later). The supported analysis methods are Rivet and Internal.

The alternative event weight names follow the MC naming convention, i.e. they are named MUR=<fac>__MUF=<fac>__LHAPDF=<id>. When using Sherpa’s interface to Rivet, Rivet analyses, the internal multi-weight handling capabilities are used, such that there is only one histogram file containing histograms all variations. Extending the naming convention, for pure strong coupling variations, an additional tag ASMZ=<val> is appended. If shower scale variations are disabled (either implicitly, because SHOWER_GENERATOR: None, or explicitly, see below), you will find ME.MUR/ME.MUF tags instead of the simple ones to make explicit that the parton-shower scales are not varied with the ME scales.

If parton-shower variations are enabled, SHOWER:REWEIGHT: true (the default if parton showering is enabled), then pure ME-only variations are included along with the full variations in the HepMC/Rivet output by default. This can be disabled using OUTPUT_ME_ONLY_VARIATIONS: false. All weight names of ME-only variations include a “ME” as part of the keys to indicate that only the ME part of the calculation has been varied, e.g. ME:MUR=<fac>__ME:MUF=<fac>__ME:LHAPDF=<id>.

The user must also be aware that, of course, the cross section of the event sample, changes when using an alternative event weight as compared to the nominal one. Any histogramming therefore has to account for this and recompute the total cross section as the sum of weights divided by the number of trials, cf. Cross section determination. For HepMC 3, Sherpa writes alternate cross sections directly to the GenCrossSection entry of the event record, such that no manual intervention is required (as long as the correct cross section variation is picked in downstream processing steps).

5.1.19.3. Varying the PDFs of a single beam

The PDF_VARIATION_BEAMS setting can be used to restrict for which beams a PDF variation is applied. Its default is [1, 2], i.e. both beams will undergo a given PDF variation. Use 1 or 2 to only apply it to a single beam. This is a global setting for all PDF variations, i.e. it is currently not possible to do this on the basis of a single PDF variation.

When using PDF_VARIATION_BEAMS, there is an ambiguity which beam’s PDF should be used to evaluate the strong coupling. For that, the setting PDF_VARIATION_ALPHAS_BEAM can be used. Its default is 0, which means that the first available beam’s PDF is used. Use 1 or 2 to select a specific beam’s PDF instead.

Having different PDFs for each beam will be reflected in the Variation output. Consider the following example: MUR=1__MUF=1__LHAPDF.BEAM1=93300__LHAPDF.BEAM2=93301, where the beams’ LHAPDF IDs are specified individually.

5.1.19.4. Variations for different event generation modes

The on-the-fly reweighting works for all event generation modes (weighted or (partially) unweighted) and all calculation types (LO, LOPS, NLO, NLOPS, NNLO, NNLOPS, MEPS@LO, MEPS@NLO and MENLOPS).

5.1.19.4.1. NLO calculations

For NLO calculations, note that some loop providers (e.g. Recola) do not provide the pole coefficients, while others do (e.g. OpenLoops). For the former, Sherpa will automatically exclude the IR pole coefficients from the scale variation. One can also manually exclude them using NLO_MUR_COEFFICIENT_FROM_VIRTUAL: false. If they are excluded, then IR pole cancellation is assumed and, thus, only the UV renormalisation term pole coefficient is considered in the scale variation.

5.1.19.4.2. Parton shower emissions

By default, the reweighting of parton shower emissions is included in the variations. It can be disabled explicitly, using SHOWER:REWEIGHT: false. This should work out of the box for all types of variations. However, parton-shower reweighting (even though formally exact), tends to be numerically less stable than the reweighting of the hard process. If numerical issues are encountered, one can try to increase SHOWER:REWEIGHT_SCALE_CUTOFF (default: 5, measured in GeV). This disables shower variations for emissions at scales below the value. An additional safeguard against rare spuriously large shower variation weights is implemented as SHOWER:MAX_REWEIGHT_FACTOR (default: 1e3). Any variation weights accumulated during an event and larger than this factor will be ignored and reset to 1.

5.1.20. MPI parallelization

MPI parallelization in Sherpa can be enabled using the configuration option -DSHERPA_ENABLE_MPI=ON. Sherpa supports OpenMPI and MPICH2 . For detailed instructions on how to run a parallel program, please refer to the documentation of your local cluster resources or the many excellent introductions on the internet. MPI parallelization is mainly intended to speed up the integration process, as event generation can be parallelized trivially by starting multiple instances of Sherpa with different random seed, cf. RANDOM_SEED. However, both the internal analysis module and the Root NTuple writeout can be used with MPI. Note that these require substantial data transfer.

Please note that the process information contained in the Process directory for both Amegic and Comix needs to be generated without MPI parallelization first. Therefore, first run

$ Sherpa INIT_ONLY=1 <Sherpa.yaml>

and, in case of using Amegic, compile the libraries. Then start your parallelized integration, e.g.

$ mpirun -n <n> Sherpa -e 0 <Sherpa.yaml>

After the integration has finished, you can submit individual jobs to generate event samples (with a different random seed for each job). Upon completion, the results can be merged.

5.2. Beam parameters

Mandatory settings to set up the colliding particle beams are

• The initial beam particles specified through BEAMS, given by their PDG particle number. For (anti)protons and (positrons) electrons, for example, these are given by \((-)2212\) or \((-)11\), respectively. The code for photons is 22. If you provide a single particle number, both beams will consist of that particle type. If the beams consist of different particles, a list of two values have to be provided.

• The energies of both incoming beams are defined through BEAM_ENERGIES, given in units of GeV. Again, single values apply to both beams, whereas a list of two values have to be given when the two beams do not have the same energy.

Examples would be

# LHC
BEAMS: 2212
BEAM_ENERGIES: 7000

# HERA
BEAMS: [-11, 2212]
BEAM_ENERGIES: [27.5, 820]

More options related to beamstrahlung and intrinsic transverse momentum can be found in the following subsections.

5.2.1. Beam Spectra

If desired, you can also specify spectra for beamstrahlung through BEAM_SPECTRA. The possible values are

Monochromatic

The beam energy is unaltered and the beam particles remain unchanged. That is the default and corresponds to ordinary hadron-hadron or lepton-lepton collisions.

Laser_Backscattering

This can be used to describe the backscattering of a laser beam off initial leptons. The energy distribution of the emerging photon beams is modelled by the CompAZ parameterisation, see [Zar03]. Note that this parameterisation is valid only for the proposed TESLA photon collider, as various assumptions about the laser parameters and the initial lepton beam energy have been made. See details below.

Simple_Compton

This corresponds to a simple light backscattering off the initial lepton beam and produces initial-state photons with a corresponding energy spectrum. See details below.

EPA

This enables the equivalent photon approximation for colliding protons, see [AGH+08]. The resulting beam particles are photons that follow a dipole form factor parameterisation, cf. [BGMS74]. The authors would like to thank T. Pierzchala for his help in implementing and testing the corresponding code. See details below.

Spectrum_Reader

A user defined spectrum is used to describe the energy spectrum of the assumed new beam particles. The name of the corresponding spectrum file needs to be given through the keywords SPECTRUM_FILES.

The BEAM_SMIN and BEAM_SMAX parameters may be used to specify the minimum/maximum fraction of cms energy squared after Beamstrahlung. The reference value is the total centre of mass energy squared of the collision, not the centre of mass energy after eventual Beamstrahlung.

The parameter can be specified using the internal interpreter, see Interpreter, e.g. as BEAM_SMIN: sqr(20/E_CMS).

5.2.1.1. Laser Backscattering

The energy distribution of the photon beams is modelled by the CompAZ parameterisation, see [Zar03], with various assumptions valid only for the proposed TESLA photon collider. The laser energies can be set by E_LASER. P_LASER sets their polarisations, defaulting to 0.. Both settings can either be set to a single value, applying to both beams, or to a list of two values, one for each beam. The LASER_MODE takes the values -1, 0, and 1, defaulting to 0. LASER_ANGLES and LASER_NONLINEARITY can be set to true or to false (default).

5.2.1.2. Simple Compton

This corresponds to a simple light backscattering off the initial lepton beam and produces initial-state photons with a corresponding energy spectrum. It is a special case of the above Laser Backscattering with LASER_MODE: -1.

5.2.1.3. EPA

The equivalent photon approximation, cf. [AGH+08], [BGMS74], has a few free parameters, listed below. Each of these parameters has to be set in the subsetting EPA, like so

EPA:
  Q2Max: 4.5

The usual rules for yaml structure apply, c.f. Input structure.

Q2Max

Parameter of the EPA spectra of the two beams, defaults to 3. in units of GeV squared. For the electron, the maximum virtuality is taken to be the minimum of this value and the kinematical limit, given by

\[Q^2_{max,kin} = \frac{(m_e x)^2}{1-x} + E_e^2 (1-x) \theta^2_{max}\]

with \(m_e\) the electron mass, \(E_e\) the electron energy, \(x\) the energy fraction that the photon carries and \(\theta_{max}\) the maximum electron deflection angle, see below.

ThetaMax

Parameter of the EPA spectrum of an electron beam, cf. [FMNR93]. Describes the maximum angle of the electron deflection, which translates to the maximum virtuality in the photon spectrum. It defaults to 0.3.

Use_old_WW

In Sherpa version 3, a more accurate Weizsäcker-Williams weight for electron beams is used, as described in [Sch96] and [FMNR93]. By default, Sherpa uses this improved version of the formula, if you would like to use the previous version, set this switch to true.

PTMin

Infrared regulator to the EPA beam spectra. Given in GeV, the value must be between 0. and 1. for EPA approximation to hold. Defaults to 0., i.e. the spectrum has to be regulated by cuts on the observable, cf Selectors.

Form_Factor

Form factor model to be used on the beams. The options are 0 (pointlike), 1 (homogeneously charged sphere, 2 (gaussian shaped nucleus), and 3 (homogeneously charged sphere, smoothed at low and high x). Applicable only to heavy ion beams. Defaults to 0.

AlphaQED

Value of alphaQED to be used in the EPA. Defaults to 0.0072992701.

Q2Max, PTMin, Form_Factor, XMin can either be set to single values that are then applied to both beams, or to a list of two values, for the respective beams.

5.2.2. Beam Polarization

Sherpa can also provide cross-sections for polarized beams. These calculations can only be provided using the AMEGIC ME generator. The value for the beam polarization can be given as a percentage e.g. 80 or in decimal form e.g. 0.8 . The flavour of BEAM_1/BEAM_2 follows the definition given to BEAMS.

POLARIZATION:
  BEAM_1: 0.8
  BEAM_2: -0.3

5.3. ISR parameters

The following parameters are used to steer the setup of beam substructure and initial state radiation (ISR).

BUNCHES

Specify the PDG ID of the first (left) and second (right) bunch particle (or both if only one value is provided), i.e. the particle after eventual Beamstrahlung specified through the beam parameters, see Beam parameters. Per default these are taken to be identical to the values set using BEAMS, assuming the default beam spectrum is Monochromatic. In case the Simple Compton or Laser Backscattering spectra are enabled the bunch particles would have to be set to 22, the PDG code of the photon.

Sherpa provides access to a variety of structure functions. They can be configured with the following parameters.

PDF_LIBRARY

This parameter takes the list of PDF interfaces to load. The following options are distributed with Sherpa:

LHAPDFSherpa

Use PDF’s from LHAPDF [B+11]. This is the default.

CT14Sherpa

Built-in library for some PDF sets from the CTEQ collaboration, cf. [D+].

NNPDFSherpa

Built-in library for PDF sets from the NNPDF group, cf. [B+].

GRVSherpa

Built-in library for the GRV photon PDF [GRV92b], [GRV92a].

GRSSherpa

Built-in library for the GRS photon PDF [GRS99].

SALSherpa

Built-in library for the SAL photon PDF [SAL06].

CJKSherpa

Built-in library for the CJK photon PDF [CJKL03], [CJK04b], [CJK04c], [CJK04a].

SASGSherpa

Built-in library for the SaSgam photon PDF [SS95], [SS96].

PDFESherpa

Built-in library for the electron structure function. The perturbative order of the fine structure constant can be set using the parameter ISR_E_ORDER (default: 1). The switch ISR_E_SCHEME allows to set the scheme of respecting non-leading terms. Possible options are 0 (“mixed choice”), 1 (“eta choice”), or 2 (“beta choice”, default).

None

No PDF. Fixed beam energy.

Furthermore it is simple to build an external interface to an arbitrary PDF and load that dynamically in the Sherpa run. See External PDF for instructions.

By default, Sherpa will try to install with the LHAPDF interface enabled. If this is not desired, for example in lepton-lepton collisions where LHAPDF is not used, the user can disable the interface with the cmake option -DCMAKE_ENABLE_LHAPDF=OFF. Sherpa will then use the internal PDF_LIBRARY for hadronic collisions, with the default set being NNPDF31_nnlo_as_0118_mc. Note that PDF variations and the evolution of ALPHAS, ALPHAS: {USE_PDF: 1}, can only be used with LHAPDF enabled.

PDF_SET

Specifies the PDF set for hadronic bunch particles. All sets available in the chosen PDF_LIBRARY can be figured by running Sherpa with the parameter SHOW_PDF_SETS: 1, e.g.:

$ Sherpa 'PDF_LIBRARY: CTEQ6Sherpa' 'SHOW_PDF_SETS: 1'

If the two colliding beams are of different type, e.g. protons and electrons or photons and electrons, it is possible to specify two different PDF sets by providing two values: PDF_SET: [pdf1, pdf2]. The special value Default can be used as a placeholder for letting Sherpa choose the appropriate PDF set (or none).

PDF_SET_VERSIONS

This parameter allows to select a specific version (member) within the chosen PDF set. It is possible to specify two different PDF sets using PDF_SET_VERSIONS: [version1, version2]

See On-the-fly event weight variations to find out how to vary PDF sets and version on-the-fly, both in the matrix element and in the parton shower.

5.4. Models

The main switch MODEL sets the model that Sherpa uses throughout the simulation run. The default is SM, the built-in Standard Model implementation of Sherpa. For BSM simulations, Sherpa offers an option to use the Universal FeynRules Output Format (UFO) [DDF+12], [Darme+23].

Please note: AMEGIC can only be used for the built-in models (SM and HEFT). For anything else, please use Comix. For more details on the Sherpa capabilities to simulate BSM physics see [HKSS15].

5.4.1. Built-in Models

5.4.1.1. Standard Model

The SM inputs for the electroweak sector can be given in nine different schemes, that correspond to different choices of which SM physics parameters are considered fixed and which are derived from the given quantities. The electroweak coupling is by default fixed, unless its running has been enabled (cf. COUPLINGS). The input schemes are selected through the EW_SCHEME parameter, whose default is Gmu. The following options are provided:

UserDefined

All EW parameters are explicitly given: Here the W, Z and Higgs masses and widths are taken as inputs, and the parameters 1/ALPHAQED(0), ALPHAQED_DEFAULT_SCALE, SIN2THETAW (weak mixing angle), VEV (Higgs field vacuum expectation value) and LAMBDA (Higgs quartic coupling) have to be specified.

By default, ALPHAQED_DEFAULT_SCALE: 8315.18 (\(=m_Z^2\)), which means that the MEs are evaluated with a value of \(\alpha=\frac{1}{128.802}\).

Note that this mode allows to violate the tree-level relations between some of the parameters and might thus lead to gauge violations in some regions of phase space.

alpha0

All EW parameters are calculated from the W, Z and Higgs masses and widths and the fine structure constant (taken from 1/ALPHAQED(0) + ALPHAQED_DEFAULT_SCALE, cf. below) using tree-level relations.

By default, ALPHAQED_DEFAULT_SCALE: 0.0, which means that the MEs are evaluated with a value of \(\alpha=\frac{1}{137.03599976}\).

alphamZ

All EW parameters are calculated from the W, Z and Higgs masses and widths and the fine structure constant (taken from 1/ALPHAQED(MZ), default 128.802) using tree-level relations.

Gmu

This choice corresponds to the G_mu-scheme. The EW parameters are calculated out of the weak gauge boson masses M_W, M_Z, the Higgs boson mass M_H, their respective widths, and the Fermi constant GF using tree-level relations.

alphamZsW

All EW parameters are calculated from the Z and Higgs masses and widths, the fine structure constant (taken from 1/ALPHAQED(MZ), default 128.802), and the weak mixing angle (SIN2THETAW) using tree-level relations. In particular, the W boson mass (and in the complex mass scheme also its width) is a derived quantity.

alphamWsW

All EW parameters are calculated from the W and Higgs masses and widths, the fine structure constant (taken from 1/ALPHAQED(MW), default 132.17), and the weak mixing angle (SIN2THETAW) using tree-level relations. In particular, the Z boson mass (and in the complex mass scheme also its width) is a derived quantity.

GmumZsW

All EW parameters are calculated from the Z and Higgs masses and widths, the Fermi constant (GF), and the weak mixing angle (SIN2THETAW) using tree-level relations. In particular, the W boson mass (and in the complex mass scheme also its width) is a derived quantity.

GmumWsW

All EW parameters are calculated from the W and Higgs masses and widths, the Fermi constant (GF), and the weak mixing angle (SIN2THETAW) using tree-level relations. In particular, the Z boson mass (and in the complex mass scheme also its width) is a derived quantity.

FeynRules

This choice corresponds to the scheme employed in the FeynRules/UFO setup. The EW parameters are calculated out of the Z boson mass M_Z, the Higgs boson mass M_H, the Fermi constant GF and the fine structure constant (taken from 1/ALPHAQED(0) + ALPHAQED_DEFAULT_SCALE, cf. below) using tree-level relations. Note, the W boson mass is not an input parameter in this scheme.

All Gmu-derived schemes, where the EW coupling is a derived quantity, possess an ambiguity on how to construct a real EW coupling in the complex mass scheme. Several conventions are implemented and can be accessed through GMU_CMS_AQED_CONVENTION.

In general, for NLO EW calculations, the EW renormalisation scheme has to be defined as well. By default, it is set to the EW input parameter scheme set through EW_SCHEME. If needed, however, it can also be set to a different scheme using EW_REN_SCHEME using the above options. Irrespective of how the EW renormalisation scheme is set, the setting is then communicated automatically to the EW loop provider.

To account for quark mixing the CKM matrix elements have to be assigned. For this purpose the Wolfenstein parameterisation [Wol83] is employed. The order of expansion in the lambda parameter is defined through

CKM:
  Order: <order>
  # other CKM settings ...

The default for Order is 0, corresponding to a unit matrix. The parameter convention for higher expansion terms reads:

• Order: 1, the Cabibbo subsetting has to be set, it parameterises lambda and has the default value 0.22537.

• Order: 2, in addition the value of CKM_A has to be set, its default is 0.814.

• Order: 3, the order lambda^3 expansion, Eta and Rho have to be specified. Their default values are 0.353 and 0.117, respectively.

The CKM matrix elements V_ij can also be read in using

CKM:
  Matrix_Elements:
    i,j: <V_ij>
    # other CKM matrix elements ...
  # other CKM settings ...

Complex values can be given by providing two values: <V_ij> -> [Re, Im]. Values not explicitly given are taken from the afore computed Wolfenstein parameterisation. Setting CKM: {Output: true} enables an output of the CKM matrix.

The remaining parameter to fully specify the Standard Model is the strong coupling constant at the Z-pole, given through ALPHAS(MZ). Its default value is 0.118. If the setup at hand involves hadron collisions and thus PDFs, the value of the strong coupling constant is automatically set consistent with the PDF fit and can not be changed by the user. Since Sherpa is compiled with LHAPDF support, it is also possible to use the alphaS evolution provided in LHAPDF by specifying ALPHAS: {USE_PDF: 1}. The perturbative order of the running of the strong coupling can be set via ORDER_ALPHAS, where the default 0 corresponds to one-loop running and 1, 2, 3 to 2,3,4-loops, respectively. If the setup at hand involves PDFs, this parameter is set consistent with the information provided by the PDF set.

If unstable particles (e.g. W/Z bosons) appear as intermediate propagators in the process, Sherpa uses the complex mass scheme to construct MEs in a gauge-invariant way. For full consistency with this scheme, by default the dependent EW parameters are also calculated from the complex masses (WIDTH_SCHEME: CMS), yielding complex values e.g. for the weak mixing angle. To keep the parameters real one can set WIDTH_SCHEME: Fixed. This may spoil gauge invariance though.

With the following switches it is possible to change the properties of all fundamental particles:

PARTICLE_DATA:
  <id>:
    <Property>: <value>
    # other properties for this particle ...
  # data for other particles

Here, <id> is the PDG ID of the particle for which one more properties are to be modified. <Property> can be one of the following:

Mass

Sets the mass (in GeV) of the particle.

Masses of particles and corresponding anti-particles are always set simultaneously.

For particles with Yukawa couplings, those are enabled/disabled consistent with the mass (taking into account the Massive parameter) by default, but that can be modified using the Yukawa parameter. Note that by default the Yukawa couplings are treated as running, cf. YUKAWA_MASSES.

Massive

Specifies whether the finite mass of the particle is to be considered in matrix-element calculations or not. Can be true or false.

Width

Sets the width (in GeV) of the particle.

Active

Enables/disables the particle with PDG id <id>. Can be true or false.

Stable

Sets the particle either stable or unstable according to the following options:

0

Particle and anti-particle are unstable

1

Particle and anti-particle are stable

2

Particle is stable, anti-particle is unstable

3

Particle is unstable, anti-particle is stable

This option applies to decays of hadrons (cf. Hadron decays) as well as particles produced in the hard scattering (cf. Hard decays). For the latter, alternatively the decays can be specified explicitly in the process setup (see Processes) to avoid the narrow-width approximation.

Priority

Allows to overwrite the default automatic flavour sorting in a process by specifying a priority for the given flavour. This way one can identify certain particles which are part of a container (e.g. massless b-quarks), such that their position can be used reliably in selectors and scale setters.

Note

PARTICLE_DATA can also be used to the properties of hadrons, you can use the same switches (except for Massive), see Hadronization.

5.4.1.2. Effective Higgs Couplings

The HEFT describes the effective coupling of gluons and photons to Higgs bosons via a top-quark loop, and a W-boson loop in case of photons. This supplement to the Standard Model can be invoked by configuring MODEL: HEFT.

The effective coupling of gluons to the Higgs boson, g_ggH, can be calculated either for a finite top-quark mass or in the limit of an infinitely heavy top using the switch FINITE_TOP_MASS: true or FINITE_TOP_MASS: false, respectively. Similarly, the photon-photon-Higgs coupling, g_ppH, can be calculated both for finite top and/or W masses or in the infinite mass limit using the switches FINITE_TOP_MASS and FINITE_W_MASS. The default choice for both is the infinite mass limit in either case. Note that these switches affect only the calculation of the value of the effective coupling constants. Please refer to the example setup H+jets production in gluon fusion with finite top mass effects for information on how to include finite top quark mass effects on a differential level.

Either one of these couplings can be switched off using the DEACTIVATE_GGH: true and DEACTIVATE_PPH: true switches. Both default to false.

5.4.2. UFO Model Interface

To use a model generated by the FeynRules package [CD09], [CdAD+11], [Darme+23], the model must be made available to Sherpa by running

$ <prefix>/bin/Sherpa-generate-model <path-to-ufo-model>

where <path-to-ufo-model> specifies the location of the directory where the UFO model can be found. UFO support must be enabled using the -DSHERPA_ENABLE_UFO=ON option of the configure script, as described in Installation. This requires Python version 3.5 or later.

The above command generates source code for the UFO model, compiles it, and installs the corresponding library, making it available for event generation. Python and the UFO model directory are not required for event generation once the above command has finished. Note that the installation directory for the created library and the paths to Sherpa libraries and headers are predetermined automatically during the installation of Sherpa. If the Sherpa installation is moved afterwards or if the user does not have the necessary permissions to install the new library in the predetermined location, these paths can be set manually.

Please run

$ <prefix>/bin/Sherpa-generate-model --help

for information on the relevant command line arguments.

An example configuration file and parameter card will be written to the working directory while the model is generated with Sherpa-generate-model. This config file shows the syntax for the respective model parameters and can be used as a template. It is also possible to use an external parameter file by specifying the path to the file with the switch UFO_PARAM_CARD in the configuration file or on the command line. Relative and absolute file paths are allowed. This option allows it to use the native UFO parameter cards, produced by FeynRules and as used by MadGraph for example.

Note that the use of the SM PARTICLE_DATA switches Mass, Massive, Width, and Stable is discouraged when using UFO models as the UFO model completely defines all particle properties and their relation to the independent model parameters. These model parameters should be set using the standard UFO parameter syntax as shown in the example run card generated by the Sherpa-generate-model command.

For parts of the simulation other than the hard process (hadronisation, underlying event, running of the SM couplings) Sherpa uses internal default values for the Standard Model fermion masses if they are massless in the UFO model. This is necessary for a meaningful simulation. In the hard process however, the UFO model masses are always respected.

For an example UFO setup, see Event generation in the MSSM using UFO. Further models are shipped with Sherpa, residing in the <prefix>/share/SHERPA-MC/Examples/BSM directory. Note, if you want to use an extremely complex model with many high-multiplicity vertices, the Sherpa-generate-model step might require a lot of CPU time and memory even though not all vertices might be necessary for the scattering processes you plan to study. In such a case it is advised to restrict the number of external particles in Lorentz and color functions to the default of --nmax 4. Of course you can increase that number if higher-point vertices are needed.

Extending Sherpa to include partial support for UFO2.0:cite:Darme:2023jdn, Sherpa now has the ability to handle models that include form factors in the vertices. Currently, the interface does not support form factors that are directly defined in the model file. Instead, they need to be defined in a separate file, compiled into a shared library, and loaded at runtime.

For more details on the Sherpa interface to FeynRules please consult [CdAD+11], [HKSS15].

Please note that AMEGIC can only be used for the built-in models (SM and HEFT). The use of UFO models is only supported by Comix.

5.5. Matrix elements

The following parameters are used to steer the matrix element calculation setup. To learn how to specify the hard scattering process and further process-specific options in its calculation, please also refer to Processes.

5.5.1. ME_GENERATORS

The list of matrix element generators to be employed during the run. When setting up hard processes, Sherpa calls these generators in order to check whether either one is capable of generating the corresponding matrix element. This parameter can also be set on the command line using option -m, see Command Line Options.

The built-in generators are

Internal

Simple matrix element library, implementing a variety of 2->2 processes.

Amegic

The AMEGIC++ generator published under [KKS02]

Comix

The Comix generator published under [GH08]

It is possible to employ an external matrix element generator within Sherpa. For advice on this topic please contact the authors, Authors.

5.5.2. RESULT_DIRECTORY

This parameter specifies the name of the directory which is used by Sherpa to store integration results and phase-space mappings. The default is Results/. It can also be set using the command line parameter -r, see Command Line Options. The directory will be created automatically, unless the option GENERATE_RESULT_DIRECTORY: false is specified. Its location is relative to a potentially specified input path, see Command Line Options.

5.5.3. EVENT_GENERATION_MODE

This parameter specifies the event generation mode. It can also be set on the command line using option -w, see Command Line Options. The three possible options are:

Weighted

(alias W) Weighted events.

Unweighted

(alias U) Events with constant weight, which have been unweighted against the maximum determined during phase space integration. In case of rare events with w > max the parton level event is repeated floor(w/max) times and the remainder is unweighted. While this leads to unity weights for all events it can be misleading since the statistical impact of a high-weight event is not accounted for. In the extreme case this can lead to a high-weight event looking like a significant bump in distributions (in particular after the effects of the parton shower).

PartiallyUnweighted

(alias P) Identical to Unweighted events, but if the weight exceeds the maximum determined during the phase space integration, the event will carry a weight of w/max to correct for that. This is the recommended option to generate unweighted events and the default setting in Sherpa.

For Unweighted and PartiallyUnweighted events the user may set OVERWEIGHT_THRESHOLD: to cap the maximal over-weight w/max taken into account.

5.5.4. COLOR_SCHEME

This parameter specifies how to perform the color algebra in hard matrix elemens. The available options are 0 for the generator-specific default, 1 for sum, and 2 for sampling.

5.5.5. HELICITY_SCHEME

This parameter specifies how to perform the helicity algebra in hard matrix elemens. The available options are 0 for the generator-specific default, 1 for sum, and 2 for sampling.

5.5.6. SCALES

This parameter specifies how to compute the renormalisation and factorisation scale and potential additional scales.

Note

In a setup with the parton shower enabled, it is strongly recommended to leave this at its default value, METS, and to instead customise the CORE_SCALE setting as described in Scale setting in multi-parton processes (METS).

Sherpa provides several built-in scale setting schemes. For each scheme the scales are then set using expressions understood by the Interpreter. Each scale setter’s syntax is

SCALES: <scale-setter>{<scale-definition>}

to define a single scale for both the factorisation and renormalisation scale. They can be set to different values using

SCALES: <scale-setter>{<fac-scale-definition>}{<ren-scale-definition>}

In parton shower matched/merged calculations a third perturbative scale is present, the resummation or parton shower starting scale. It can be set by the user in the third argument like

SCALES: <scale-setter>{<fac-scale-definition>}{<ren-scale-definition>}{<res-scale-definition>}

If the final state of your hard scattering process contains QCD partons, their kinematics fix the resummation scale for subsequent emissions (cf. the description of the METS scale setter below). With the CS Shower, you can instead specify your own resummation scale also in such a case: Set SHOWER:RESPECT_Q2: true and use the third argument to specify your resummation scale as above.

Note

For all scales their squares have to be given. See Predefined scale tags for some predefined scale tags.

More than three scales can be set as well to be subsequently used, e.g. by different couplings, see COUPLINGS.

5.5.6.1. Scale setters

The scale setter options which are currently available are

METS

METS is the default scale scheme in Sherpa and employed for multi-leg merging, both at leading and next-to-leading order. Since it is important and complex at the same time, it will be described in detail in the next section.

VAR

The variable scale setter is the simplest scale setter available. Scales are simply specified by additional parameters in a form which is understood by the internal interpreter, see Interpreter. If, for example the invariant mass of the lepton pair in Drell-Yan production is the desired scale, the corresponding setup reads

SCALES: VAR{Abs2(p[2]+p[3])}

Renormalisation and factorisation scales can be chosen differently. For example in Drell-Yan + jet production one could set

SCALES: VAR{Abs2(p[2]+p[3])}{MPerp2(p[2]+p[3])}

FASTJET

This scale setter can be used to set a scale based on jet-, rather than parton-momenta, using FastJet.

The final state parton configuration is first clustered using FastJet and resulting jet momenta are then added back to the list of non strongly interacting particles. The numbering of momenta therefore stays effectively the same as in standard Sherpa, except that final state partons are replaced with jets, if applicable (a parton might not pass the jet criteria and get “lost”). In particular, the indices of the initial state partons and all EW particles are unaffected. Jet momenta can then be accessed as described in Predefined scale tags through the identifiers p[i], and the nodal values of the clustering sequence can be used through MU_n2. The syntax is

SCALES: FASTJET[<jet-algo-parameter>]{<scale-definition>}

Therein the parameters of the jet algorithm to be used to define the jets are given as a comma separated list of

• the jet algorithm A:kt,antikt,cambridge,siscone (default antikt)

• phase space restrictions, i.e. PT:<min-pt>, ET:<min-et>, Eta:<max-eta>, Y:<max-rap> (otherwise unrestricted)

• radial parameter R:<rad-param> (default 0.4)

• f-parameter for Siscone f:<f-param> (default 0.75)

• recombination scheme C:E,pt,pt2,Et,Et2,BIpt,BIpt2 (default E)

• b-tagging mode B:0,1,2 (default 0) This parameter, if specified different from its default 0, allows to use b-tagged jets only, based on the parton-level constituents of the jets. There are two options: With B:1 both b and anti-b quarks are counted equally towards b-jets, while for B:2 they are added with a relative sign as constituents, i.e. a jet containing b and anti-b is not tagged.

• scale setting mode M:0,1 (default 1) It is possible to specify multiple scale definition blocks, each enclosed in curly brackets. The scale setting mode parameter then determines, how those are interpreted: In the M:0 case, they specify factorisation, renormalisation and resummation scale separately in that order. In the M:1 case, the n given scales are used to calculate a mean scale such that \(\alpha_s^n(\mu_\text{mean})=\alpha_s(\mu_1)\dots\alpha_s(\mu_n)\) This scale is then used for factorisation, renormalisation and resummation scale.

Consider the example of lepton pair production in association with jets. The following scale setter

SCALES: FASTJET[A:kt,PT:10,R:0.4,M:0]{sqrt(PPerp2(p[4])*PPerp2(p[5]))}

reconstructs jets using the kt-algorithm with R=0.4 and a minimum transverse momentum of 10 GeV. The scale of all strong couplings is then set to the geometric mean of the hardest and second hardest jet. Note M:0.

Similarly, in processes with multiple strong couplings, their renormalisation scales can be set to different values, e.g.

SCALES: FASTJET[A:kt,PT:10,R:0.4,M:1]{PPerp2(p[4])}{PPerp2(p[5])}

sets the scale of one strong coupling to the transverse momentum of the hardest jet, and the scale of the second strong coupling to the transverse momentum of second hardest jet. Note M:1 in this case.

The additional tags MU_22 .. MU_n2 (n=2..njet+1), hold the nodal values of the jet clustering in descending order.

Please note that currently this type of scale setting can only be done within the process block (Processes) and not within the (me) section.

VBF

Very similar to the METS scale setter and thus also applicable in multi-leg merged setups, but catering specifically to topologies with two colour-separated parton lines like in VBF/VBS processes for the incoming quarks.

5.5.6.2. Scale setting in multi-parton processes (METS)

METS is the default scale setting in Sherpa, since it is employed for multi-leg merging, both at leading and next-to-leading order. It dynamically defines the three tags MU_F2, MU_R2 and MU_Q2 as will be explained below. Those can then be employed in the actual <scale-definition> in the scale setter. The default is

SCALES: METS{MU_F2}{MU_R2}{MU_Q2}

The tags may be omitted, i.e.

SCALES: METS

leads to an identical scale definition.

METS is a very dynamic scheme and depends on two ingredients to construct a scale that preserves the logarithmic accuracy of the parton evolution defined by the parton shower:

1. A sequential recombination algorithm to cluster the multi-leg matrix element onto a core configuration (typically 2->2) using an inversion of the current parton shower. The clustered flavours are determined using run-time information from the matrix element generator. The clustering stops, when no combination is found that corresponds to a parton shower branching, or if two subsequent branchings are unordered in terms of the parton shower evolution parameter. That defines the core process.

2. A freely selectable scale in the core process, CORE_SCALE.

These are then defined to calculate MU_R2 from the core scale and the individual clustering scales such that:

\[\alpha_s(\mu_{R}^2)^{n+k} = \alpha_s(\mu_{R,\text{core-scale}}^2)^k \alpha_s(k_{t,1}^2) \dots \alpha_s(k_{t,n}^2)\]

where \(n\) is the order in strong coupling of the core process and \(k\) is the number of clusterings, \(k_{t,i}\) are the relative transverse momenta at each clustering.

The definition of MU_F2 and MU_Q2 are passed directly on from the core scale setter.

The functional form of the core scale can be defined by the user in the MEPS settings block as follows:

MEPS:
  CORE_SCALE: <core-scale-setter>{<core-fac-scale-definition>}{<core-ren-scale-definition>}{<core-res-scale-definition>}

Again, for core scale setters which define MU_F2, MU_R2 and MU_Q2 the actual scale listing can be dropped.

Possible choices for the core scale setter are:

Default

The core scales are defined depending on the core process and as the list and functional form is regularly extended to more core processes, its definition is most easily seen in the source code

VAR

Variable core scale setter for free functional definition by the user. Syntax is identical to variable scale setter.

QCD

QCD core scale setter. Scales are set to harmonic mean of s, t and u. Only useful for 2->2 cores as alternative to the Default core scale.

TTBar

Core scale setter for processes involving top quarks. Implementation details are described in Appendix C of [HHL+13].

SingleTop

Core scale setter for single-top production in association with one jet. If the W is in the t-channel (s-channel), the squared scales are set to the Mandelstam variables t=2*p[0]*p[2] (t=2*p[0]*p[1]).

Photons

Core scale setter for photon(s)+jets production. Sets the following scales for the possible core processes:

• \(\gamma\gamma\): \(\mu_f=\mu_r=\mu_q=m_{\gamma\gamma}\)

• \(\gamma j\): \(\mu_f=\mu_r=\mu_q=p_{\perp,\gamma}\)

• \(jj\): same as QCD core scale (harmonic mean of s, t, u)

Unordered cluster histories are by default not allowed. Instead, if during clustering a new smaller scale is encountered, the previous maximal scale will be used, or alternatively a user-defined scale specified, e.g.

MEPS:
  UNORDERED_SCALE: VAR{H_Tp2/sqr(N_FS-2)}

If instead you want to allow unordered histories you can also enable them with ALLOW_SCALE_UNORDERING: 1.

Clusterings onto 2->n (n>2) configurations is possible and for complicated processes can warrant the implementation of a custom core scale, cf. Customization.

Occasionally, users might encounter the warning message

METS_Scale_Setter::CalculateScale(): No CSS history for '<process name>' in <percentage>% of calls. Set \hat{s}.

As long as the percentage quoted here is not too high, this does not pose a serious problem. The warning occurs when - based on the current colour configuration and matrix element information - no suitable clustering is found by the algorithm. In such cases the scale is set to the invariant mass of the partonic process.

One final word of caution: The METS scale scheme might be subject to changes to enable further classes of processes for merging in the future and integration results might thus change slightly between different Sherpa versions.

5.5.6.3. Custom scale implementation

When the flexibility of the VAR scale setter above is not sufficient, it is also possible to implement a completely custom scale scheme within Sherpa as C++ class plugin. For details please refer to the Customization section.

5.5.6.4. Predefined scale tags

There exist a few predefined tags to facilitate commonly used scale choices or easily implement a user defined scale.

p[n]

Access to the four momentum of the nth particle. The initial state particles carry n=0 and n=1, the final state momenta start from n=2. Their ordering is determined by Sherpa’s internal particle ordering and can be read e.g. from the process names displayed at run time. Please note, that when building jets out of the final state partons first, e.g. through the FASTJET scale setter, these parton momenta will be replaced by the jet momenta ordered in transverse momenta. For example the process u ub -> e- e+ G G will have the electron and the positron at positions p[2] and p[3] and the gluons on positions p[4] and p[5]. However, when finding jets first, the electrons will still be at p[2] and p[3] while the harder jet will be at p[4] and the softer one at p[5].

H_T2

Square of the scalar sum of the transverse momenta of all final state particles.

H_TM2

Square of the scalar sum of the transverse energies of all final state particles, i.e. contrary to H_T2 H_TM2 takes particle masses into account.

H_TY2(<factor>,<exponent>)

Square of the scalar sum of the transverse momenta of all final state particles weighted by their rapidity distance from the final state boost vector. Thus, takes the form

H_T^{(Y)} = sum_i pT_i exp [ fac |y-yboost|^exp ]

Typical values to use would by 0.3 and 1.

H_Tp2

Scale setter for lepton-pair production in association with jets only, implements

H_T' = sqrt(m_ll^2 + pT(ll)^2) + sum_i pT_i (i not l)

DH_Tp2(<recombination-method>,<dR>)

Implements a version of H_Tp2 which dresses charged particles first. The parameter <recombination-method> can take the following values: Cone, kt, CA or antikt, while <dR> is the respective algorithm’s angular distance parameter.

TAU_B2

Square of the beam thrust.

MU_F2, MU_R2, MU_Q2

Tags holding the values of the factorisation, renormalisation scale and resummation scale determined through backwards clustering in the METS scale setter.

MU_22, MU_32, ..., MU_n2

Tags holding the nodal values of the jet clustering in the FASTJET scale setter, cf. Scale setters.

All of those objects can be operated upon by any operator/function known to the Interpreter.

5.5.6.5. Scale schemes for NLO calculations

For next-to-leading order calculations it must be guaranteed that the scale is calculated separately for the real correction and the subtraction terms, such that within the subtraction procedure the same amount is subtracted and added back. Starting from version 1.2.2 this is the case for all scale setters in Sherpa. Also, the definition of the scale must be infrared safe w.r.t. to the radiation of an extra parton. Infrared safe (for QCD-NLO calculations) are:

• any function of momenta of NOT strongly interacting particles

• sum of transverse quantities of all partons (e.g. H_T2)

• any quantity referring to jets, constructed by an IR safe jet algorithm, see below.

Not infrared safe are

• any function of momenta of specific partons

• for processes with hadrons in the initial state: any quantity that depends on parton momenta along the beam axis, including the initial state partons itself.

Since the total number of partons is different for different pieces of the NLO calculation any explicit reference to a parton momentum will lead to an inconsistent result.

5.5.6.6. Explicit scale variations

The (nominal) factorisation and renormalisation scales in the fixed-order matrix elements can be scaled explicitly simply by introducing a prefactor into the scale definition, e.g.

SCALES: VAR{0.25*H_T2}{0.25*H_T2}

for setting both the renormalisation and factorisation scales to H_T/2.

However, to calculate several variations in a single event generation run, you need to use On-the-fly event weight variations. See the instructions given there to find out how to vary factorisation and renormalisation scale factors on-the-fly, both in the matrix element and in the parton shower.

The starting scale of the parton shower resummation in a ME+PS merged sample, MU_Q2, can at the moment not be varied on-the-fly. To change the (nominal) starting scale explicitly, a scale factor can be introduced in the third argument of the METS scale setter:

SCALES: METS{MU_F2}{MU_R2}{4.0*MU_Q2}

5.5.7. COUPLINGS

Within Sherpa, strong and electroweak couplings can be computed at any scale specified by a scale setter (cf. SCALES). The COUPLINGS tag links the argument of a running coupling to one of the respective scales. This is better seen in an example. Assuming the following input

SCALES: VAR{...}{PPerp2(p[2])}{Abs2(p[2]+p[3])}
COUPLINGS:
  - "Alpha_QCD 1"
  - "Alpha_QED 2"

Sherpa will compute any strong couplings at scale one, i.e. PPerp2(p[2]) and electroweak couplings at scale two, i.e. Abs2(p[2]+p[3]). Note that counting starts at zero.

5.5.8. KFACTOR

This parameter specifies how to evaluate potential K-factors in the hard process. This is equivalent to the COUPLINGS specification of Sherpa versions prior to 1.2.2. To list all available K-factors, the tag SHOW_KFACTOR_SYNTAX: 1 can be specified on the command line. Currently available options are

None

No reweighting

VAR

Couplings specified by an additional parameter in a form which is understood by the internal interpreter, see Interpreter. The tags Alpha_QCD and Alpha_QED serve as links to the built-in running coupling implementation.

If for example the process g g -> h g in effective theory is computed, one could think of evaluating two powers of the strong coupling at the Higgs mass scale and one power at the transverse momentum squared of the gluon. Assuming the Higgs mass to be 125 GeV, the corresponding reweighting would read

SCALES:    VAR{...}{PPerp2(p[3])}
COUPLINGS: "Alpha_QCD 1"
KFACTOR:   VAR{sqr(Alpha_QCD(sqr(125))/Alpha_QCD(MU_12))}

As can be seen from this example, scales are referred to as MU_<i>2, where <i> is replaced with the appropriate number. Note that counting starts at zero.

It is possible to implement a dedicated K-factor scheme within Sherpa. For advice on this topic please contact the authors, Authors.

5.5.9. YUKAWA_MASSES

This parameter specifies whether the Yukawa couplings are evaluated using running or fixed quark masses: YUKAWA_MASSES: Running is the default since version 1.2.2 while YUKAWA_MASSES: Fixed was the default until 1.2.1.

5.5.10. Dipole subtraction

There is one general switch that governs the behaviour of the Catani-Seymour subtraction [CS97] as implemented in Sherpa [GK08, Sch18]. NLO_SUBTRACTION_MODE defines which type of divergences will be subtracted (both off the virtual and real amplitudes). Options are:

QCD

Only QCD infrared divergences will be subtracted. This is the default as most users will be familiar with this setting corresponding to the abilities of older Sherpa versions.

QED

Only QED infrared divergences will be subtracted.

QCD+QED

All Standard Model infrared divergences will be subtracted.

Further, the following list of parameters can be used to optimise the performance of the dipole subtraction. These dipole parameters are specified as subsettings to the DIPOLES setting, like this:

DIPOLES:
  ALPHA: <alpha>
  NF_GSPLIT: <nf>
  # other dipole settings ...

The following parameters can be customised:

SCHEME

Defines the finite parts of the splitting functions used. Options are:

CS, this is the standard Catani-Seymour subtraction definition of the splitting functions. This is the default for fixed-order calculations.

Dire, this selects the modified splitting functions used in the Dire dipole shower. It is the default for MC@NLO calculations matching to Dire.

CSS, this selects the modified splitting functions used in the CSS parton shower. It is the default for MC@NLO calculations matching to the CSS.

ALPHA

Specifies a dipole cutoff in the nonsingular region [Nag03]. Changing this parameter shifts contributions from the subtracted real correction piece (RS) to the piece including integrated dipole terms (I), while their sum remains constant. This parameter can be used to optimize the integration performance of the individual pieces. Also the average calculation time for the subtracted real correction is reduced with smaller choices of “ALPHA” due to the (on average) reduced number of contributing dipole terms. For most processes a reasonable choice is between 0.01 and 1 (default). See also Choosing DIPOLES ALPHA

ALPHA_FF, ALPHA_FI, ALPHA_IF, ALPHA_II

Specifies the above dipole alpha only for FF, FI, IF, or II dipoles, respectively.

AMIN

Specifies the cutoff of real correction terms in the infrared region to avoid numerical problems with the subtraction. The default is 1.e-8.

NF_GSPLIT

Specifies the number of quark flavours that are produced from gluon splittings. This number must be at least the number of massless flavours (default). If this number is larger than the number of massless quarks the massive dipole subtraction [CDST02] is employed.

KAPPA

Specifies the kappa-parameter in the massive dipole subtraction formalism [CDST02]. The default is 2.0/3.0.

LIST

If set to 1 all generated dipoles will be listed for all generated processes.

5.6. Processes

In addition to the general matrix-element calculation settings specified as described in Matrix elements, the hard scattering process has to be defined and further process-specific calculation settings can be specified. This happens in the PROCESSES part of the input file and is described in the following section.

A simple example looks like:

PROCESSES:
- 93 93 -> 11 -11 93{4}:
    Order: {QCD: 0, EW: 2}
    CKKW: 20

In general, the process setup takes the following form:

PROCESSES:
# Process 1:
- <process declaration>:
    <parameter>: <value>
    <multiplicities-to-be-applied-to>:
      <parameter>: <value>
      ...
# Process 2:
- <process declaration>
    ...

i.e. PROCESSES followed by a list of process definitions.

Each process definition starts with the declaration of the (core) process itself. The initial and final state particles are specified by their PDG codes, or by particle containers, see Particle containers. Examples are

- 93 93 -> 11 -11

Sets up a Drell-Yan process group with light quarks in the initial state.

- 11 -11 -> 93 93 93{3}

Sets up jet production in e+e- collisions with up to three additional jets.

Special features of the process declaration will be documented in the following. The remainder of the section then documents all additional parameters for the process steering, e.g. the coupling order, which can be nested as key: value pairs within a given process declaration.

An advanced syntax feature shall be mentioned already here, since it will be used in some of the examples in the following: Most of the parameters can be grouped under a multiplicity key, which can either be a single or a range of multiplicities, e.g. 2->2-4: { <settings for 2->2, 2->3 and 2->4 processes> }. The usefulness of this will hopefully become clear in the examples in the following.

5.6.1. Special features of the process declaration

5.6.1.1. PDG codes

Initial and final state particles are specified using their PDG codes (cf. PDG). A list of particles with their codes, and some of their properties, is printed at the start of each Sherpa run, when the OUTPUT is set at level 2.

5.6.1.2. Particle containers

Sherpa contains a set of containers that collect particles with similar properties, namely

• lepton (carrying number 90),

• neutrino (carrying number 91),

• fermion (carrying number 92),

• jet (carrying number 93),

• quark (carrying number 94).

These containers hold all massless particles and anti-particles of the denoted type and allow for a more efficient definition of initial and final states to be considered. The jet container consists of the gluon and all massless quarks, as set by

PARTICLE_DATA:
  <id>:
    Mass: 0
    # ... and/or ...
    Massive: false

A list of particle containers is printed at the start of each Sherpa run, when the OUTPUT is set at level 2.

It is also possible to define a custom particle container using the keyword PARTICLE_CONTAINERS. The container must be given an unassigned particle ID (kf-code) and its name (freely chosen by you) and the flavour content must be specified. An example would be the collection of all down-type quarks using the unassigned ID 98, which could be declared as

PARTICLE_CONTAINERS:
  98:
    Name: downs
    Flavs: [1, -1, 3, -3, 5, -5]

Note that, if wanted, you have to add both particles and anti-particles.

5.6.1.3. Parentheses

The parenthesis notation allows to group a list of processes with different flavor content but similar structure. This is most useful in the context of simulations containing heavy quarks. In a setup with massive b-quarks, for example, the b-quark will not be part of the jets container. In order to include b-associated processes easily, the following can be used:

PARTICLE_DATA:
  5: {Massive: true}
PARTICLE_CONTAINERS:
  98: {Name: B, Flavours: [5, -5]}
PROCESSES:
- 11 -11 -> (93,98) (93,98):
  ...

5.6.1.4. Curly brackets

The curly bracket notation when specifying a process allows up to a certain number of jets to be included in the final state. This is easily seen from an example, 11 -11 -> 93 93 93{3} sets up jet production in e+e- collisions. The matrix element final state may be 2, 3, 4 or 5 light partons or gluons.

5.6.2. Decay

Specifies the exclusive decay of a particle produced in the matrix element. The virtuality of the decaying particle is sampled according to a Breit-Wigner distribution. In practice this amounts to selecting only those diagrams containing s-channels of the specified flavour while the phase space is kept general. Consequently, all spin correlations are preserved. An example would be

- 11 -11 -> 6[a] -6[b]:
   Decay:
   - 6[a] -> 5 24[c]
   - -6[b] -> -5 -24[d]
   - 24[c] -> -13 14
   - -24[d] -> 94 94

5.6.3. DecayOS

Specifies the exclusive decay of a particle produced in the matrix element. The decaying particle is on mass-shell, i.e. a strict narrow-width approximation is used. This tag can be specified alternatively as DecayOS. In practice this amounts to selecting only those diagrams containing s-channels of the specified flavour and the phase space is factorised as well. Nonetheless, all spin correlations are preserved. An example would be

- 11 -11 -> 6[a] -6[b]:
    DecayOS:
    - 6[a] -> 5 24[c]
    - -6[b] -> -5 -24[d]
    - 24[c] -> -13 14
    - -24[d] -> 94 94

5.6.4. No_Decay

Remove all diagrams associated with the decay/s-channel of the given flavours. Serves to avoid resonant contributions in processes like W-associated single-top production. Note that this method breaks gauge invariance! At the moment this flag can only be set for Comix. An example would be

- 93 93 -> 6[a] -24[b] 93{1}:
    Decay: 6[a] -> 5 24[c]
    DecayOS:
    - 24[c] -> -13 14
    - -24[b] -> 11 -12
    No_Decay: -6

5.6.5. Color_Scheme

Sets a process-specific color scheme. For the corresponding syntax see COLOR_SCHEME.

5.6.6. Helicity_Scheme

Sets a process-specific helicity scheme. For the corresponding syntax see HELICITY_SCHEME.

5.6.7. Scales

Sets a process-specific scale. For the corresponding syntax see SCALES.

5.6.8. Couplings

Sets process-specific couplings. For the corresponding syntax see COUPLINGS.

5.6.9. CKKW

Sets up multijet merging according to [HKSS09]. The additional argument specifies the parton separation criterion (“merging cut”) \(Q_{\text{cut}}\) in GeV. It can be given in any form which is understood by the internal interpreter, see Interpreter. Examples are

• Hadronic collider: CKKW: 20

• Leptonic collider: CKKW: pow(10,-2.5/2.0)*E_CMS

• DIS: CKKW: $(QCUT)/sqrt(1.0+sqr($(QCUT)/$(SDIS))/Abs2(p[2]-p[0]))

See On-the-fly event weight variations to find out how to vary the merging cut on-the-fly.

5.6.10. Process_Selectors

Using Selectors: [<selector 1>, <selector 2>] in a process definition sets up process-specific selectors. They use the same syntax as described in Selectors.

5.6.11. Order

Restricts the coupling order of the process calculation at the squared-amplitude level. For example, the process 1 -1 -> 2 -2, i.e. \(d\bar{d}\to u\bar{u}\), could have orders {QCD: 2, EW: 0}, {QCD: 1, EW: 1} and {QCD: 0, EW: 2}. There can also be further entries with different names, that are model specific (e.g. for EFT couplings). Half-integer orders are so far supported only by Comix, e.g. {EW: 4.5, NP: 0.5}.

To set coupling orders at the amplitude level, e.g. to get more predictable Feynman diagram output, you may use the Amplitude_Order setting.

The word “Any” can be used as a wildcard, but might lead to problems when external matrix elements (e.g. loops) are used which require an exact specification of the order.

Note that for decay chains this setting applies to the full process, see Decay and DecayOS.

5.6.12. Max_Order

Maximum coupling order allowed. Same syntax as in Order.

5.6.13. Min_Order

Minimum coupling order allowed. Same syntax as in Order.

5.6.14. Amplitude_Order

Restricts the coupling order of the process calculation at the (non-squared) amplitude level. For example, the process 1 -1 -> 2 -2 could have amplitude orders of {QCD: 2, EW: 0} and {QCD: 0, EW: 2}.

See Order for the syntax and additional information.

5.6.15. Min_Amplitude_Order

Minimum coupling order allowed at the amplitude level. See Amplitude_Order.

5.6.16. Max_Amplitude_Order

Maximum coupling order allowed at the amplitude level. See Amplitude_Order.

5.6.17. Min_N_Quarks

Limits the minimum number of quarks in the process to the given value.

5.6.18. Max_N_Quarks

Limits the maximum number of quarks in the process to the given value.

5.6.19. Min_N_TChannels

Limits the minimum number of t-channel propagators in the process to the given value.

5.6.20. Max_N_TChannels

Limits the maximum number of t-channel propagators in the process to the given value.

5.6.21. Print_Graphs

Writes out Feynman graphs in LaTeX format. The parameter specifies a directory name in which the diagram information is stored. This directory is created automatically by Sherpa. The LaTeX source files can be compiled using the command

$ ./plot_graphs <graphs directory>

which creates an html page in the graphs directory that can be viewed in a web browser.

5.6.22. Name_Suffix

Defines a unique name suffix for the process.

5.6.23. Integration_Error

Sets a process-specific relative integration error target. An example to specify an error target of 2% for 2->3 and 2->4 processes would be:

- 93 93 -> 93 93 93{2}:
    2->3-4:
      Integration_Error: 0.02

5.6.24. Max_Epsilon

Sets epsilon for maximum weight reduction. The key idea is to allow weights larger than the maximum during event generation, as long as the fraction of the cross section represented by corresponding events is at most the epsilon factor times the total cross section. In other words, the relative contribution of overweighted events to the inclusive cross section is at most epsilon.

5.6.25. NLO_Mode

This setting specifies whether and in which mode an NLO calculation should be performed. Possible values are:

None

perform a leading-order calculation (this is the default)

Fixed_Order

perform a fixed-order next-to-leading order calculation

MC@NLO

perform an MC@NLO-type matching of a fixed-order next-to-leading order calculation to the resummation of the parton shower

The usual multiplicity identifier applies to this switch as well. Note that using a value other than None implies NLO_Part: BVIRS for the relevant multiplicities. For fixed-order NLO calculations (NLO_Mode: Fixed_Order), this can be overridden by setting NLO_Part explicitly, see NLO_Part.

Note that Sherpa includes only a very limited selection of one-loop corrections. For processes not included external codes can be interfaced, see External one-loop ME

5.6.26. NLO_Part

In case of fixed-order NLO calculations this switch specifies which pieces of a NLO calculation are computed, also see NLO_Mode. Possible choices are

B

born term

V

virtual (one-loop) correction

I

integrated subtraction terms

RS

real correction, regularized using Catani-Seymour subtraction terms

Different pieces can be combined in one processes setup. Only pieces with the same number of final state particles and the same order in alpha_S and alpha can be treated as one process, otherwise they will be automatically split up.

5.6.27. NLO_Order

Specifies the relative order of the NLO correction wrt. the considered Born process. For example, NLO_Order: {QCD: 1, EW: 0} specifies a QCD correction while NLO_Order: {QCD: 0, EW: 1} specifies an EW correction.

5.6.28. Subdivide_Virtual

Allows to split the virtual contribution to the total cross section into pieces. Currently supported options when run with BlackHat are LeadingColor and FullMinusLeadingColor. For high-multiplicity calculations these settings allow to adjust the relative number of points in the sampling to reduce the overall computation time.

5.6.29. ME_Generator

Set a process specific nametag for the desired tree-ME generator, see ME_GENERATORS.

5.6.30. RS_ME_Generator

Set a process specific nametag for the desired ME generator used for the real minus subtraction part of NLO calculations. See also ME_GENERATORS.

5.6.31. Loop_Generator

Set a process specific nametag for the desired loop-ME generator. The only Sherpa-native option is Internal with a few hard coded loop matrix elements. Other loop matrix elements are provided by external libraries.

5.6.32. Associated_Contributions

Set a process specific list of associated contributions to be computed. Valid values are EW (approximate EW corrections), LO1 (first subleading leading-order correction), LO2 (second subleading leading-order correction), LO3 (third subleading leading-order correction). They can be combined, e.g. {[EW, LO1, LO2, LO3]}. Please note, the associated contributions will not be added to the nominal event weight but instead are available to be included in the on-the-fly calculation of alternative event weights, cf. EWVirt.

5.6.33. Integrator

Sets a process-specific integrator, see INTEGRATOR.

5.6.34. PSI_ItMin

Sets the number of points per optimization step, see PSI.

5.6.35. RS_PSI_ItMin

Sets the number of points per optimization step in real-minus-subtraction parts of fixed-order and MC@NLO calculations, see PSI.

5.6.36. Special Group

Note

Needs update to Sherpa 3.x YAML syntax.

Allows to split up individual flavour processes within a process group for integrating them separately. This can help improve the integration/unweighting efficiency. Note: Only works with Comix so far. Example for usage:

Process 93 93 -> 11 -11 93
Special Group(0-1,4)
[...]
End process
Process 93 93 -> 11 -11 93
Special Group(2-3,5-7)
[...]
End process

The numbers for each individual process can be found using a script in the AddOns directory: AddOns/ShowProcessIds.sh Process/Comix.zip

5.6.37. Event biasing

In the default event generation mode, events will be distributed “naturally” in the phase space according to their differential cross sections. But sometimes it is useful, to statistically enhance the event generation for rare phase space regions or processes/multiplicities. This is possible with the following options in Sherpa. The generation of more events in a rare region will then be compensated through event weights to yield the correct differential cross section. These options can be applied both in weighted and unweighted event generation.

5.6.37.1. Enhance_Factor

Factor with which the given process/multiplicity should be statistically biased. In the following example, the Z+1j process is generated 10 times more often than naturally, compared to the Z+0j process. Each Z+1j event will thus receive a weight of 1/10 to compensate for the bias.

- 93 93 -> 11 -11 93{1}:
    2->3:
      Enhance_Factor: 10.0

5.6.37.2. RS_Enhance_Factor

Sets an enhance factor (see Enhance_Factor) for the RS-piece of an MC@NLO process.

5.6.37.3. Enhance_Function

Specifies a phase-space dependent biasing of parton-level events (before showering). The given parton-level observable defines a multiplicative enhancement on top of the normal matrix element shape. Example:

- 93 93 -> 11 -11 93{1}:
  2->3:
    Enhance_Function: VAR{PPerp2(p[2]+p[3])/400}

In this example, Z+1-jet events with \(p_\perp(Z)\leq 20\) GeV and Z+0-jet events will come with no enhancement, while other Z+1-jet events will be enhanced with \((p_\perp(Z)/20)^2\). Note: if you would define the enhancement function without the normalisation to \(1/20^2\), the Z+1-jet would come with a significant overall enhancement compared to the unenhanced Z+0-jet process, which would have a strong impact on the statistical uncertainty in the Z+0-jet region.

Optionally, a range can be specified over which the multiplicative biasing should be applied. The matching at the range boundaries will be smooth, i.e. the effective enhancement is frozen to its value at the boundaries. Example:

- 93 93 -> 11 -11 93{1}:
  2->3:
    Enhance_Function: VAR{PPerp2(p[2]+p[3])/400}|1.0|100.0

This implements again an enhancement with \((p_\perp(Z)/20)^2\) but only in the range of 20-2000 GeV. As you can see, you have to take into account the normalisation, here the factor \(1/20\), also in the range specification.

5.6.37.4. Enhance_Observable

Specifies a phase-space dependent biasing of parton-level events (before showering). Events will be statistically flat in the given observable and range. An example would be:

- 93 93 -> 11 -11 93{1}:
  2->3:
    Enhance_Observable: VAR{log10(PPerp(p[2]+p[3]))}|1|3

Here, the 1-jet process is flattened with respect to the logarithmic transverse momentum of the lepton pair in the limits 1.0 (10 GeV) to 3.0 (1 TeV). For the calculation of the observable one can use any function available in the algebra interpreter (see Interpreter).

The matching at the range boundaries will be smooth, i.e. the effective enhancement is frozen to its value at the boundaries.

This can have unwanted side effects for the statistical uncertainty when used in a multi-jet merged sample, because the flattening is applied in each multiplicity separately, and also affects the relative selection weights of each sub-sample (e.g. 2-jet vs. 3-jet).

Note

The convergence of the Monte Carlo integration can be worse if enhance functions/observables are employed and therefore the integration can take significantly longer. The reason is that the default phase space mapping, which is constructed according to diagrammatic information from hard matrix elements, is not suited for event generation including enhancement. It must first be adapted, which, depending on the enhance function and the final state multiplicity, can be an intricate task.

If Sherpa cannot achieve an integration error target due to the use of enhance functions, it might be appropriate to locally redefine this error target, see Integration_Error.

5.7. Selectors

Sherpa provides the following selectors that set up cuts at the matrix element level:

Some selectors modify the momenta and flavours of the set of final state particles. These selectors also take a list of subselectors which then act on the modified flavours and momenta. Details are explained in the respective selectors’ description.

5.7.1. Inclusive selectors

The selectors listed here implement cuts on the matrix element level, based on event properties. The corresponding syntax is

SELECTORS:
  - [<keyword>, <parameter 1>, <parameter 2>, ...]
  - # other selectors ...

Parameters that accept numbers can also be given in a form that is understood by the internal algebra interpreter, see Interpreter. The selectors act on all particles in the event. Their respective keywords are

[N, <kf>, <min value>, <max value>]

Minimum and maximum multiplicity of flavour <kf> in the final state.

[PTmis, <min value>, <max value>]

Missing transverse momentum cut (at the moment only neutrinos are considered invisible)

[ETmis, <min value>, <max value>]

Missing transverse energy cut (at the moment only neutrinos are considered invisible)

[IsolationCut, <kf>, <dR>, <exponent>, <epsilon>, <optional: mass_max>]

Smooth cone isolation [Fri98], the parameters given are the flavour <kf> to be isolated against massless partons and the isolation cone parameters.

[NJ, <N>, <algo>, <min value>, <max value>]

NJettiness from [SJW10], where <algo> specifies the jet finding algorithm to determine the hard jet directions and <N> is their multiplicity. algo=kt|antikt|cambridge|siscone,PT:<ptmin>,R:<dR>[,[ETA:<etamax>,Y:<ymax>]]

5.7.2. One particle selectors

The selectors listed here implement cuts on the matrix element level, based on single particle kinematics. The corresponding syntax is

SELECTORS:
  - [<keyword>, <flavour code>, <min value>, <max value>]
  - # other selectors ...

<min value> and <max value> are floating point numbers, which can also be given in a form that is understood by the internal algebra interpreter, see Interpreter. The selectors act on all possible particles with the given flavour. Their respective keywords are

PT

transverse momentum cut

ET

transverse energy cut

Y

rapidity cut

Eta

pseudorapidity cut

PZIN

cut on the z-component of the momentum, acts on initial-state flavours only (commonly used in DIS analyses)

HT

Visible transverse energy cut

E

energy cut

Polar_Angle

Polar Angle cut in radians. An optional boolean can be provided to switch to degrees e.g [<keyword>, <flavour code>, <min value>, <max value>, <radians>]

5.7.3. Two particle selectors

The selectors listed here implement cuts on the matrix element level, based on two particle kinematics. The corresponding is

SELECTORS:
  - [<keyword>, <flavour1 code>, <flavour2 code>, <min value>, <max value>]
  - # other selectors ...

<min value> and <max value> are floating point numbers, which can also be given in a form that is understood by the internal algebra interpreter, see Interpreter. The selectors act on all possible particles with the given flavour. Their respective keywords are

Mass

invariant mass

Q2

DIS-like virtuality

PT2

pair transverse momentum

MT2

pair transverse mass

DY

rapidity separation

DEta

pseudorapidity separation

DPhi

azimuthal separation

DR

angular separation (build from eta and phi)

DR(y)

angular separation (build from y and phi)

INEL

inelasticity, one of the flavours must be in the initial-state (commonly used in DIS analyses)

5.7.4. Decay selectors

The selectors listed here implement cuts on the matrix element level, based on particle decays, see Decay and DecayOS.

DecayMass

Invariant mass of a decaying particle. The syntax is

- [DecayMass, <flavour code>, <min value>, <max value>]

Decay

Any kinematic variable of a decaying particle. The syntax is

- [Decay(<expression>), <flavour code>, <min value>, <max value>]

where <expression> is an expression handled by the internal interpreter, see Interpreter.

Decay2

Any kinematic variable of a pair of decaying particles. The syntax is

- [Decay2(<expression>), <flavour1 code>, <flavour2 code>, <min value>, <max value>]

where <expression> is an expression handled by the internal interpreter, see Interpreter.

Particles are identified by flavour, i.e. the cut is applied on all decaying particles that match <flavour code>. <min value> and <max value> are floating point numbers, which can also be given in a format that is understood by the internal algebra interpreter, see Interpreter.

5.7.5. Particle dressers

5.7.6. Jet selectors

There are two different types of jet finders

NJetFinder

k_T-type algorithm to select on a given number of jets

FastjetFinder

Select on a given number of jets using FastJet algorithms

Their respective syntax and defaults are

SELECTORS:
- NJetFinder:
    N: 0
    PTMin: 0.0
    ETMin: 0.0
    R: 0.4
    Exp: 1
    EtaMax: None
    YMax: None
    MassMax: 0.0
- FastjetFinder:
    Algorithm: kt
    N: 0
    PTMin: 0.0
    ETMin: 0.0
    DR: 0.4
    f: 0.75        # Siscone f parameter
    EtaMax: None
    YMax: None
    Nb: -1
    Nb2: -1

Note that all parameters are optional. If they are not specified, their respective default values as indicated in the above snippet is used. However, at the very least the number of jets, N, should be specified to require a non-zero number of jets.

The NJetFinder allows to select for kinematic configurations with at least <N> jets that satisfy both, the <PTMin> and the <ETMin> minimum requirements and that are in a pseudo-rapidity region |eta|. The <Exp> (exponent) allows to apply a kt-algorithm (1) or an anti-kt algorithm (-1). As only massless partons are clustered by default, the <MassMax> allows to also include partons with a mass up to the specified values. This is useful e.g. in calculations with massive b-quarks which shall nonetheless satisfy jet criteria.

The second option FastjetFinder allows to use the FastJet plugin, through fjcore. It takes the following arguments: <Algorithm> can take the values kt,antikt,cambridge,siscone,eecambridge,jade, <N> is the minimum number of jets to be found, <PTMin> and <ETMin> are the minimum transverse momentum and/or energy, <DR> is the radial parameter. Optional arguments are: <f> (default 0.75, only relevant for the Siscone algorithm), <EtaMax> and <YMax> as maximal absolute (pseudo-)rapidity, <Nb> and <Nb2> set the number of required b-jets, where for the former both b and anti-b quarks are counted equally towards b-jets, while for the latter they are added with a relative sign as constituents, i.e. a jet containing b and anti-b is not tagged (default: -1, i.e. no b jets are required). Note that only <Algorithm>, <N> and <PTMin> are relevant for the lepton-lepton collider algorithms.

The selector FastjetVeto allows to use the FastJet plugin to apply jet veto cuts. Its syntax is identical to FastjetFinder.

The momenta and nodal values of the jets found with FastJet can also be used to calculate more elaborate selector criteria. The syntax of this selector is

- FastjetSelector:
    Expression: <expression>
    Algorithm: kt
    N: 0
    PTMin: 0.0
    ETMin: 0.0
    DR: 0.4
    f: 0.75
    EtaMax: None
    YMax: None
    BMode: 0

wherein Algorithm can take the values kt,antikt,cambridge,siscone,eecambridge,jade. In the algebraic <expression>, MU_n2 (n=2..njet+1) signify the nodal values of the jets found and p[i] are their momenta. For details see Scale setters. For example, in lepton pair production in association with jets

- FastjetSelector:
    Expression: Mass(p[4]+p[5])>100
    Algorithm: antikt
    N: 2
    PTMin: 40
    ETMin: 0
    DR: 0.5

selects all phase space points where two anti-kt jets with at least 40 GeV of transverse momentum and an invariant mass of at least 100 GeV are found. The expression must calculate a boolean value. The BMode parameter, if specified different from its default 0, allows to use b-tagged jets only, based on the parton-level constituents of the jets. There are two options: With BMode: 1 both b and anti-b quarks are counted equally towards b-jets, while for BMode: 2 they are added with a relative sign as constituents, i.e. a jet containing b and anti-b is not tagged. Note that only <epression>, <algorithm>, <n> and <ptmin> are relevant when using the lepton-lepton collider algorithms.

5.7.7. Isolation selector

Instead of the simple IsolationCut (Inclusive selectors), you may also use the more flexible Isolation_Selector to require photons (or other particles) with a smooth cone isolation and additionally apply further criteria to them. Example:

SELECTORS:
- Isolation_Selector:
    Isolation_Particle: 22
    Rejection_Particles: [93]
    Isolation_Parameters:
      R: 0.1
      EMAX: 0.1
      EXP: 2
      PT: 0.
      Y: 2.7
    NMin: 2
    Remove_Nonisolated: true
    Subselectors:
    - VariableSelector:
        Variable: PT
        Flavs: [22]
        Ranges:
        - [20, E_CMS]
        - [18, E_CMS]
        Ordering: [PT_UP]
    - [DR, 22, 22, 0.2, 10000.0 ]
    #for integration efficiency: m_yy >= sqrt(2 pTmin1 pTmin2 (1-cos dR))
    - [Mass, 22, 22, 3.7, E_CMS]

5.7.8. Universal selector

The universal selector is intended to implement non-standard cuts on the matrix element level. Its syntax is

SELECTORS:
- VariableSelector:
    Variable: <variable>
    Flavs: [<kf1>, ..., <kfn>]
    Ranges:
    - [<min1>, <max1>]
    - ...
    - [<minn>, <maxn>]
    Ordering: [<order1>, ..., <orderm>]

The Variable parameter defines the name of the variable to cut on. The keywords for available predefined can be figured by running Sherpa SHOW_VARIABLE_SYNTAX: true. Or alternatively, an arbitrary cut variable can be constructed using the internal interpreter, see Interpreter. This is invoked with the command Calc(...). In the formula specified there you have to use place holders for the momenta of the particles: p[0] … p[n] hold the momenta of the respective particles kf1 … kfn. A list of available vector functions and operators can be found here Interpreter.

<kf1>,.., specify the PDG codes of the particles the variable has to be calculated from. The ranges [<min>, <max>] then define the cut regions.

If the Ordering parameter is not given, the order of cuts is determined internally, according to Sherpa’s process classification scheme. This then has to be matched if you want to have different cuts on certain different particles in the matrix element. To do this, you should put enough (for the possible number of combinations of your particles) arbitrary ranges at first and run Sherpa with debugging output for the universal selector: Sherpa 'FUNCTION_OUTPUT: {"Variable_Selector::Trigger": 15}'. This will start to produce lots of output during integration, at which point you can interrupt the run (Ctrl-c). In the Variable_Selector::Trigger(): {...} output you can see, which particle combinations have been found and which cut range your selector has held for them (vs. the arbitrary range you specified). From that you should get an idea, in which order the cuts have to be specified.

If the fourth argument is given, particles are ordered before the cut is applied. Possible orderings are PT_UP, ET_UP, E_UP, ETA_UP and ETA_DOWN, (increasing p_T, E_T, E, eta, and decreasing eta). They have to be specified for each of the particles, separated by commas.

Examples

SELECTORS:
# two-body transverse mass
- VariableSelector:
    Variable: mT
    Flavs: [11, -12]
    Ranges:
    - [50, E_CMS]

# cut on the pT of only the hardest lepton in the event
- VariableSelector:
    Variable: PT
    Flavs: 90
    Ranges:
    - [50, E_CMS]
    Ordering: [PT_UP]

# using bool operations to restrict eta of the electron to |eta| < 1.1 or
# 1.5 < |eta| < 2.5
- VariableSelector:
    Variable: Calc(abs(Eta(p[0]))<1.1||(abs(Eta(p[0]))>1.5&&abs(Eta(p[0]))<2.5))
    Flavs: 11
    Ranges:
    - [1, 1]  # NOTE: this means true for bool operations

# requesting opposite side tag jets in VBF
- VariableSelector:
    Variable: Calc(Eta(p[0])*Eta(p[1]))
    Flavs: [93, 93]
    Ranges:
    - [-100, 0]
    Ordering: [PT_UP, PT_UP]

# restricting electron+photon mass to be outside of [87.0,97.0]
- VariableSelector:
    Variable: Calc(Mass(p[0]+p[1])<87.0||Mass(p[0]+p[1])>97.0)
    Flavs: [11, 22]
    Ranges:
    - [1, 1]

# in ``Z[lepton lepton] Z[lepton lepton]``, cut on mass of lepton-pairs
# produced from Z's
- VariableSelector:
    Variable: m
    Flavs: [90, 90]
    # here we use knowledge about the internal ordering to cut only on the
    # correct lepton pairs
    Ranges:
    - [80, 100]
    - [0, E_CMS]
    - [0, E_CMS]
    - [0, E_CMS]
    - [0, E_CMS]
    - [80, 100]

5.7.9. Minimum selector

This selector can combine several selectors to pass an event if either those passes the event. It is mainly designed to generate more inclusive samples that, for instance, include several jet finders and that allows a specification later. The syntax is

SELECTORS:
- MinSelector:
    Subselectors:
    - <selector 1>
    - <selector 2>
    ...

The Minimum selector can be used if constructed with other selectors mentioned in this section

5.8. Integration

The following parameters are used to steer the integration:

5.8.1. INTEGRATION_ERROR

Specifies the relative integration error target.

5.8.2. INTEGRATOR

Specifies the integrator. The possible integrator types depend on the matrix element generator. In general users should rely on the default value and otherwise seek the help of the authors, see Authors. Within AMEGIC++ the options AMEGIC: {INTEGRATOR: <type>, RS_INTEGRATOR: <type>} can be used to steer the behaviour of the default integrator.

• 4: building up the channels is achieved through respecting the peak structure given by the propagators. The algorithm works recursively starting from the initial state.

• 5: this is an extension of option 4. In the case of competing peaks (e.g. a Higgs boson decaying into W+W-, which further decay), additional channels are produced to account for all kinematical configurations where one of the propagating particles is produced on its mass shell.

• 6: in contrast to option 4 the algorithm now starts from the final state. The extra channels described in option 5 are produced as well. This is the default integrator if both beams are hadronic.

• 7: Same as option 4 but with tweaked exponents. Optimised for the integration of real-subtracted matrix-elements. This is the default integrator when at least one of the beams is not hadronic.

In addition, a few ME-generator independent integrators have been implemented for specific processes:

• Rambo: RAMBO [KSE86]. Generates isotropic final states.

• VHAAG: Vegas-improved HAAG integrator [vHP02].

• VHAAG_res: is an integrator for a final state of a weak boson, decaying into two particles plus two or more jets based on HAAG [vHP02]. This integrator can be further configured using VHAAG sub-settings, i.e. VHAAG: {<sub-setting>: <value>}. The following sub-settings are available. RES_KF specifies the kf-code of the weak boson, the default is W (24). RES_D1 and RES_D2 define the positions of the Boson decay products within the internal naming scheme, where 2 is the position of the first outgoing particle. The defaults are 2 and 3, respectively, which is the correct choice for all processes where the decay products are the only not strongly interacting final state particles.

5.8.3. VEGAS_MODE

Specifies the mode of the Vegas adaptive integration. 0 disables Vegas, 2 enables it (default).

5.8.4. FINISH_OPTIMIZATION

Specifies whether the full Vegas optimization is to be carried out. The two possible options are true (default) and false.

5.8.5. PSI

The sub-settings for the phase space integrator can be customised as follows:

PSI:
  <sub-setting>: <value>
  # more PSI settings ...

The following sub-settings exist:

ITMIN

The minimum number of points used for every optimisation cycle. Please note that it might be increased automatically for complicated processes.

ITMAX

The maximum number of points used for every optimisation cycle. Please note that for complicated processes the number given might be insufficient for a meaningful optimisation.

NPOWER

The power of two, by which the number of points increases with every step of the optimisation.

NOPT

The number of optimization cycles.

MAXOPT

The minimal number of integration cycles after the optimization is done.

STOPOPT

The maximal number of additional cycles in the integration performed to reach the integration error goal.

ITMIN_BY_NODE

Same as ITMIN, but specified per node to allow tuning of integration performance in large-scale MPI runs.

ITMAX_BY_NODE

Same as ITMAX, but specified per node to allow tuning of integration performance in large-scale MPI runs.

5.9. Hard decays

The handler for decays of particles produced in the hard scattering process (e.g. W, Z, top, Higgs) can be enabled and configured using the HARD_DECAYS collection of settings (and a small number of other other top-level settings). Which (anti)particles IDs should be treated as unstable is determined by the PARTICLE_DATA:<id>:Stable switch described in Models.

The syntax to configure HARD_DECAYS sub-settings is:

HARD_DECAYS:
  <sub-setting>: <value>
  # more sub-settings ...
  Channels:
    <channel id>:
      <channel sub-setting>: <value>
      # more sub-settings for <channel>
    # more channels ...

The central setting to enable the hard decays is

HARD_DECAYS:
  Enabled: true

The channel ID codes are of the form a,b,c,..., where a is the PDG ID of the decaying particle and b,c,... are the decay products. The IDs for the decay channels can also be found in the decay table printed to screen during the run.

This decay module can also be used on top of NLO matrix elements, but it does not include any NLO corrections in the decay matrix elements themselves.

Note that the decay handler is an afterburner at the event generation level. It does not affect the calculation and integration of the hard scattering matrix elements. The cross section is thus unaffected during integration, and the branching ratios (if any decay channels have been disabled) are only taken into account for the event weights and cross section output at the end of event generation (if not disabled with the HARD_DECAYS:Apply_Branching_Ratios option, cf. below). Furthermore any cuts or scale definitions are not affected by decays and operate only on the inclusively produced particles before decays.

5.9.1. Status

This sub-setting to each channel defined in HARD_DECAYS:Channels allows to explicitly force or disable a decay channel. The status can take the following values:

Status: -1

Decay channel is disabled and does not contribute to total width.

Status: 0

Decay channel is disabled but contributes to total width.

Status: 1 (default)

Decay channel is enabled.

Status: 2

Decay channel is forced.

For example, to disable the hadronic decay channels of the W boson one would use:

HARD_DECAYS:
  Channels:
    24,2,-1:  { Status: 0 }
    24,4,-3:  { Status: 0 }
    -24,-2,1: { Status: 0 }
    -24,-4,3: { Status: 0 }

In the same way, the bottom decay mode of the Higgs could be forced using:

25,5,-5:  { Status: 2 }

Note that the ordering of the decay products in <channel id> is important and has to be identical to the ordering in the decay table printed to screen. It is also possible to request multiple forced decay channels (Status: 2) for the same particle, all other channels will then automatically be disabled.

5.9.2. Width

This option allows to overwrite the calculated partial width (in GeV) of a given decay channel, and even to add new inactive channels which contribute to the total width. This is useful to adjust the branching ratios, which are used for the relative contributions of different channels and also influence the cross section during event generation, as well as the total width which is used for the lineshape of the resonance.

An example to set (/add) the partial widths of the H->ff, H->gg and H->yy channels can be seen in the following. The values have been taken from LHC Higgs WG:

PARTICLE_DATA:
  25:
    Mass: 125.09
    Width: 0.0041

HARD_DECAYS:
  Enabled: true
  Channels:
    25,5,-5:    { Width: 2.382E-03 }
    25,15,-15:  { Width: 2.565E-04 }
    25,13,-13:  { Width: 8.901E-07 }
    25,4,-4:    { Width: 1.182E-04 }
    25,3,-3:    { Width: 1E-06 }
    25,21,21:   { Width: 3.354E-04 }
    25,22,22:   { Width: 9.307E-06 }
    25,23,22:   { Width: 6.318E-06 }

Another example, setting the leptonic and hadronic decay channels of W and Z bosons to the PDG values, would be specified as follows:

HARD_DECAYS:
  Enabled: true
  Channels:
    24,2,-1:    { Width: 0.7041 }
    24,4,-3:    { Width: 0.7041 }
    24,12,-11:  { Width: 0.2256 }
    24,14,-13:  { Width: 0.2256 }
    24,16,-15:  { Width: 0.2256 }
    -24,-2,1:   { Width: 0.7041 }
    -24,-4,3:   { Width: 0.7041 }
    -24,-12,11: { Width: 0.2256 }
    -24,-14,13: { Width: 0.2256 }
    -24,-16,15: { Width: 0.2256 }
    23,1,-1:    { Width: 0.3828 }
    23,2,-2:    { Width: 0.2980 }
    23,3,-3:    { Width: 0.3828 }
    23,4,-4:    { Width: 0.2980 }
    23,5,-5:    { Width: 0.3828 }
    23,11,-11:  { Width: 0.0840 }
    23,12,-12:  { Width: 0.1663 }
    23,13,-13:  { Width: 0.0840 }
    23,14,-14:  { Width: 0.1663 }
    23,15,-15:  { Width: 0.0840 }
    23,16,-16:  { Width: 0.1663 }
    6,24,5:     { Width: 1.32 }
    -6,-24,-5:  { Width: 1.32 }

See also Use_HO_SM_Widths below for a global automatic switch to set these values.

5.9.3. Use_HO_SM_Widths

The partial decay widths (and thus BRs) calculated and used by the decay handler are only LO accurate. For SM setups, we provide pre-defined decay widths taking higher-order corrections into account. By default (HARD_DECAYS: { Use_HO_SM_Widths: true }) these will overwrite the LO widths with the values given in the Width example above.

5.9.4. Spin_Correlations

Spin correlations between the hard scattering process and the following decay processes are enabled by default. If you want to disable them, e.g. for spin correlation studies, you can specify the option Spin_Correlations: 0.

5.9.5. Store_Results

The decay table and partial widths are calculated on-the-fly during the initialization phase of Sherpa from the given model and its particles and interaction vertices. To store these results in the Results/Decays directory, one has to specify HARD_DECAYS: { Store_Results: 1 }. In case existing decay tables are to be read in the same configuration should be done. Please note, that Sherpa will delete decay channels present in the read in results but not in the present model with present parameters by default. To prevent Sherpa from updating the decay table files accordingly specify HARD_DECAYS: { Store_Results: 2 }.

5.9.6. Result_Directory

Specifies the name of the directory where the decay results are to be stored. Defaults to the value of the top-level setting RESULT_DIRECTORY.

5.9.7. Set_Widths

The decay handler computes LO partial and total decay widths and generates decays with corresponding branching fractions, independently from the particle widths specified by PARTICLE_DATA:<id>:Width. The latter are relevant only for the core process and should be set to zero for all unstable particles appearing in the core-process final state. This guarantees on-shellness and gauge invariance of the core process, and subsequent decays can be handled by the afterburner. In contrast, PARTICLE_DATA:<id>:Width should be set to the physical width when unstable particles appear (only) as intermediate states in the core process, i.e. when production and decay are handled as a full process or using Decay/DecayOS. In this case, the option HARD_DECAYS: { Set_Widths: true } permits to overwrite the PARTICLE_DATA:<id>:Width values of unstable particles by the LO widths computed by the decay handler.

5.9.8. Apply_Branching_Ratios

By default (HARD_DECAYS: { Apply_Branching_Ratios: true }), weights for events which involve a hard decay are multiplied with the corresponding branching ratios (if decay channels have been disabled). This also means that the total cross section at the end of the event generation run already includes the appropriate BR factors. If you want to disable that, e.g. because you want to multiply with your own modified BR, you can set the option {HARD_DECAYS: { Apply_Branching_Ratios: false }.

5.9.9. Mass_Smearing

With the default of HARD_DECAYS: { Mass_Smearing: 1 } the kinematic mass of the unstable propagator is distributed according to a Breit-Wigner shape a posteriori. All matrix elements are still calculated in the narrow-width approximation with onshell particles. Only the kinematics are affected. To keep all intermediate particles onshell HARD_DECAYS: { Mass_Smearing: 0 }.

5.9.10. Resolve_Decays

There are different options how to decide when a 1->2 process should be replaced by the respective 1->3 processes built from its decaying daughter particles.

Resolve_Decays: Threshold

(default) Only when the sum of decay product masses exceeds the decayer mass.

Resolve_Decays: ByWidth

As soon as the sum of 1->3 partial widths exceeds the 1->2 partial width.

Resolve_Decays: None

No 1->3 decays are taken into account.

In all cases, one can exclude the replacement of a particle below a given width threshold using Min_Prop_Width: (default 0.0). Both settings are sub-settings of HARD_DECAYS:

HARD_DECAYS:
  Resolve_Decays: <mode>
  Min_Prop_Width: <threshold>

5.9.11. Decay_Tau

By default, the tau lepton is decayed by the hadron decay module, Hadron decays, which includes not only the leptonic decay channels but also the hadronic modes. If Decay_Tau: true is specified, the tau lepton will be decayed in the hard decay handler, which only takes leptonic and partonic decay modes into account. Note, that in this case the tau needs to also be set massive:

PARTICLE_DATA:
  15:
    Massive: true
HARD_DECAYS:
  Decay_Tau: true

5.9.12. Decay table integration settings

Three parameters can be used to steer the accuracy and time consumption of the calculation of the partial widths in the decay table: Int_Accuracy: 0.01 specifies a relative accuracy for the integration. The corresponding target reference is either the given total width of the decaying particle (Int_Target_Mode: 0, default) or the calculated partial decay width (Int_Target_Mode: 1). The option Int_NIter: 2500 can be used to change the number of points per integration iteration, and thus also the minimal number of points to be used in an integration. All decay table integration settings are sub-settings of HARD_DECAYS.

5.9.13. Simulation of polarized cross sections for intermediate particles

This sections documents how Sherpa can be used to simulate polarized cross sections for unstable intermediate state particles. At the moment, only the simulation of polarized cross sections for massive vector bosons (VBs) is supported. Sherpa can simulate polarized cross sections of all possible polarization combinations in one simulation run. The polarized cross sections are handled during event generation and printed out as additional event weights similar to variation weights.

By default, the cross sections for all polarization combinations of the intermediate particles are output. In addition to that, an additional weight is added describing the totaled interference between different polarizations of the current event. For massive VBs also all transversely polarized cross sections are calculated automatically. Sherpa supports two different definitions of transversely polarized cross sections, for details see section Transversely polarized cross sections. Beside this, user-specified cross sections can be produced as described in section Custom polarized cross sections. Weight names for automatically provided cross sections have the form PolWeight_ReferenceSystem.particle1.polarization1_particle2.polarization2... with + denoting right(plus)-, - left-handed (minus) and 0 longitudinal polarization. For a right(+)-handed \(\mathrm{W}^+\) boson and left(-)-handed \(\mathrm{W}^+\) boson in \(\mathrm{W}^+\mathrm{W}^+\) scattering, the weight name becomes PolWeight_ReferenceSystem.W+.+_W+.-. The sequence of the particles in the weight name corresponds to Sherpa’s internal particle ordering which can be obtained from the ordering in the process printed out when Sherpa starts running. The ReferenceSystem denotes the reference system which needs to be specified for an unambitious polarization definition (cf. section Reference system). The totaled interference contribution is called PolWeight_ReferenceSystem.int.

Polarized cross sections in SHERPA can currently be calculated at fixed leading order, LO+PS and in merged calculations. Furthermore, polarized NLO QCD corrections on the VB production part (not on the decays) can be simulated approximately by neglecting effects of virtual corrections as well as ultra-soft and ultra-collinear contributions below the parton shower IR cut-off on polarization fractions. This is currently only possible on particle level using SHERPA’s MC@NLO implementation for matching NLO hard matrix elements to the parton shower. Note that the resulting unpolarized prediction which is also used to compute the polarized cross sections from the polarization fractions contains all NLO QCD corrections.

More details about the definition of polarization for intermediate VBs and the implementation in Sherpa than covered by this manual entry can be found in [HSchonherrS24].

5.9.13.1. General procedure

The definition of polarization for particles in intermediate states is only possible for processes which can be factorized into a production and decay of them. To neglect possible not-fully-resonant diagrams (i.e. diagrams where not each final state decay product particle comes from the decay of a resonant intermediate particle), for which this factorization and the definition of polarization for intermediate particles are not possible, Sherpa applies an extended narrow-width approximation. All intermediate particles are considered as on-shell but all spin correlations are preserved. The production part of the process is specified in the Processes part of the run card whereas the possible decays are characterized in the Hard decays section. Details about PROCESSES and HARD_DECAYS definition are described in the corresponding sections of this manual. The following example shows PROCESSES and HARD_DECAYS definition of the same-sign \(\mathrm{W}^+ \mathrm{W}^+\) scattering with the \(\mathrm{W}^+\) boson decaying to electrons or muons.

PARTICLE_DATA:
  24:
    Width: 0
  23:
    Width: 0

WIDTH_SCHEME: Fixed

HARD_DECAYS:
  Enabled: true
  Spin_Correlations: 1  # can be omitted (default)
  Mass_Smearing: 1      # can be omitted (default)
  Channels:
   24,12,-11: {Status: 2}
   24,14,-13: {Status: 2}

PROCESSES:
- 93 93 -> 24 24 93 93:
   Order: {QCD: 0, EW: 4}

Things to notice:

• In PARTICLE_DATA the Width of the intermediate particles must be set to zero since they are handled as stable for the hard process matrix element calculation. The particles are then decayed by the internal (hard) decay module. If VBs are considered as intermediate particles, the width of all VBs must be set to zero to preserve SU(2) Ward-Identities. This also holds true for processes where only one VB type participates as intermediate particle (e.g. same-sign \(\mathrm{W}^\pm \mathrm{W}^\pm\) scattering process).

• For the calculation of polarized cross sections, spin correlations between production and decay of the intermediate particles must be enabled (which is the default).

• Enabling the smearing of the mass of the intermediate VBs according to a Breit-Wigner distribution improves the applied spin-correlated narrow-width approximation by also retaining some of the off- shell effects, details cf. Hard decays section (corresponding setting can be omitted since it is the default).

• WIDTH_SCHEME is set to Fixed to be consistent with setting all VB widths to zero.

The central setting to enable the calculation of polarized cross sections is:

HARD_DECAYS:
  Pol_Cross_Section:
    Enabled: true

The polarization vectors of massive VBs are implemented according to [Dit99], equation (3.19). Specifically, the polarization vectors are expressed in terms of Weyl spinors. For that, an arbitrary light-like vector needs to be chosen. The definition of VB polarization is not unambiguous. It can be specified by the following options described in the subsequent sections: Pol_Cross_Section:Spin_Basis and Pol_Cross_Section:Reference_System.

5.9.13.2. Spin basis

For massive particles the choice of a light-like vector for their description in the Weyl spinor formalism is not really arbitrary since it characterizes the spin axis chosen to define the polarization. By default, the reference vector is selected such that polarization vectors are expressed in the helicity basis since this is the common choice for VB polarization:

HARD_DECAYS:
  Pol_Cross_Section:
    Enabled: true
    Spin_Basis: Helicity

The polarization vectors are then eigenvectors of the helicity operator and have the same form as in (3.15) in [Dit99] after transformation from spinor to vector representation. Sherpa provides several gauge choices for the Weyl spinors. To really get the polarization vectors in the described form, the following spinor gauge choice must be chosen:

COMIX_DEFAULT_GAUGE: 0

If Spin_Basis: ComixDefault is selected, the COMIX default reference vector specified by COMIX_DEFAULT_GAUGE (default 1 which corresponds to (1.0, 0.0, 1/\(\sqrt{2}\), 1/\(\sqrt{2}\))) will be used. Furthermore, it is possible to hand over any constant reference vector:

HARD_DECAYS:
  Pol_Cross_Section:
    Enabled: true
    Spin_Basis: 1.0, 0.0, 1.0, 0.0

5.9.13.3. Reference system

The helicity of a massive particle is not Lorentz invariant. Therefore, a reference system needs to be chosen to define its polarization unambiguously. Sherpa supports the following options:

Reference_System: Lab (default)

Particle polarization is defined in the laboratory frame.

Reference_System: COM

Particle polarization is defined in the center of mass system of all hard-decaying particles.

Reference_System: PPFr

Particle polarization is defined in the center of mass system of the two interacting partons.

It is possible to obtain polarized cross sections for several different polarization definitions (differing in the reference systems chosen) with a single simulation run:

HARD_DECAYS:
  Pol_Cross_Section:
    Enabled: true
    Reference_System: [Lab, COM]

Additionally to the options explained above, any reference system defined by one or several hard process initial or final state particles can be used. This can be specified by the particle numbers of the desired particles according to the Sherpa numbering scheme. Distinct particle numbers should only be separated by a single white space, at least if more than one reference system is specified. The second reference frame in the following example is the parton-parton rest frame.

HARD_DECAYS:
  Pol_Cross_Section:
    Enabled: true
    Reference_System: [Lab, 0 1]

In the Sherpa event output, polarized cross sections of VBs defined in different frames are distinguished by adding the corresponding reference frame keyword to the weight names, e.g. PolWeight_Lab.W+.+_W+.-. For reference systems defined by particle numbers, refsystemn is added to avoid commas in weight names. n is the place in the reference system list specified in the YAML-File starting at 0. For the example above, this means e.g. PolWeight_refsystem1.W+.+_W+.-.

5.9.13.4. Transversely polarized cross sections

If some of the intermediate particles are VBs, also transversely polarized cross sections are output per default. Sherpa provides two different definitions of transversely polarized cross sections which can be selected by Transverse_Weights_Mode:

Transverse_Weights_Mode: 0

Transversely polarized cross sections result from adding the left(-)- and right(+)-handed polarized contribution (= incoherent definition). Transverse polarized particles are characterized by a small t in corresponding weight names.

Transverse_Weights_Mode: 1 (default)

Transversely polarized cross sections result from adding the left(-)- and right(+)-handed polarized contribution as well as left-right interference terms (= coherent definition). Transverse polarized particles are characterized by a capital T in corresponding weight names. If this definition of the transverse polarized signals is chosen also a new interference weight is added containing the interference terms which are not in included in one of the transverse polarized weights. To distinguish it from the original interference weight, it is referred to as PolWeight_ReferenceSystem.coint.

Transverse_Weights_Mode: 2

Both, incoherently and coherently defined transverse polarized cross sections are simulated.

5.9.13.5. Custom polarized cross sections

Sherpa provides the calculation of two different types of custom polarized cross sections. On the one hand, it is possible to specify a comma separated list of weight names from the automatically calculated cross sections. Corresponding cross sections are then added by Sherpa and printed out as additional event weights. On the other hand, partially unpolarized cross sections can be calculated. Those can be specified by the numbers of the particles which should be considered as unpolarized in the run card. Again, the numbering of the particles follows the Sherpa numbering scheme. Noteworthy, the partially unpolarized cross sections also contain contributions from terms describing the interference between different polarizations of the unpolarized intermediate particles. Therefore, an additional interference weight is added to the output describing the sum of the remaining interference contributions. If particles remaining polarized are massive VBs, Sherpa also output transversely polarized cross sections for the partially unpolarized cross sections.

Custom weights are generally specified by the option Weight in the run card. By adding numbers to Weight e.g. Weight1, Weight2 … more than one custom cross section can be calculated. The number is limited to Weight10 by default but can be increased by using Number_Of_Custom_Weights. In the following example, the \(\mathrm{W}^-\) boson is considered as unpolarized, Weight1 shows an example for how to specify polarized cross sections which should be added to a new weight. The result here would be the same as W+.t_W-.0.

HARD_DECAYS:
 Enabled: true
 Mass_Smearing: 1
 Channels:
  24,12,-11: {Status: 2}
  -24,-14,13: {Status: 2}
 Pol_Cross_Section:
   Enabled: true
   Weight1: W+.+_W-.0, W+.-_W-.0
   Weight2: 3

PROCESSES:
 - 93 93 -> 24 -24 93 93:
   Order: {QCD: 0, EW: 4}

The weight naming pattern is adjusted for custom polarized cross sections. The polarization of the unpolarized particles in the weight names is set to U and their spin labels are moved to the beginning of the weight name. If more than one intermediate particle is considered as unpolarized, the particle ordering among the unpolarized particles is preserved. The weight name is then prefixed by the name of the custom weight as specified in the run card. Thus, for the single-polarized cross section of a right-handed \(\mathrm{W}^+\) boson in opposite sign \(\mathrm{W}^+\mathrm{W}^-\) production with polarization defined in the laboratory frame (named Weight2 in the example run card above), the final weight name becomes PolWeight_Lab.Weight1_W-.U_W+.+. For custom cross sections specified by weight names (e.g. Weight1 in the example above), PolWeight_refsystem.Weightn is used instead to avoid long weight names. Hereby, Weightn corresponds to the corresponding setting in the run card.

The weight name syntax can also be used if a single or a sum of certain interference terms are of interest. Interference weight names have two instead of one polarization index per particle (first index stands for the polarization of the particle in the corresponding matrix element, the second index for its polarization in the complex conjugate matrix element). The example below is an excerpt of a run card for the simulation of polarized cross sections for single \(\mathrm{W}^+\) boson production in association with one jet at LO; Weight1 and Weight2 illustrate how single interference cross sections (Weight2) or a sum of selected ones (Weight1) can be printed out. Weight1 leads to the same result as W+.T (coherent transverse polarization definition) which is calculated automatically if Transverse_Weights_Mode: 1 or Transverse_Weights_Mode: 2.

HARD_DECAYS:
 Enabled: true
 Channels:
  24,12,-11: {Status: 2}
 Pol_Cross_Section:
   Enabled: true
   Weight1: W+.++, W+.+-, W+.-+, W+.--
   Weight2: W+.0+

PROCESSES:
 - 93 93 -> 24 93:
   Order: {QCD: 1, EW: 1}

5.10. Parton showers

The following parameters are used to steer the shower setup.

5.10.1. SHOWER_GENERATOR

There are two shower generators in Sherpa, Dire (default) and CSS. See the module summaries in Basic structure for details about these showers.

Other shower modules are in principle supported and more choices will be provided by Sherpa in the near future. To list all available shower modules, the tag SHOW_SHOWER_GENERATORS: 1 can be specified on the command line.

SHOWER_GENERATOR: None switches parton showering off completely. However, even in the case of strict fixed order calculations, this might not be the desired behaviour as, for example, then neither the METS scale setter, cf. SCALES, nor Sudakov rejection weights can be employed. To circumvent when using the Dire or CS Shower see Sherpa Shower options.

5.10.2. JET_CRITERION

This option uses the value for SHOWER_GENERATOR as its default. Correspondingly, the only natively supported options in Sherpa are CSS and Dire. The corresponding jet criterion is described in [HKSS09]. A custom jet criterion, tailored to a specific experimental analysis, can be supplied using Sherpa’s plugin mechanism.

5.10.3. MASSIVE_PS

This option instructs Sherpa to treat certain partons as massive in the shower, which have been considered massless by the matrix element. The argument is a list of parton flavours, for example MASSIVE_PS: [4, 5], if both c- and b-quarks are to be treated as massive.

5.10.4. MASSLESS_PS

When hard decays are used, Sherpa treats all flavours as massive in the parton shower. This option instructs Sherpa to treat certain partons as massless in the shower nonetheless. The argument is a list of parton flavours, for example MASSLESS_PS: [1, 2, 3], if u-, d- and s-quarks are to be treated as massless.

5.10.5. Sherpa Shower options

Sherpa’s default shower module is based on [SK08b]. A new ordering parameter for initial state splitters was introduced in [HKSS09] and a novel recoil strategy for initial state splittings was proposed in [HSS10]. While the ordering variable is fixed, the recoil strategy for dipoles with initial-state emitter and final-state spectator can be changed for systematics studies. Setting SHOWER:KIN_SCHEME: 0 corresponds to using the recoil scheme proposed in [HSS10], while SHOWER:KIN_SCHEME: 1 (default) enables the original recoil strategy. The lower cutoff of the shower evolution can be set via SHOWER:FS_PT2MIN and SHOWER:IS_PT2MIN for final and initial state shower, respectively. Note that this value is specified in GeV^2. Scale factors for the evaluation of the strong coupling in the parton shower are given by SHOWER:FS_AS_FAC and SHOWER:IS_AS_FAC. They multiply the ordering parameter, which is given in units of GeV^2.

Setting SHOWER:MAXEM: forces the CS Shower to truncate its evolution at the Nth emission. Note that in this case not all of the Sudakov weights might be computed correctly. On the other hand, the use of CS Shower in the METS scale setter is not affected, cf. SCALES.

The parton shower coupling scales, PDF scales and PDF themselves can be varied on-the-fly, along with the on-the-fly variations of the corresponding matrix element parameters. See On-the-fly event weight variations to find out how specify the variations and enable them in the shower.

Most parton showers available in Sherpa allow the same options. These options are specified as follows:

SHOWER:
  KIN_SCHEME: <scheme>
  IS_AS_FAC: <factor>
  # other shower settings ...

When the parton shower is used for MC@NLO matching, the options can be set differently. They are then specified as follows:

MC@NLO:
  IS_AS_FAC: <factor>
  # other shower settings ...

5.10.6. CS Shower options

By default, only QCD splitting functions are enabled in the CS shower. If you also want to allow for photon splittings, you can enable them by using SHOWER:EW_MODE: true. Note, that if you have leptons in your matrix-element final state, they are by default treated by a soft photon resummation as explained in QED corrections. To avoid double counting, this has to be disabled as explained in that section.

The evolution variable of the CS shower can be changed using SHOWER:EVOLUTION_SCHEME. Several options are currently implemented:

0

transverse momentum ordering

1

modified transverse momentum ordering.

2

like 0 but parton masses taken into account

3

like 1 but parton masses taken into account

20

like 0 but parton masses taken into account only for g->QQ

30

like 1 but parton masses taken into account only for g->QQ

The scale can be set differently for final- and initial-state shower. The two values are combined as FS+100*IS, where FS is the choice for the final state, and IS is the choice for the initial state. The scale at which the strong coupling for shower splittings is evaluated can be chosen with SHOWER:SCALE_SCHEME:

The default is to evaluate the strong coupling at the transverse momentum in the parton splitting. Gluon splittings into quarks in the final state are evaluated at the virtuality of the gluon, as are branchings into a soft t-channel gluon in the initial state. Options are additive.

0

default

1

evaluate final-state gluon splitting into quarks at the transverse momentum

2

evaluate initial-state quark to gluon splittings at the transverse momentum

20

evaluate initial-state gluon splitting into soft t-channel gluons at the transverse momentum

Additionally, the CS shower allows to disable splittings at scales below the on-shell mass of heavy quarks. The upper limit for the corresponding heavy quark mass is set using SHOWER:MASS_THRESHOLD.

Likewise, by default the CS shower forces heavy quarks to be produced from gluon splittings below their mass threshold. This behaviour can be steered using SHOWER:FORCED_IS_QUARK_SPLITTING. Its precise kinematics are governed by SHOWER:FORCED_SPLITTING_GLUON_SCALING.

5.11. Multiple interactions

The basic MPI model is described in [SvZ87] while Sherpa’s implementation details are discussed in [A+a].

The following parameters are used to steer the MPI setup:

5.11.1. MI_HANDLER

Specifies the MPI handler. The two possible values at the moment are None and Amisic.

5.11.2. AMISIC

Amisic can simulate the interaction of three different combinations of incoming particles: proton–proton, photon–proton and photon–photon collision. The parameters for the simulation of photonic multiple interactions can be found in [SS94]. It has several parameters to control the simulation of the multiple-parton interactions, they are listed below. Each of these parameters has to be set in the subsetting AMISIC, like so

AMISIC:
  PT_0: 2.5

The usual rules for yaml structure apply, c.f. Input structure.

PT_0(ref)

Value \(p_\text{T,0}^\text{(ref)}\) for the calculation of the IR regulator, see formula below. Defaults to 2.05.

PT_0(IR)

The absolute minimum of the IR regulator, see formula below. Defaults to 0.5.

PT_Min(ref)

Value \(p_\text{T,min}^\text{(ref)}\) for the calculation of the IR cutoff, see formula below. Defaults to 2.25.

Eta

The pseudorapidity \(\eta\) used to calculate the IR cutoff and regulator, \(p_\text{T,min}\) and \(p_\text{T,0}\). Defaults to 0.16.

E(ref)

Reference energy to normalise the actual cms energy for the calculation of the IR cutoff and regulator. Defaults to 7000.

PT_Min

The IR cut-off for the 2->2 scatters. It is calculated as

\[p_\text{T,min} = p_\text{T,min}^\text{(ref)} \left( \frac{E_\text{cms}}{E_\text{cms}^\text{(ref)}} \right)^{2\eta}\]

but can also be set explicitly.

PT_0

IR regulator \(p_\text{T,0}\) in the propagator and in the strong coupling. It is calculated as

\[p_\text{T,0} = p_\text{T,0}^\text{(ref)} \left( \frac{E_\text{cms}}{E_\text{cms}^\text{(ref)}} \right)^{2\eta}\]

but can also be set explicitly.

MU_R_SCHEME

Defaults to PT scheme. More schemes have yet to be added.

MU_R_FACTOR

Factor to scale the renormalisation scale \(\mu_R\), defaults to 0.5.

MU_F_FACTOR

Factor to scale the factorisation scale \(\mu_F\), defaults to 1.0.

SIGMA_ND_NORM

Specifies the factor to scale the non-diffractive cross section calculated in the MPI initialisation. Defaults to 1.02.

nPT_bins

Controls the number of bins for the numerical integration of

\[\int_{p_T^2}^{s/4} dp_T^2 \frac{d \sigma}{dp_T^2}\]

Defaults to 200.

nMC_points

Number of points to estimate the the cross-section during the integration. The error should behave as \(\frac{1}{\sqrt{n_\text{MC}}}\). Defaults to 1000.

nS_bins

Number of points to sample in the center-of-mass energy \(\sqrt{s}\). This is only used if the energy is not fixed, i.e. in the case of EPA photons. Defaults to 40.

The total cross-section is calculated with

\[\sigma_{tot} = X s^\epsilon + Y s^\eta\]

where \(s\) is the Mandelstam invariant.

PomeronIntercept

The parameter \(\epsilon\) in the above equation, defaults to 0.0808.

ReggeonIntercept

The parameter \(\eta\) in the above equation, defaults to -0.4525.

The single- and double-diffractive cross-sections in the Regge picture have two free parameters:

PomeronSlope

The parameter \(\alpha^\prime\), default is 0.25.

TriplePomeronCoupling

The parameter \(g_{3\mathbb{P}}\) at an input scale of 20 GeV, given in \(\text{mb}^{-0.5}\), with default 0.318.

5.11.3. MI ISR parameters

The following two parameters can be used to overwrite the ISR parameters in the context of multiple interactions: MPI_PDF_SET, MPI_PDF_SET_VERSIONS.

5.12. Beam Remnants

Details for the handling of the beam remnants in Sherpa will be described in our forthcoming publication.

Broadly speaking, the beam remnants include the parameterisation of the form factors for hadrons or the hadronic components of photons and the treatment of the beam break-up, most importantly the intrinsic transverse momentum distribution of the partons and how the recoils are distributed.

The following parameters are used to steer the beam remnant handling:

5.12.1. BEAM_REMNANTS

Specifies whether beam remnants are taken into account, with possible values ‘On’ and ‘Off’.

5.12.2. REMNANTS

Sherpa organises the remnant handling by particle, with the PDG code as tag-line.

REMNANTS:
  2212:
    KT_Form: Gauss_limited

The usual rules for yaml structure apply, c.f. Input structure. Longitudinal momenta for sea partons in hadrons are distributed according to a probability distribution in their light-cone momentum \(x\) given by \(P(x)=x^{-1.5}\). If there are two valence partons left in the beam remnant after the shower initiators have been treated, the first of the two (usually the quark) will have a longitudinal momentum with \(P(x)=\exp(-1/x)\), while the last remaining valence parton (usually the di-quark for nucleons) carries the remaining longitudinal momentum.

For the intrinsic transverse momentum, Sherpa differentiates between the transverse momentum for shower initiators (SHOWER_INITIATOR_MEAN etc.) and for beam spectators (BEAM_SPECTATOR_MEAN etc.), and it offers different strategies to compensate the transverse momentum between the two sets of partons per beam, see below (KT_RECOIL).

KT_FORM (default: Gauss_Limited)

This parameter specifies the scheme to calculate the intrinsic transverse momentum of partons within beams. Available options are:

• Gauss: a simple Gaussian with mean and width;

• Dipole: a dipole form parameterised by \(Q^2\);

• Gauss_Limited, dipole_Limited: as above but further modified by a polynomial function of the form \(1-(k_{T}/k_{T,\rm{max}})^\eta\), where \(k_{T,\rm{max}}\) and \(\eta\) are given by the KTMAX and KTEXPO tags;

• None: no intrinsic transverse momentum is assigned.

KT_RECOIL (default: Beam_vs_Shower)

Transverse momenta for all partons inside the beam are generated independently from each other according to the form and parameterisation specified for them in KT_FORM and SHOWER_INITIATOR_MEAN etc., or BEAM_SPECTATOR_MEAN etc.. This will lead to a net residual transverse momentum of partons that needs to be compensated within the beams, to guarantee that the remnants do not create a total beam transverse momentum. Sherpa has implemented two strategies to achieve this:

• Democratic: the overall residual transverse momentum is distributed over all partons in the beam according to their energies.

• Beam_vs_Shower: the residual transverse momentum of all spectators is distributed over the shower initiators according to their energies and vice versa.

SHOWER_INITIATOR_MEAN (default for nucleons: 1.0)

This parameter specifies the mean in GeV for the intrinsic transverse momentum in case of a limited or unlimited Gaussian distribution.

BEAM_SPECTATOR_MEAN   (default for nucleons: 0.0)

Same as for SHOWER_INITIATOR_MEAN.

SHOWER_INITIATOR_SIGMA (default for nucleons: 1.1)

This parameter specifies the sigma in GeV for the intrinsic transverse momentum in case of a limited or unlimited Gaussian distribution.

BEAM_SPECTATOR_SIGMA   (default for nucleons: 0.25)

Same as for SHOWER_INITIATOR_SIGMA.

SHOWER_INITIATOR_Q2 (default for nucleons: 1.1)

This parameter specifies the \(Q^2\) in \({\rm GeV}^2\) of the limited or unlimited dipole distribution for the intrinsic transverse momentum.

BEAM_SPECTATOR_Q2   (default for nucleons: 0.25)

Same as for SHOWER_INITIATOR_Q2.

SHOWER_INITIATOR_KTMAX (default for nucleons: 2.7)

This parameter specifies the \(k_{T,\rm{max}}\) in \({\rm GeV}\) of the limited dipole or Gaussian distributions for the intrinsic transverse momentum.

BEAM_SPECTATOR_KTMAX   (default for nucleons: 1.0)

Same as for SHOWER_INITIATOR_KTMAX.

SHOWER_INITIATOR_KTEXPO (default for nucleons: 5.12)

This parameter specifies the \(\eta\) in the equation above that limits the intrinsic transverse momentum distribution.

BEAM_SPECTATOR_KTEXPO   (default for nucleons: 5.0)

Same as for SHOWER_INITIATOR_KTEXPO.

REFERENCE_ENERGY (default: 7000)

This parameter specifies the reference scale in GeV in the energy extrapolation of the mean and width of the Gaussian distribution and of the \(Q^2\) of the dipole distribution of intrinsic transverse momentum, and of the maximally allowed \(k_T\) in the case of limited distributions.

ENERGY_SCALING_EXPO (default: 0.08)

This parameter specifies the energy extrapolation exponent.

MATTER_FORM (default: Single_Gaussian)

Double_Gaussian can be used to model the overlap between the colliding particles. None switches this off.

MATTER_RADIUS1 (default for nucleons: 0.86, for mesons/photons: 0.75)

The radius of the (inner) Gaussian in fm. If used with the double-Gaussian matter form, this value must be smaller than MATTER_RADIUS2.

MATTER_FRACTION1

Only to be used for double-Gaussian matter form, where it will control the distribution of matter over the two Gaussians. It assumes that a fraction \(f^2\) is distributed by the inner Gaussian \(r_1\), another fraction \((1-f)^2\) is distributed by the outer Gaussian \(r_2\), and the remaining fraction \(2f(1-f)\) is distributed by the combined radius \(r_\text{tot} = \sqrt{\frac{r_1^2+r_2^2}{2}}\). Defaults to 0.5.

MATTER_RADIUS2

Defaults to 1.0. It is only used for the case of a double-Gaussian overlap, see below.

If the option BEAM_REMNANTS: false is specified at top level, pure parton-level events are simulated, i.e. no beam remnants are generated. Accordingly, partons entering the hard scattering process do not acquire primordial transverse momentum.

5.13. Colour_Reconnections

The colour reconnections setup covers the non-perturbative reshuffling of parton colours before the partons fragment into primordial hadrons. In the current implementation Sherpa collects all \(N\) colourful partons entering colour reconnections and probes \(N^2\) pairs of colour connections between two partons \(i\) and \(j\). Their Lund-inspired distance in phase space is given by \(d_{ij} = p_ip_j-m_im_j\), where the gluon momenta are divided equally between both colours they carry.

The reshuffling of colour from old pairings \(\langle ij\rangle\) and \(\langle kl\rangle\) to new pairings \(\langle il\rangle\) and \(\langle kj\rangle\) is decided probabilistically, with

\(P(\langle ij\rangle\langle kl\rangle\to\langle il\rangle\langle kj\rangle) = R\cdot \left\{1-\exp[-\eta_Q(D_{ij}+D_{kl}-D_{il}-D_{kj})]\right\}\).

For a power-law in the definition of the \(D_{ij}\) we also calculate the average length of all colour connections \(ij\) as \(\langle D_{ij}\rangle = \frac{1}{N}\sum_{ij}d_{ij}^\kappa\).

COLOUR_RECONNECTIONS:
  MODE:      On
  PMODE:     Log
  Q_0:       1.
  RESHUFFLE: 0.11

MODE (default: )

Switches the colour reconnections on or off.

PMODE (default: log)

This switch defines how the distances of two partons in colour space are being calculated. Available options define the distances \(D_{ij}\) used in the decision whether colours are reshuffled as follows:

• Log: \(D_{ij} = \log(1+d_{ij}/Q_0^2)\)

• Power: \(D_{ij} = \frac{d_{ij}^\kappa}{\langle D_{ij}\rangle}\)

Q_0 (default: 1.)

\(Q_0\) in the logarithmic version of the momentum-space distance.

ETA_Q (default: 0.1)

\(\eta_Q\) in the probability above.

RESHUFFLE (default: 1/9)

The colour suppression factor \(R\) in the probability above.

KAPPA (default: 1.)

The exponent \(\kappa\) in the equations above.

5.14. Hadronization

The hadronisation setup covers the fragmentation of partons into primordial hadrons as well as the decays of unstable hadrons into stable final states.

5.14.1. Fragmentation

5.14.1.1. Fragmentation models

The FRAGMENTATION parameter sets the fragmentation module to be employed during event generation.

• The default is Ahadic, enabling Sherpa’s native hadronisation model AHADIC++ [CK22], based on the cluster fragmentation model introduced in [FW83], [Web84], [GM87], and [MW88].

• The hadronisation can be disabled with the value None.

• To evaluate uncertainties stemming from the hadronisation, Sherpa also provides an interface to the Lund string fragmentation in Pythia 8.3 [B+22] by using the setting Pythia8. In this case, the standard Pythia settings can be used to steer the behaviour of the Lund string, see [B+22]. They are specified in their usual form in Pythia in a dedicated settings block. Additionally a choice can be made to let Pythia directly handle hadron decays via the DECAYS setting (separate from the Model switch mentioned below) and whether Pythias or Sherpas default masses and widths should be used through the SHERPA_MASSES setting. By default the choice of generator for the masses and widths setting aligns with the decay setting.

SHERPA_LDADD: SherpaPythia
FRAGMENTATION: Pythia8
PYTHIA8:
  PARAMETERS:
    - StringZ:aLund: 0.68
    - StringZ:bLund: 0.98
      ...
  DECAYS: true
  SHERPA_MASSES: false

5.14.1.2. Hadron constituents

The constituent masses of the quarks and diquarks are given by

• M_UP_DOWN (0.3 GeV),

• M_STRANGE (0.4 GeV),

• M_CHARM (1.8 GeV), and

• M_BOTTOM (5.1 GeV).

The diquark masses are composed of the quark masses and some additional parameters,

with

• M_DIQUARK_OFFSET (0.3 GeV),

• M_BIND_0 (0.12 GeV), and

• M_BIND_1 (0.5 GeV).

Like all settings related to cluster fragmentation these are grouped under AHADIC.

AHADIC:
  - M_UP_DOWN: 0.3
    ...
  - M_DIQUARK_OFFSET: 0.3

5.14.1.3. Hadron multiplets

For the selection of hadrons emerging in such cluster transitions and decays, an overlap between the cluster flavour content and the flavour part of the hadronic wave function is formed. This may be further modified by production probabilities, organised by multiplet and given by the parameters

• MULTI_WEIGHT_R0L0_PSEUDOSCALARS (default 1.0),

• MULTI_WEIGHT_R0L0_VECTORS (default 1.0),

• MULTI_WEIGHT_R0L0_TENSORS2 (default 0.75),

• MULTI_WEIGHT_R0L1_SCALARS (default 0.0),

• MULTI_WEIGHT_R0L1_AXIALVECTORS (default 0.0),

• MULTI_WEIGHT_R0L2_VECTORS (default 0.0),

• MULTI_WEIGHT_R0L0_N_1/2 (default 1.0),

• MULTI_WEIGHT_R1L0_N_1/2 (default 0.0),

• MULTI_WEIGHT_R2L0_N_1/2 (default 0.0),

• MULTI_WEIGHT_R1_1L0_N_1/2 (default 0.0),

• MULTI_WEIGHT_R0L0_DELTA_3/2 (default 0.25),

In addition, there is a suppression factors applied to meson singlets,

• SINGLET_SUPPRESSION (default 1.0).

For the latter, Sherpa also allows to redefine the mixing angles through parameters such as

• Mixing_0+ (default -14.1/180*M_PI),

• Mixing_1- (default 36.4/180*M_PI),

• Mixing_2+ (default 27.0/180*M_PI),

• Mixing_3- (default 0.5411),

• Mixing_4+ (default 0.6283),

And finally, some modifiers are applied to individual hadrons:

• ETA_MODIFIER (default 0.12),

• ETA_PRIME_MODIFIER (default 1.0),

5.14.1.4. Cluster transition to hadrons - flavour part

The phase space effects due to these masses govern to a large extent the flavour content of the non-perturbative gluon splittings at the end of the parton shower and in the decay of clusters. They are further modified by relative probabilities with respect to the production of up/down flavours through the parameters

• STRANGE_FRACTION (default 0.42),

• BARYON_FRACTION (default 1.0),

• CHARM_BARYON_MODIFIER (default 1.0),

• BEAUTY_BARYON_MODIFIER (default 1.0),

• P_{QS/P_{QQ}} (default 0.2),

• P_{SS/P_{QQ}} (default 0.04), and

• P_{QQ_1/P_{QQ_0}} (default 0.20).

The transition of clusters to hadrons is governed by the following considerations:

• Clusters can be interpreted as excited hadrons, with a continuous mass spectrum.

• When a cluster becomes sufficiently light such that its mass is below the largest mass of any hadron with the same flavour content, it must be re-interpreted as such a hadron. In this case it will be shifted on the corresponding hadron mass, and the recoil will be distributed to the “neighbouring” clusters or by emitting a soft photon. This comparison of masses clearly depends on the multiplets switched on in AHADIC++.

• In addition, clusters may becomes sufficiently light such that they should decay directly into two hadrons instead of two clusters. This decision is based on the heaviest hadrons accessible in a decay, modulated by another offset parameter,

  • DECAY_THRESHOLD (default 500 MeV).

• If both options, transition and decay, are available, there is a competition between

5.14.1.5. Cluster transition and decay weights

The probability for a cluster C to be transformed into a hadron H is given by a combination of weights, obtained from the overlap with the flavour part of the hadronic wave function, the relative weight of the corresponding multiplet and a kinematic weight taking into account the mass difference of cluster and hadron and the width of the latter.

For the direct decay of a cluster into two hadrons the overlaps with the wave functions of all hadrons, their respective multiplet suppression weights, the flavour weight for the creation of the new flavour q and a kinematical factor are relevant. Here, yet another tuning parameter enters,

• MASS_EXPONENT (default 4.0)

which partially compensates phase space effects favouring light hadrons,

5.14.1.6. Cluster decays - kinematics

Cluster decays are generated by firstly emitting a non-perturbative “gluon” from one of the quarks, using a transverse momentum distribution as in the non-perturbative gluon decays, see below, and by then splitting this gluon into a quark–antiquark of anti-diquark–diquark pair, again with the same kinematics. In the first of these splittings, the emission of the gluon, though, the energy distribution of the gluon is given by the quark splitting function, if this quark has been produced in the perturbative phase of the event. If, in contrast, the quark stems from a cluster decay, the energy of the gluon is selected according to a flat distribution.

In clusters decaying to hadrons, the transverse momentum is chosen according to a distribution given by an infrared-continued strong coupling and a term inversely proportional to the infrared-modified transverse momentum,

constrained to be below a maximal transverse momentum.

5.14.1.7. Splitting kinematics

In each splitting, the kinematics is given by the transverse momentum, the energy splitting parameter and the azimuthal angle. The latter, the azimuthal angle is always selected according to a flat distribution, while the energy splitting parameter will either be chosen according to the quark-to-gluon splitting function (if the quark is a leading quark, i.e. produced in the perturbative phase), to the gluon-to-quark splitting function, or according to a flat distribution. The transverse momentum is given by the same distribution as in the cluster decays to hadrons.

5.14.2. Hadron decays

The treatment of hadron and tau decays is steered by the parameters in a block named HADRON_DECAYS, e.g.

HADRON_DECAYS:
  Model: HADRONS++
  Max_Proper_Lifetime: 10.0
  QED_Corrections: 1

• Hadron properties like mass, width, and active can be set in full analogy to the settings for fundamental particles using PARTICLE_DATA, cf. Models.

• Max_Proper_Lifetime: [mm] (default: 10.0) Parameter for maximum proper lifetime (in mm) up to which hadrons are considered unstable. This will make long-living particles stable, even if they are set unstable by default or by the user. If you do not want to set this globally, set this to a value of -1 and steer the stability through PARTICLE_DATA:<id>:Stable, cf. Models.

• QED_Corrections: [0,1] (default: 1) Whether to dress hadron decays with QED corrections.

• Model: [HADRONS++, Off] (default: HADRONS++) It defaults to Hadrons to employ Sherpa’s built-in hadron decay module HADRONS++ described below. Another option is to use the hadron decays from Pythia8 directly in the corresponding hadronisation interface, cf. Fragmentation above. To disable hadron decays completely, it can be disabled with the option Off.

HADRONS++ is the built-in module within the Sherpa framework which is responsible for treating hadron and tau decays. It contains decay tables with branching ratios for approximately 2500 decay channels, of which many have their kinematics modelled according to a matrix element with corresponding form factors. Especially decays of the tau lepton and heavy mesons have form factor models similar to dedicated codes like Tauola [JWDK93] and EvtGen [Lan01].

Its settings are also steered within the HADRON_DECAYS block as follows:

• Mass_Smearing: [0,1,2] (default: 1) Determines whether particles entering the hadron decay event phase should be put off-shell according to their mass distribution. It is taken care that no decay mode is suppressed by a potentially too low mass. HADRONS++ determines this dynamically from the chosen decay channel. Choosing option 2 instead of 1 will only set unstable (decayed) particles off-shell, but leave stable particles on-shell.

• Spin_Correlations: [0,1] (default: 0) A spin correlation algorithm is implemented and can be switched on with this setting. This might slow down event generation slightly.

• Channels: Many aspects of the decay tables and individual decay channels can be adjusted within this sub-block. The default settings of the Sherpa hadron decay data can be found in <prefix>/share/SHERPA-MC/Decaydata.yaml and can be overwritten individually in the run card, e.g. as follows:

  HADRON_DECAYS:
    Channels:
      111:
        22,22:
          BR: [0.98823, 0.00034]
          Origin: PDG2023
      15:
        16,-12,11:
          BR: [0.1782, 0.0004]
          Status: [1, 2, 1]
  

  The levels are structured first by decaying particle and then by decay products. For each decay channel the following settings are available:

  • BR: [<br>, <deltabr>] branching ratio and its uncertainty

  • Origin: <...> origin of BR for documentation purposes

  • Status: TODO

  • ME: lists the matrix elements used for the decay kinematics and the permutation that maps the external momenta of the decay into the internal convention in the ME implementation. Additionally, parameters for the ME calculation can be specified. Example:

    HADRON_DECAYS:
      Channels:
        521:
          321,11,-11:
            BR: [5.5e-07, 7e-08]
            Origin: PDG
            ME:
              - B_K_Semileptonic[0,1,2,3]:
                  Factor: [1.0, 0.0]
                  LD: 0
                  C1: -0.248
                  C2: 1.107
                  C3: 0.011
                  C4: -0.026
                  C5: 0.007
                  C6: -0.031
                  C7eff: -0.313
                  C9: 4.344
                  C10: -4.669
    

    If no ME information is specified, Sherpa will fall back to a generic matrix element based on the spins of the external particles.

    One special type of ME used very often is Current_ME which corresponds to the contraction of two (V-A) currents that then have to be specified separately and can contain form factors etc. This structure allows to combine known currents flexibly without needing to implement a dedicated ME for each of these decays. Examples are semileptonic B/D-decays which can contain a leptonic current and a hadronic one or tau decays which can contain either two leptonic currents or also one hadronic one. Syntax example:

    HADRON_DECAYS:
      Channels:
        521:
          -423,12,-11:
            BR: [0.0558, 0.0022]
            Origin: PDG2022
            ME:
              - Current_ME:
                  J1:
                    Type: VA_F_F
                    Indices: [2,3]
                  J2:
                    Type: VA_P_V
                    Indices: [0,1]
                    FORM_FACTOR: 3
    
          -411,211,12,-11:
            BR: [0.0002, 0.0002]
            Origin: FS
            ME:
              - Current_ME:
                  J1:
                    Type: VA_F_F
                    Indices: [3,4]
                  J2:
                    Type: VA_B_DPi
                    Indices: [0,1,2]
                    Vxx: 0.04
    

  • PhaseSpace lists the phase-space mappings and optionally their (relative) weights. Example:

    PhaseSpace:
      - TwoResonances_a(1)(1260)+_2_rho(770)+_13:
          Weight: 0.5
      - TwoResonances_a(1)(1260)+_3_rho(770)+_12:
          Weight: 0.5
    

  • CPAsymmetryS: For CP violation in the interference between mixing and decay, cf. below.

  • CPAsymmetryC: For CP violation in the interference between mixing and decay, cf. below.

  • IntResults: This line stores the results from the phase space integration of the decay channel (width, MC uncertainty, maximum for unweighting). If they are missing, HADRONS++ integrates this channel during the initialization.

    Consequently, if some parameters are changed (also masses of incoming and outgoing particles) the maximum might change such that a new integration is needed in order to obtain correct kinematical distributions. In this case the IntResults line should be removed and replaced by the new one printed out to screen after integration.

• Constants Some globally used constants

• Aliases Create alias particles, e.g. to enforce specific decay chains. Example:

  HADRON_DECAYS:
    Aliases:
      999521: 521
  
    Channels:
      300553:
        999521,-999521:
          BR: 0.5
          [...]
        511,-511:
          BR: 0.5
          [...]
  
      999521:
        -423,12,-11:
          BR: [0.0558, 0.0022]
          Status: 2
          [...]
  

• Mixing: This block contains globally needed parameters for neutral meson mixing. Setting Mixing_<...> = 1 enables explicit mixing in the event record according to the time evolution of the flavour states. The Interference_X = 1 switch would enable rate asymmetries due to CP violation in the interference between mixing and decay (cf. CPAsymmetry settings below). By default, the mixing parameters are set to the following values:

  HADRON_DECAYS:
    Mixing:
      Mixing_D: 1
      Interference_D: 0
      x_D: 0.0032
      y_D: 0.0069
      qoverp2_D: 1.0
  
      Mixing_B: 1
      Interference_B: 0
      x_B: 0.770
      y_B: 0.0
      qoverp2_B: 1.0
  
      Mixing_B(s): 1
      Interference_B(s): 0
      x_B(s): 26.72
      y_B(s): 0.130
      qoverp2_B(s): 1.0
  

  If one wants to include time dependent CP asymmetries through interference between mixing and decay one can set the coefficients of the cos and sin terms respectively for each decay channel as described above (CPAsymmetryS/C). HADRONS++ will then respect these asymmetries between particle and anti-particle in the choice of decay channels.

• Partonics Some partonic decay tables (for c and b) that will be used to complement the decay table of hadrons if they don’t contain 100% BR and have spectators specified in their own setup like:

  521:
    Spectators: [ 2: { Weight: 1.0 } ]
  

• CreateBooklet: true to create a Latex booklet of all decay channels read in.

5.15. QED corrections

Higher order QED corrections are effected both on hard interaction and, upon their formation, on each hadron’s subsequent decay. The Photons [SK08a] module is called in both cases for this task. It employes a YFS-type resummation [YFS61] of all infrared singular terms to all orders and is equipped with complete first order corrections for the most relevant cases (all other ones receive approximate real emission corrections built up by Catani-Seymour splitting kernels). The module is also equipped with an algorithm to allow any photons produced to split into charged particle pairs.

5.15.1. General Switches

The relevant switches to steer the higher order QED corrections are collected in the YFS settings group and are modified like this:

YFS:
  <option1>: <value1>
  <option2>: <value2>
  ...

The options are

5.15.1.1. MODE

The keyword MODE determines the mode of operation of Photons. MODE: None switches Photons off. Consequently, neither the hard interaction nor any hadron decay will be corrected for soft or hard photon emission. MODE: Soft sets the mode to “soft only”, meaning soft emissions will be treated correctly to all orders but no hard emission corrections will be included. With MODE: Full these hard emission corrections will also be included up to first order in alpha_QED. This is the default setting.

5.15.1.2. USE_ME

The switch USE_ME tells Photons how to correct hard emissions to first order in alpha_QED. If USE_ME: 0, then Photons will use collinearly approximated real emission matrix elements. Virtual emission matrix elements of order alpha_QED are ignored. If, however, YFS_USE_ME=1, then exact real and/or virtual emission matrix elements are used wherever possible. These are presently available for V->FF, V->SS, S->FF, S->SS, S->Slnu, S->Vlnu type decays, Z->FF decays and leptonic tau and W decays. For all other decay types general collinearly approximated matrix elements are used. In both approaches all hadrons are treated as point-like objects. The default setting is USE_ME: 1. This switch is only effective if MODE: Full.

5.15.1.3. IR_CUTOFF

IR_CUTOFF sets the infrared cut-off dividing the real emission in two regions, one containing the infrared divergence, the other the “hard” emissions. This cut-off is currently applied in the rest frame of the multipole of the respective decay. It also serves as a minimum photon energy in this frame for explicit photon generation for the event record. In contrast, all photons below with energy less than this cut-off will be assumed to have negligible impact on the final-state momentum distributions. The default is IR_CUTOFF: 1E-3 (GeV). Of course, this switch is only effective if Photons is switched on, i.e. MODE is not set to None.

5.15.1.4. PHOTON_SPLITTER_MODE

The parameter PHOTON_SPLITTER_MODE determines which particles, if any, may be produced in photon splittings:

0

All photon splitting functions are turned off.

1

Photons may split into electron-positron pairs;

2

muons;

4

tau leptons;

8

light hadrons up to PHOTON_SPLITTER_MAX_HADMASS.

The settings are additive, e.g. PHOTON_SPLITTER_MODE: 3 allows splittings into electron-positron and muon-antimuon pairs. The default is PHOTON_SPLITTER_MODE: 15 (all splittings turned on). This parameter is of course only effective if the Photons module is switched on using the MODE keyword.

5.15.1.5. PHOTON_SPLITTER_MAX_HADMASS

PHOTON_SPLITTER_MAX_HADMASS sets the mass (in GeV) of the heaviest hadron which may be produced in photon splittings. Note that vector splitting functions are currently not implemented: only fermions, scalars and pseudoscalars up to this cutoff will be considered. The default is 0.5 GeV.

5.15.2. QED Corrections to the Hard Interaction

The switches to steer QED corrections to the hard scattering are collected in the ME_QED settings group and are modified like this:

ME_QED:
  <option1>: <value1>
  <option2>: <value2>
  ...

The following options can be customised:

5.15.2.1. ENABLED

ENABLED: false turns the higher order QED corrections to the matrix element off. The default is true. Switching QED corrections to the matrix element off has no effect on QED Corrections to Hadron Decays. The QED corrections to the matrix element will only be effected on final state not strongly interacting particles. If a resonant production subprocess for an unambiguous subset of all such particles is specified via the process declaration (cf. Processes) this can be taken into account and dedicated higher order matrix elements can be used (if YFS: { MODE: Full, USE_ME: 1 }).

5.15.2.2. CLUSTERING_ENABLED

CLUSTERING_ENABLED: false switches the phase space point dependent identification of possible resonances within the hard matrix element on or off, respectively. The default is true. Resonances are identified by recombining the electroweak final state of the matrix element into resonances that are allowed by the model. Competing resonances are identified by their on-shell-ness, i.e. the distance of the decay product’s invariant mass from the nominal resonance mass in units of the resonance width.

5.15.2.3. CLUSTERING_THRESHOLD

Sets the maximal distance of the decay product invariant mass from the nominal resonance mass in units of the resonance width in order for the resonance to be identified. The default is CLUSTERING_THRESHOLD: 10.0.

5.15.3. QED Corrections to Hadron Decays

If the Photons module is switched on, all hadron decays are corrected for higher order QED effects.

5.15.4. QED Corrections for Lepton-Lepton Collisions

The YFS resummation can be enabled for lepton-lepton scattering by setting MODE to ISR.

The options are

5.15.4.1. BETA

Higher order matrix element corrections can be included by setting BETA to either 1/2 to the desired order of accuray. For example BETA: 0 disables all higer-order corrections:cite:Jadach:2000ir

5.15.4.2. COULOMB

The Coulomb threshold corrections [BBD93] [FKM93] to the \(W^+W^-\) threshold can be included with COULOMB: True. Double counting of the virtual corrections with the YFS form-factor is avoided by using analytical subtraction in the threshold limit [KPSchonherr22].

5.16. Approximate Electroweak Corrections

As an alternative to the complete set of NLO EW corrections, methods restricted to the leading effects due to EW loops are available in Sherpa. In particular at energy scales \(Q\) large compared to the masses of the EW gauge bosons, contributions from virtual W- and Z-boson exchange and corresponding collinear real emissions dominate. The leading contributions are Sudakov-type logarithms of the form [CC99, Sud56].

\[\frac{\alpha}{4\pi \sin^2\theta_W}\log^2\left(\frac{Q^2}{M^2_W}\right)\quad\text{and}\quad \frac{\alpha}{4\pi \sin^2\theta_W}\log\left(\frac{Q^2}{M^2_W}\right)\,.\]

The one-loop EW Sudakov approximation, dubbed EWSud, has been developed for general processes in [DP01a, DP01b]. A corresponding automated implementation in the Sherpa framework, applicable to all common event generation modes of Sherpa, including multijet-merged calculations, has been presented in [BN20] and [BNSchonherr+21].

Another available approximation, dubbed EWVirt, was devised in [KLMaierhofer+16]. It comprises exact renormalised NLO EW virtual corrections and integrated approximate real-emission subtraction terms, thereby neglecting in particular hard real-emission contributions. However, both methods qualify for a rather straightforward inclusion of the dominant EW corrections in state-of-the-art matrix-element plus parton-shower simulations.

In the following we will discuss how to enable the calculation of the EWSud and EWVirt corrections, and what options are available to steer their evaluation, beginning with EWVirt.

5.16.1. EWVirt

One option to enable EWVirt corrections is to use KFACTOR: EWVirt. Note that this only works for LO calculations (both with and without the shower, including MEPSatLO). The EW virtual matrix element must be made available (for all process multiplicities) using a suitable Loop_Generator. The EWVirt correction will then be directly applied to the nominal event weight.

The second option, which is only available for MEPSatNLO, applies the EWVirt correction (and optionally subleading LO corrections) to all QCD NLO multiplicities. For this to work, one must use the the following syntax:

ASSOCIATED_CONTRIBUTIONS_VARIATIONS:
- [EW]
- [EW, LO1]
- [EW, LO1, LO2]
- [EW, LO1, LO2, LO3]

Each entry of ASSOCIATED_CONTRIBUTIONS_VARIATIONS defines a variation and the different associated contributions that should be taken into account for the corresponding alternative weight. Note that the respective associated contribution must be listed in the process setting Associated_Contributions.

The additional event weights can then be written into the event output. The alternative event weight names are either ASSOCIATED_CONTRIBUTIONS.<contrib>, ASSOCIATED_CONTRIBUTIONS.MULTI<contrib>, or ASSOCIATED_CONTRIBUTIONS.EXP<contrib> for additive, multiplicative, and exponentiated combinations, correspondingly. See On-the-fly event weight variations for more information on variation weights and the variation weight naming scheme.

5.16.2. EWSud

The EWSud module must be enabled during configuration of Sherpa using the -DSHERPA_ENABLE_EWSUD=ON switch.

Similar to EWVirt, also with the EWSud corrections there is the option to use it via KFACTOR: EWSud, which will apply the corrections directly to the nominal event weight, or as on-the-fly variations adding the following entry to the list of variations (also cf. On-the-fly event weight variations):

VARIATIONS:
- EWSud

Using the latter, corrections are provided as alternative event weights. The most useful entries of the event weight list are accessed using the keys EWSud.KFactor and EWSud.KFactorExp. The first is the nominal event weight corrected by the NLL EWSud corrections, while the latter first exponentiates the corrections prior to applying it to the nominal event weight, thus giving a resummed NLL result.

In order for the EWSud corrections to make sense, Goldstone bosons need to be made available. This is achieved by ensuring that the following is set

MODEL: SMGold

Additionally, a coupling order must be set to correctly initialize the couplings for this model, see Processes for more details

PROCESSES:
  ...
  Order{QCD:xx, EW:yy, SMGold: 0}
  ...

The following configuration snippet shows the options steering the EWSud calculation, along with their default values:

EWSUD:
  THRESHOLD: 1.0
  INCLUDE_SUBLEADING: true
  CLUSTERING_THRESHOLD: 10.0

• THRESHOLD . Strictly speaking the EWSudakov corrections are only valid in the high-energy limit, that is where all possible invariant masses, formed by pairing external particles, are much larger than the W mass. In practice, we need to define how much is much larger. The THRESHOLD option, gives the minimal invariant mass (in units of :math:m_W) that each pairing of external particles can have to respect the high energy limit, and below which no EWSudakov correction is computed. To clarify, a large threshold, say for example 10 (10 times the W mass), would result in little to no corrections at all, except for regions of phase-space truly in the high-energy limit. This result is thus only expected to match exact EW corrections only when all invariants are larger than this threshold. Conversely a lower value, say 1, would apply the correction more uniformly at the price of violating the theoretically sound region where these corrections are derived, but is seen to better reproduce the effect of exact EW corrections across kinematical distributions.

• INCLUDE_SUBLEADING determines whether a formally subleading term proportional to \(\log^2(r_{kl} / \hat s)\) is included, where \(\hat s\) is the Mandelstam variable for the partonic process, see [BNSchonherr+21]. Note that depending on the value of THRESHOLD these may become numerically significant. For lower threshold values, it is recommended to leave this option true, as default.

• CLUSTERING_THRESHOLD determines the number of vector boson decay widths, for which a given lepton pair with the right quantum numbers is still allowed to be clustered prior to the calculation of the EWSud correction. For reasoning, see again [BNSchonherr+21].

We next list all possible technical parameters under the scope of EWSUD. They are mostly meant for internal or consistency checks and are advisable only to expert users.

• RS boolean flag to determine whether or not to apply the EWSudakov corrections to RS type events, defaults to true.

• CHECK boolean flag to enable/disable internal checks on the logarithmic coefficients for various simple processes. Defaults to false and prevents normal running when set to true, in that it terminates the run after having checked the coefficients.

• CHECK_KFACTOR Same as CHECK but at the level of KFACTOR.

• CHECK_LOG_FILE Specify a filename in which to store the result of CHECK, defaults to a null string.

• CHECKINVARIANTRATIOS boolean flag used to enforce a stricter definition of High Energy Limit, defaults to false.

• COEFF_REMOVED_LIST list of logarithmic coefficients that can be ignored, defaults to empty, meaning that all coefficients are included. The available options are: LSC, Z, SSC, C, Yuk, PR and I. See [BN20] for further details.

• C_COEFF_IGNORES_VECTOR_BOSONS boolean flag to control whether or not Vector Boson contributions should be included in the calculation of the C coefficient. Defaults to false, and can be used to check the PR logarithms, given that for some procs the contributions to C from vector bosons and the PR coefficients cancel.

• HIGH_ENERGY_SCHEME different implementations of the High Energy limit conditions. At the moment only Default is fully implemented, all other available options imply that no check is enforced on the configurations, and a contribution is calculated independently on whether or we are in the high energy limit.

• PRINT_GRAPHS sets the name of the directory where to save graphs associated to processes generated by the EWSudakov calculation. Same as Print_Graphs.

NOTE that at the moment EW Sudakov corrections do not work for processes that feature a four-vector boson vertex, such as a four-gluon vertex.

5.17. Minimum bias events

Minimum bias events are simulated through the Shrimps module in Sherpa.

5.17.1. Physics of Shrimps

5.17.1.1. Inclusive part of the model

Shrimps is based on the KMR model [RMK09], which is a multi-channel eikonal model. The incoming hadrons are written as a superposition of Good-Walker states, which are diffractive eigenstates that diagonalise the T-matrix. This allows to include low-mass diffractive excitation. Each combination of colliding Good-Walker states gives rise to a single-channel eikonal. The final eikonal is the superposition of the single-channel eikonals. The number of Good-Walker states is 2 in Shrimps (the original KMR model includes 3 states).

Each single-channel eikonal can be seen as the product of two parton densities, one from each of the colliding Good-Walker states. The evolution of the parton densities in rapidity due to extra emissions and absorption on either of the two hadrons is described by a set of coupled differential equations. The parameter Delta, which can be interpreted as the Pomeron intercept, is the probability for emitting an extra parton per unit of rapidity. The strength of absorptive corrections is quantified by the parameter lambda, which can also be seen as the triple-Pomeron coupling. A small region of size deltaY around the beams is excluded from the evolution due to the finite longitudinal size of the parton densities.

The boundary conditions for the parton densities are form factors, which have a dipole form characterised by the parameters Lambda2, beta_02(mb), kappa and xi.

In this framework the eikonals and the cross sections for the different modes (elastic, inelastic, single- and double-diffractive) are calculated.

5.17.1.2. Exclusive part of the model

The description of this part of the model is outdated and needs to be updated. Please contact the Authors if you need more information.

5.17.2. Parameters and settings

Below is a list of all relevant parameters to steer the Shrimps module.

5.17.2.1. Generating minimum bias events

To generate minimum bias events with Shrimps EVENT_TYPE has to be set to MinimumBias and SOFT_COLLISIONS to Shrimps.

5.17.2.2. Shrimps Mode

The setup of minimum bias events is done via top-level settings. The exact choice is steered through the parameter Shrimps_Mode (default Inelastic), which allows the following settings:

• Xsecs, which will only calculate total, elastic, inelastic, single- and double-diffractive cross sections at various relevant energies and write them to a file, typically ‘InclusiveQuantities/Xsecs.dat’;

• Elastic generates elastic events at a fixed energy;

• Single-diffractive generates low-mass single-diffractive events at a fixed energy, modelled by the transition of one of the protons to a N(1440) state;

• Double-diffractive generates low-mass single-diffractive events at a fixed energy, modelled by the transition of both protons to N(1440) states;

• Quasi-elastic generates a combination of elastic, single- and double-diffractive events in due proportion;

• Inelastic generates inelastic minimum bias events through the exchange of t-channel gluons or singlets (pomerons). This mode actually will include large mass diffraction;

• All generates a combination of quasi-elastic and inelastic events in due proportion.

5.17.2.3. Parameters of the eikonals

The parameters of the differential equations for the parton densities are

• Delta (default 0.3): perturbative Pomeron intercept

• lambda (default 0.5): triple Pomeron coupling

• deltaY (default 1.5): rapidity interval excluded from evolution

The form factors are of the form:

\[F_{1/2}(q_T) = \beta_0^2 (1 \pm \kappa) \frac{\exp(\frac{-\xi (1 \pm \kappa)q_T^2}{\Lambda^2})}{(1 + (1 \pm \kappa)q_T^2/\Lambda^2)^2}\]

with the parameters

• \(\Lambda^2\) (default 1.7 GeV^2)

• \(\beta_0^2(mb)\) (default 25.0 mb)

• \(\kappa\) (default 0.6)

• \(\xi\) (default 0.2)

5.17.2.4. Parameters for event generation

The description of these parameters is outdated and needs to be updated. Please contact the Authors if you need more information.

6. Tips and tricks

6.1. Shell completion

Sherpa will install a file named $prefix/share/SHERPA-MC/sherpa-completion which contains tab completion functionality for the bash shell. You simply have to source it in your active shell session by running

$ .  $prefix/share/SHERPA-MC/sherpa-completion

and you will be able to tab-complete any parameters on a Sherpa command line.

To permanently enable this feature in your bash shell, you’ll have to add the source command above to your ~/.bashrc.

6.2. Rivet analyses

Sherpa is equipped with an interface to the analysis tool Rivet [B+20]. To enable it, Rivet and HepMC [DH01] have to be installed (e.g. using the Rivet bootstrap script) and your Sherpa compilation has to be configured with the following options:

$ cmake -DHepMC3_DIR=/path/to/hepmc3 -DRIVET_DIR=/path/to/rivet

(Note: Both paths are equal if you used the Rivet bootstrap script.) In the case that the packages are installed in standard locations, you can instead use -DSHERPA_ENABLE_HEPMC3=ON and -DSHERPA_ENABLE_RIVET=ON, respectively.

To use the interface, you need to enable it using the ANALYSIS option and to configure it it using the RIVET settings group as follows:

ANALYSIS: Rivet
RIVET:
  --analyses:
    - D0_2008_S7662670
    - CDF_2007_S7057202
    - D0_2004_S5992206
    - CDF_2008_S7828950

The analyses list specifies which Rivet analyses to run and the histogram output file can be changed with the normal ANALYSIS_OUTPUT switch.

Further Rivet options can be passed through the interface. The following ones are currently implemented:

ANALYSIS: Rivet
RIVET:
  --analyses:
    - MC_ZINC
  --ignore-beams: 1
  --skip-weights: 0
  --match_weights: ".*MUR.*"
  --unmatch-weights: "NTrials"
  --nominal-weight: "Weight"
  --weight-cap: 100.0
  --nlo-smearing: 0.1

You can also use rivet-mkhtml (distributed with Rivet) to create plot webpages from Rivet’s output files:

$ source /path/to/rivetenv.sh   # see below
$ rivet-mkhtml -o output/ file1.yoda [file2.yoda, ...]
$ firefox output/index.html &

If your Rivet installation is not in a standard location, the bootstrap script should have created a rivetenv.sh which you have to source before running the rivet-mkhtml script. If you want to employ custom Rivet analyses you might need to set the corresponding Rivet path variable, for example via

$ export RIVET_ANALYSIS_PATH=$RIVET_ANALYSIS_PATH:<path to custom analysis lib>

The RIVET: block can be used with further options especially suitable for detailed studies. Adding JETCONTS: 1 will create separate histograms split by jet multiplicity as created by the hard process. SPLITSH: 1 creates histograms split by soft and hard events, and SPLITPM: 1 creates histograms split by events with positive and negative event weights. Finally, SPLITCOREPROCS: 1 will split by different processes if multiple ones are specified in the runcard.

6.3. MCFM interface

Sherpa is equipped with an interface to the NLO library of MCFM for dedicated processes. To enable it, MCFM has to be installed and compiled into a single library @code{libmcfm.so} by using the -Dwith_library=ON flag when configuring MCFM using CMake.

Finally, your Sherpa compilation has to be configured with the following option:

$ cmake -DMCFM_DIR=/path/to/MCFM

Or, if MCFM is installed in a standard location:

$ cmake -DSHERPA_ENABLE_MCFM=ON

To use the interface, specify

Loop_Generator: MCFM

in the process section of the run card and add it to the list of generators in ME_GENERATORS. MCFM’s process.DAT file should automatically be copied to the current run directory during initialisation.

Note that for unweighted event generation, there is also an option to choose different loop-amplitude providers for the pilot run and the accepted events via the Pilot_Loop_Generator option.

6.4. Debugging a crashing/stalled event

6.4.1. Crashing events

If an event crashes, Sherpa tries to obtain all the information needed to reproduce that event and writes it out into a directory named

Status__<date>_<time>

If you are a Sherpa user and want to report this crash to the Sherpa team, please attach a tarball of this directory to your email. This allows us to reproduce your crashed event and debug it.

To debug it yourself, you can follow these steps (Only do this if you are a Sherpa developer, or want to debug a problem in an addon library created by yourself):

• Copy the random seed out of the status directory into your run path:

  $ cp  Status__<date>_<time>/random.dat  ./
  

• Run your normal Sherpa commandline with an additional parameter:

  $ Sherpa [...] 'STATUS_PATH: ./'
  

  Sherpa will then read in your random seed from “./random.dat” and generate events from it.

• Ideally, the first event will lead to the crash you saw earlier, and you can now turn on debugging output to find out more about the details of that event and test code changes to fix it:

  $ Sherpa [...] --output 15 'STATUS_PATH: ./'
  

6.4.2. Stalled events

If event generation seems to stall, you first have to find out the number of the current event. For that you would terminate the stalled Sherpa process (using Ctrl-c) and check in its final output for the number of generated events. Now you can request Sherpa to write out the random seed for the event before the stalled one:

$ Sherpa [...] --events <#events - 1> 'SAVE_STATUS: Status/'

(Replace <#events - 1> using the number you figured out earlier.)

The created status directory can either be sent to the Sherpa developers, or be used in the same steps as above to reproduce that event and debug it.

6.5. Versioned installation

If you want to install different Sherpa versions into the same prefix (e.g. /usr/local), you have to enable versioning of the installed directories by using the configure option -DSHERPA_ENABLE_VERSIONING=ON. Optionally you can even pass an argument to this parameter of what you want the version tag to look like.

6.6. NLO calculations

6.6.1. Choosing DIPOLES ALPHA

A variation of the parameter DIPOLES:ALPHA (see Dipole subtraction) changes the contribution from the real (subtracted) piece (RS) and the integrated subtraction terms (I), keeping their sum constant. Varying this parameter provides a nice check of the consistency of the subtraction procedure and it allows to optimize the integration performance of the real correction. This piece has the most complicated momentum phase space and is often the most time consuming part of the NLO calculation. The optimal choice depends on the specific setup and can be determined best by trial.

Hints to find a good value:

• The smaller DIPOLES:ALPHA is the less dipole term have to be calculated, thus the less time the evaluation/phase space point takes.

• Too small choices lead to large cancellations between the RS and the I parts and thus to large statistical errors.

• For very simple processes (with only a total of two partons in the initial and the final state of the born process) the best choice is typically DIPOLES: {ALPHA: 1}. The more complicated a process is the smaller DIPOLES:ALPHA should be (e.g. with 5 partons the best choice is typically around 0.01).

• A good choice is typically such that the cross section from the RS piece is significantly positive but not much larger than the born cross section.

6.6.2. Integrating complicated Loop-ME

For complicated processes the evaluation of one-loop matrix elements can be very time consuming. The generation time of a fully optimized integration grid can become prohibitively long. Rather than using a poorly optimized grid in this case it is more advisable to use a grid optimized with either the born matrix elements or the born matrix elements and the finite part of the integrated subtraction terms only, working under the assumption that the distributions in phase space are rather similar.

This can be done by one of the following methods:

1. Employ a dummy virtual (requires no computing time, returns a finite value as its result) to optimise the grid. This only works if V is not the only NLO_Part specified.

   1. During integration set the Loop_Generator to Dummy. The grid will then be optimised to the phase space distribution of the sum of the Born matrix element and the finite part of the integrated subtraction term, plus a finite value from Dummy.

      Note

      The cross section displayed during integration will also correspond to these contributions.

   2. During event generation reset Loop_Generator to your generator supplying the virtual correction. The events generated then carry the correct event weight.

2. Suppress the evaluation of the virtual and/or the integrated subtraction terms. This only works if Amegic is used as the matrix element generator for the BVI pieces and V is not the only NLO_Part specified.

   1. During integration add AMEGIC: { NLO_BVI_MODE: <num> } to your configuration. <num> takes the following values: 1-B, 2-I, and 4-V. The values are additive, i.e. 3-BI.

      Note

      The cross section displayed during integration will match the parts selected by NLO_BVI_MODE.

   2. During event generation remove the switch again and the events will carry the correct weight.

Note

this will not work for the RS piece!

6.6.3. Avoiding misbinning effects

Close to the infrared limit, the real emission matrix element and corresponding subtraction events exhibit large cancellations. If the (minor) kinematics difference of the events happens to cross a parton-level cut or analysis histogram bin boundary, then large spurious spikes can appear.

These can be smoothed to some extend by shifting the weight from the subtraction kinematic to the real-emission kinematic if the dipole measure alpha is below a given threshold. The fraction of the shifted weight is inversely proportional to the dipole measure, such that the final real-emission and subtraction weights are calculated as:

w_r -> w_r + sum_i [1-x(alpha_i)] w_{s,i}
foreach i: w_{s,i} -> x(alpha_i) w_{s,i}

with the function \(x(\alpha)=(\frac{\alpha}{|\alpha_0|})^n\) for \(\alpha<\alpha_0\) and \(1\) otherwise.

The threshold can be set by the parameter NLO_SMEAR_THRESHOLD: <alpha_0> and the functional form of alpha and thus interpretation of the threshold can be chosen by its sign (positive: relative dipole kT in GeV, negative: dipole alpha). In addition, the exponent n can be set by NLO_SMEAR_POWER: <n>.

6.6.4. Enforcing the renormalisation scheme

Sherpa takes information about the renormalisation scheme from the loop ME generator. The default scheme is MSbar, and this is assumed if no loop ME is provided, for example when integrated subtraction terms are computed by themselves. This can lead to inconsistencies when combining event samples, which may be avoided by setting AMEGIC: { LOOP_ME_INIT: 1 }.

6.6.5. Checking the pole cancellation

To check whether the poles of the dipole subtraction and the interfaced one-loop matrix element cancel for each phase space point, specify AMEGIC: { CHECK_POLES: true } and/or COMIX: { CHECK_POLES: true }.

In the same way, the finite contributions of the infrared subtraction and the one-loop matrix element can be checked using CHECK_FINITE, and the Born matrix element via CHECK_BORN. The accuracy to which the poles, finite parts and Born matrix elements are checked is set via CHECK_THRESHOLD. These three settings are only supported by Amegic and are thus set using AMEGIC: { <PARAMETER>: <VALUE> }, where <VALUE> is false or true for CHECK_FINITE/CHECK_BORN, or a number specifying the desired accuracy for CHECK_THRESHOLD.

6.7. A posteriori scale variations

There are several ways to compute the effects of changing the scales and PDFs of any event produced by Sherpa. They can computed explicitly, cf. Explicit scale variations, on-the-fly, cf. On-the-fly event weight variations (restricted to multiplicative factors), or reconstructed a posteriori. The latter method needs plenty of additional information in the event record and is (depending on the actual calculation) available in two formats:

6.7.1. A posteriori scale and PDF variations using the HepMC GenEvent Output

Events generated in a LO, LOPS, NLO, NLOPS, MEPS@LO, MEPS@NLO or MENLOPS calculation can be written out in the HepMC format including all information to carry out arbitrary scale variations a posteriori. For this feature HepMC of at least version 2.06 is necessary and both HEPMC_USE_NAMED_WEIGHTS: true and HEPMC_EXTENDED_WEIGHTS: true have to enabled. Detailed instructions on how to use this information to construct the new event weight can be found here https://sherpa.hepforge.org/doc/ScaleVariations-Sherpa-2.2.0.pdf.

6.7.2. A posteriori scale and PDF variations using the ROOT NTuple Output

Events generated at fixed-order LO and NLO can be stored in ROOT NTuples that allow arbitrary a posteriori scale and PDF variations, see Event output formats. An example for writing and reading in such ROOT NTuples can be found here: Production of NTuples. The internal ROOT Tree has the following Branches:

id

Event ID to identify correlated real sub-events.

nparticle

Number of outgoing partons.

E/px/py/pz

Momentum components of the partons.

kf

Parton PDG code.

weight

Event weight, if sub-event is treated independently.

weight2

Event weight, if correlated sub-events are treated as single event.

me_wgt

ME weight (w/o PDF), corresponds to ‘weight’.

me_wgt2

ME weight (w/o PDF), corresponds to ‘weight2’.

id1

PDG code of incoming parton 1.

id2

PDG code of incoming parton 2.

fac_scale

Factorisation scale.

ren_scale

Renormalisation scale.

x1

Bjorken-x of incoming parton 1.

x2

Bjorken-x of incoming parton 2.

x1p

x’ for I-piece of incoming parton 1.

x2p

x’ for I-piece of incoming parton 2.

nuwgt

Number of additional ME weights for loops and integrated subtraction terms.

usr_wgt[nuwgt]

Additional ME weights for loops and integrated subtraction terms.

6.7.3. Computing (differential) cross sections of real correction events with statistical errors

Real correction events and their counter-events from subtraction terms are highly correlated and exhibit large cancellations. Although a treatment of sub-events as independent events leads to the correct cross section the statistical error would be greatly overestimated. In order to get a realistic statistical error sub-events belonging to the same event must be combined before added to the total cross section or a histogram bin of a differential cross section. Since in general each sub-event comes with it’s own set of four momenta the following treatment becomes necessary:

1. An event here refers to a full real correction event that may contain several sub-events. All entries with the same id belong to the same event. Step 2 has to be repeated for each event.

2. Each sub-event must be checked separately whether it passes possible phase space cuts. Then for each observable add up weight2 of all sub-events that go into the same histogram bin. These sums \(x_{id}\) are the quantities to enter the actual histogram.

3. To compute statistical errors each bin must store the sum over all \(x_{id}\) and the sum over all \(x_{id}^2\). The cross section in the bin is given by \(\langle x\rangle = \frac{1}{N} \cdot \sum x_{id}\), where \(N\) is the number of events (not sub-events). The \(1-\sigma\) statistical error for the bin is \(\sqrt{ (\langle x^2\rangle-\langle x\rangle^2)/(N-1) }\)

Note: The main difference between weight and weight2 is that they refer to a different counting of events. While weight corresponds to each event entry (sub-event) counted separately, weight2 counts events as defined in step 1 of the above procedure. For NLO pieces other than the real correction weight and weight2 are identical.

6.7.4. Computation of cross sections with new PDF’s

6.7.4.1. Born and real pieces

Notation:

f_a(x_a) = PDF 1 applied on parton a, F_b(x_b) = PDF 2 applied on
parton b.

The total cross section weight is given by:

weight = me_wgt f_a(x_a)F_b(x_b)

6.7.4.2. Loop piece and integrated subtraction terms

The weights here have an explicit dependence on the renormalisation and factorization scales.

To take care of the renormalisation scale dependence (other than via alpha_S) the weight w_0 is defined as

w_0 = me_wgt + usr_wgts[0] log((\mu_R^new)^2/(\mu_R^old)^2) +
usr_wgts[1] 1/2 [log((\mu_R^new)^2/(\mu_R^old)^2)]^2

To address the factorization scale dependence the weights w_1,...,w_8 are given by

w_i = usr_wgts[i+1] + usr_wgts[i+9] log((\mu_F^new)^2/(\mu_F^old)^2)

The full cross section weight can be calculated as

weight = w_0 f_a(x_a)F_b(x_b)
          + (f_a^1 w_1 + f_a^2 w_2 + f_a^3 w_3 + f_a^4 w_4) F_b(x_b)
          + (F_b^1 w_5 + F_b^2 w_6 + F_b^3 w_7 + F_b^4 w_8) f_a(x_a)

where

f_a^1 = f_a(x_a) (a=quark), \sum_q f_q(x_a) (a=gluon),
f_a^2 = f_a(x_a/x'_a)/x'_a (a=quark), \sum_q f_q(x_a/x'_a)x'_a (a=gluon),
f_a^3 = f_g(x_a),
f_a^4 = f_g(x_a/x'_a)/x'_a

The scale dependence coefficients usr_wgts[0] and usr_wgts[1] are normally obtained from the finite part of the virtual correction by removing renormalisation terms and universal terms from dipole subtraction. This may be undesirable, especially when the loop provider splits up the calculation of the virtual correction into several pieces, like leading and sub-leading color. In this case the loop provider should control the scale dependence coefficients, which can be enforced with option USR_WGT_MODE: false.

Warning

The loop provider must support this option or the scale dependence coefficients will be invalid!

7. Customization

Customizing Sherpa according to your needs.

Sherpa can be easily extended with certain user defined tools. To this extent, a corresponding C++ class must be written, and compiled into an external library:

$ g++ -shared \
      -I`$SHERPA_PREFIX/bin/Sherpa-config --incdir` \
      `$SHERPA_PREFIX/bin/Sherpa-config --ldflags` \
      -o libMyCustomClass.so My_Custom_Class.C

This library can then be loaded in Sherpa at runtime with the option SHERPA_LDADD, e.g.:

SHERPA_LDADD:
- MyCustomClass

Several specific examples of features which can be extended in this way are listed in the following sections.

7.1. Exotic physics

It is possible to add your own models to Sherpa in a straightforward way. To illustrate, a simple example has been included in the directory Examples/BSM/SM_ZPrime, showing how to add a Z-prime boson to the Standard Model.

The important features of this example include:

• The Model.C file.

  This file contains the initialisation of the Z-prime boson and the definition of the Z-prime boson’s interactions. The remaining physics settings are inherited from the internal standard model implementation. The properties of the Z-prime are set here, such as mass, width, electromagnetic charge, spin etc as well as the right- and left-handed couplings to each of the fermions are set there.

• An example Makefile.

  This shows how to compile the sources above into a shared library.

• The example run card Sherpa.yaml. Note in particular:

• The line SHERPA_LDADD: SherpaSMZprime in the config file.

  This line tells Sherpa to load the extra libraries created from the *.C files above.

• The line MODEL: SMZprime in the config file.

  This line tells Sherpa which model to use for the run.

• The following lines in the config file:

  PARTICLE_DATA:
    32:
      Mass: 1000
      Width: 50
  

  These lines show how you can overrule the choices you made for the properties of the new particle in the Model.C file. For more information on changing parameters in Sherpa, see Input structure and Parameters.

• The lines

  Zprime:
    Zp_cpl_L: 0.3
    Zp_cpl_R: 0.6
  

  set the couplings to left and right handed fermions.

To use this model, create the libraries for Sherpa to use by running

$ make

in this directory. Then run Sherpa as normal:

$ ../../../bin/Sherpa

To implement your own model, copy these example files anywhere and modify them according to your needs.

Note: You don’t have to modify or recompile any part of Sherpa to use your model. As long as the SHERPA_LDADD parameter is specified as above, Sherpa will pick up your model automatically.

Furthermore note: New physics models with an existing implementation in FeynRules, cf. [CD09] and [CdAD+11], can directly be invoked using Sherpa’s support for the UFO model format, see UFO Model Interface.

7.2. Custom scale setter

You can write a custom calculator to set the factorisation, renormalisation and resummation scales. It has to be implemented as a C++ class which derives from the Scale_Setter_Base base class and implements only the constructor and the Calculate method.

Here is a snippet for a very simple one, which sets all three scales to the invariant mass of the two incoming partons.

#include "PHASIC++/Scales/Scale_Setter_Base.H"
#include "ATOOLS/Org/Message.H"

using namespace PHASIC;
using namespace ATOOLS;

namespace PHASIC {

  class Custom_Scale_Setter: public Scale_Setter_Base {
  protected:

  public:

    Custom_Scale_Setter(const Scale_Setter_Arguments &args) :
      Scale_Setter_Base(args)
    {
      m_scale.resize(3); // by default three scales: fac, ren, res
                         // but you can add more if you need for COUPLINGS
      SetCouplings(); // the default value of COUPLINGS is "Alpha_QCD 1", i.e.
                      // m_scale[1] is used for running alpha_s
                      // (counting starts at zero!)
    }

    double Calculate(const std::vector<ATOOLS::Vec4D> &p,
                  const size_t &mode)
    {
      double muF=(p[0]+p[1]).Abs2();
      double muR=(p[0]+p[1]).Abs2();
      double muQ=(p[0]+p[1]).Abs2();

      m_scale[stp::fac] = muF;
      m_scale[stp::ren] = muR;
      m_scale[stp::res] = muQ;

      // Switch on debugging output for this class with:
      // Sherpa "OUTPUT=2[Custom_Scale_Setter|15]"
      DEBUG_FUNC("Calculated scales:");
      DEBUG_VAR(m_scale[stp::fac]);
      DEBUG_VAR(m_scale[stp::ren]);
      DEBUG_VAR(m_scale[stp::res]);

      return m_scale[stp::fac];
    }

  };

}

// Some plugin magic to make it available for SCALES=CUSTOM
DECLARE_GETTER(Custom_Scale_Setter,"CUSTOM",
            Scale_Setter_Base,Scale_Setter_Arguments);

Scale_Setter_Base *ATOOLS::Getter
<Scale_Setter_Base,Scale_Setter_Arguments,Custom_Scale_Setter>::
operator()(const Scale_Setter_Arguments &args) const
{
  return new Custom_Scale_Setter(args);
}

void ATOOLS::Getter<Scale_Setter_Base,Scale_Setter_Arguments,
                 Custom_Scale_Setter>::
PrintInfo(std::ostream &str,const size_t width) const
{
  str<<"Custom scale scheme";
}

If the code is compiled into a library called libCustomScale.so, then this library is loaded dynamically at runtime with the switch SHERPA_LDADD: CustomScale either on the command line or in the run section, cf. Customization. This then allows to use the custom scale like a built-in scale setter by specifying SCALES: CUSTOM (cf. SCALES).

7.3. External one-loop ME

Sherpa includes only a very limited selection of one-loop matrix elements. To make full use of the implemented automated dipole subtraction it is possible to link external one-loop codes to Sherpa in order to perform full calculations at QCD next-to-leading order.

In general Sherpa can take care of any piece of the calculation except one-loop matrix elements, i.e. the born ME, the real correction, the real and integrated subtraction terms as well as the phase space integration and PDF weights for hadron collisions. Sherpa will provide sets of four-momenta and request for a specific parton level process the helicity and colour summed one-loop matrix element (more specific: the coefficients of the Laurent series in the dimensional regularisation parameter epsilon up to the order epsilon^0).

An example setup for interfacing such an external one-loop code, following the Binoth Les Houches interface proposal [B+10] of the 2009 Les Houches workshop, is provided in Zbb production. To use the LH-OLE interface, Sherpa has to be configured with -DSHERPA_ENABLE_LHOLE=ON.

The interface:

• During an initialization run Sherpa stores setup information (schemes, model information etc.) and requests a list of parton-level one-loop processes that are needed for the NLO calculation. This information is stored in a file, by default called OLE_order.lh. The external one-loop code (OLE) should confirm these settings/requests and write out a file OLE_contract.lh. Both filenames can be customised using LHOLE_ORDERFILE: <order-file> and <LHOLE_CONTRACTFILE: <contract-file>. For the syntax of these files and more details see [B+10].

  For Sherpa the output/input of the order/contract file is handled in LH_OLE_Communicator.[CH]. The actual interface is contained in LH_OLE_Interface.C. The parameters to be exchanged with the OLE are defined in the latter file via

  lhfile.AddParameter(...);
  

  and might require an update for specific OLE or processes. Per default, in addition to the standard options MatrixElementSquareType, CorrectionType, IRregularisation, AlphasPower, AlphaPower and OperationMode the masses and width of the W, Z and Higgs bosons and the top and bottom quarks are written out in free format, such that the respective OLE parameters can be easily synchronised.

• At runtime the communication is performed via function calls. To allow Sherpa to call the external code the functions

  void OLP_Start(const char * filename);
  void OLP_EvalSubProcess(int,double*,double,double,double*);
  

  which are defined and called in LH_OLE_Interface.C must be specified. For keywords and possible data fields passed with this functions see [B+10].

  The function OLP_Start(...) is called once when Sherpa is starting. The function OLP_EvalSubProcess(...) will be called many times for different subprocesses and momentum configurations.

The setup (cf. example Zbb production):

• The line Loop_Generator: LHOLE tells the code to use the interface for computing one-loop matrix elements.

• The switch SHERPA_LDADD has to be set to the appropriate library name (and path) of the one-loop generator.

• The IR regularisation scheme can be set via LHOLE_IR_REGULARISATION. Possible values are DRED (default) and CDR.

• Per default, Sherpa generates phase space points in the lab frame. If LHOLE_BOOST_TO_CMS: true is set, these phase space points are boosted to the centre of mass system before they are passed to the OLE.

• The original BLHA interface does not allow for run-time parameter passing. While this is discussed for an updated of the accord a workable solution is implemented for the use of GoSam and enabled through LHOLE_OLP: GoSam. The LHOLE_BOOST_TO_CMS is also automatically active with this setup. This, of course, can be adapted for other one-loop programs if need be.

• Sherpa’s internal analysis package can be used to generate a few histograms. Thus, then when installing Sherpa the option -DSHERPA_ENABLE_ANALYSIS=ON must be include on the command line when Sherpa is configured, see ANALYSIS.

7.4. External RNG

To use an external Random Number Generator (RNG) in Sherpa, you need to provide an interface to your RNG in an external dynamic library. This library is then loaded at runtime and Sherpa replaces the internal RNG with the one provided.

In this case Sherpa will not attempt to set, save, read or restore the RNG

The corresponding code for the RNG interface is

#include "ATOOLS/Math/Random.H"

using namespace ATOOLS;

class Example_RNG: public External_RNG {
public:
  double Get()
  {
    // your code goes here ...
  }
};// end of class Example_RNG

// this makes Example_RNG loadable in Sherpa
DECLARE_GETTER(Example_RNG,"Example_RNG",External_RNG,RNG_Key);
External_RNG *ATOOLS::Getter<External_RNG,RNG_Key,Example_RNG>::operator()(const RNG_Key &) const
{ return new Example_RNG(); }
// this eventually prints a help message
void ATOOLS::Getter<External_RNG,RNG_Key,Example_RNG>::PrintInfo(std::ostream &str,const size_t) const
{ str<<"example RNG interface"; }

If the code is compiled into a library called libExampleRNG.so, then this library is loaded dynamically in Sherpa using the command SHERPA_LDADD: ExampleRNG either on the command line or in Sherpa.yaml. If the library is bound at compile time, like e.g. in cmt, you may skip this step.

Finally Sherpa is instructed to retrieve the external RNG by specifying EXTERNAL_RNG: Example_RNG on the command line or in Sherpa.yaml.

7.5. External PDF

To use an external PDF (not included in LHAPDF) in Sherpa, you need to provide an interface to your PDF in an external dynamic library. This library is then loaded at runtime and it is possible within Sherpa to access all PDFs included.

The simplest C++ code to implement your interface looks as follows

#include "PDF/Main/PDF_Base.H"

using namespace PDF;

class Example_PDF: public PDF_Base {
public:
  void Calculate(double x,double Q2)
  {
    // calculate values x f_a(x,Q2) for all a
  }
  double GetXPDF(const ATOOLS::Flavour a)
  {
    // return x f_a(x,Q2)
  }
  virtual PDF_Base *GetCopy()
  {
    return new Example_PDF();
  }
};// end of class Example_PDF

// this makes Example_PDF loadable in Sherpa
DECLARE_PDF_GETTER(Example_PDF_Getter);
PDF_Base *Example_PDF_Getter::operator()(const Parameter_Type &args) const
{ return new Example_PDF(); }
// this eventually prints a help message
void Example_PDF_Getter::PrintInfo
(std::ostream &str,const size_t width) const
{ str<<"example PDF"; }
// this lets Sherpa initialize and unload the library
Example_PDF_Getter *p_get=NULL;
extern "C" void InitPDFLib()
{ p_get = new Example_PDF_Getter("ExamplePDF"); }
extern "C" void ExitPDFLib() { delete p_get; }

If the code is compiled into a library called libExamplePDFSherpa.so, then this library is loaded dynamically in Sherpa using PDF_LIBRARY: ExamplePDFSherpa either on the command line, or in the Sherpa.yaml. If the library is bound at compile time, like e.g. in cmt, you may skip this step. It is now possible to list all accessible PDF sets by specifying SHOW_PDF_SETS: 1 on the command line.

Finally Sherpa is instructed to retrieve the external PDF by specifying PDF_SET: ExamplePDF on the command line or in the Sherpa.yaml.

7.6. Python Interface

Certain Sherpa classes and methods can be made available to the Python interpreter in the form of an extension module. This module can be loaded in Python and provides access to certain functionalities of the Sherpa event generator in Python. In order to build the module, Sherpa must be configured with the option -DSHERPA_ENABLE_PYTHON=ON. Running make then invokes the automated interface generator SWIG [Bea03] to create the Sherpa module using the Python C/C++ API. SWIG version 1.3.x or later is required for a successful build. Problems might occur if more than one version of Python is present on the system since automake currently doesn’t always handle multiple Python installations properly. If you have multiple Python versions installed on your system, please set the PYTHON environment variable to the Python 3 executable via

$ export PYTHON=<path-to-python3>

before executing cmake script (see. Certain Sherpa classes and methods can be made available to the Python interpreter in the form of an extension module. This module can be loaded in Python and provides access to certain functionalities of the Sherpa event generator in Python. It was designed specifically for the computation of matrix elements in python (Using the Python interface) and its features are currently limited to this purpose. In order to build the module, Sherpa must be configured with the option -DSHERPA_ENABLE_PYTHON=ON. Running make then invokes the automated interface generator SWIG [Bea03] to create the Sherpa module using the Python C/C++ API. SWIG version 1.3.x or later is required for a successful build. Problems might occur if more than one version of Python is present on the system since automake currently doesn’t always handle multiple Python installations properly. A possible workaround is to temporarily uninstall one version of python, configure and build Sherpa, and then reinstall the temporarily uninstalled version of Python.

The following script is a minimal example that shows how to use the Sherpa module in Python. In order to load the Sherpa module, the location where it is installed must be added to the PYTHONPATH. There are several ways to do this, in this example the sys module is used. The sys module also allows it to directly pass the command line arguments used to run the script to the initialization routine of Sherpa. The script can thus be executed using the normal command line options of Sherpa (see Command Line Options). Furthermore it illustrates how exceptions that Sherpa might throw can be taken care of. If a run card is present in the directory where the script is executed, the initialization of the generator causes Sherpa to compute the cross sections for the processes specified in the run card. See Computing matrix elements for individual phase space points using the Python Interface for an example that shows how to use the Python interface to compute matrix elements or Generate events using scripts to see how the interface can be used to generate events in Python.

Note that if you have compiled Sherpa with MPI support, you need to source the mpi4py module using from mpi4py import MPI.

#!/usr/bin/python
import sys
sys.path.append('<sherpa-prefix>/lib/<your-python-version>/site-packages/>')
import Sherpa

# set up the generator
Generator=Sherpa.Sherpa(len(sys.argv),sys.argv)

# initialize the generator, pass command line arguments to initialization routine
try:
  Generator.InitializeTheRun()

 # catch exceptions
 except Sherpa.Exception as exc:
   print exc

8. Examples

Some example set-ups are included in Sherpa, in the <prefix>/share/SHERPA-MC/Examples/ directory. These may be useful to new users to practice with, or as templates for creating your own Sherpa run-cards. In this section, we will look at some of the main features of these examples.

8.1. Vector boson + jets production

To change any of the following LHC examples to production at different collider energies or beam types, e.g. proton anti-proton at the Tevatron, simply change the beam settings accordingly:

BEAMS: [2212, -2212]
BEAM_ENERGIES: 980

8.1.1. W+jets production

This is an example setup for inclusive W production at hadron colliders. The inclusive process is calculated at next-to-leading order accuracy matched to the parton shower using the MC@NLO prescription detailed in [HKSS12]. The next few higher jet multiplicities, calculated at next-to-leading order as well, are merged into the inclusive sample using the MEPS@NLO method – an extension of the CKKW method to NLO – as described in [HKSS13] and [GHK+13]. Finally, even higher multiplicities, calculated at leading order, are merged on top of that. A few more things to note are detailed below the example.

# Sherpa configuration for W[lv]+Jets production

# set up beams for LHC run 2
BEAMS: 2212
BEAM_ENERGIES: 6500

# matrix-element calculation
ME_GENERATORS:
- Comix
- Amegic
- OpenLoops

# optional: use a custom jet criterion
#SHERPA_LDADD: MyJetCriterion
#JET_CRITERION: FASTJET[A:antikt,R:0.4,y:5]

# exclude tau (15) from (massless) lepton container (90)
PARTICLE_DATA:
  15:
    Massive: 1

# pp -> W[lv]+jets
PROCESSES:
- 93 93 -> 90 91 93{4}:
    Order: {QCD: 0, EW: 2}
    CKKW: 20
    # set up NLO+PS final-state multiplicities
    2->2-4:
      NLO_Mode: MC@NLO
      NLO_Order: {QCD: 1, EW: 0}
      ME_Generator: Amegic
      RS_ME_Generator: Comix
      Loop_Generator: OpenLoops
    # make integration of higher final-state multiplicities faster
    2->4-6:
      Integration_Error: 0.05

SELECTORS:
# Safety cuts to avoid PDF calls with muF < 1 GeV
- [Mass, 11, -12, 1.0, E_CMS]
- [Mass, 13, -14, 1.0, E_CMS]
- [Mass, -11, 12, 1.0, E_CMS]
- [Mass, -13, 14, 1.0, E_CMS]

Things to notice:

• The Order in the process definition in a multi-jet merged setup defines the order of the core process (here 93 93 -> 90 91 with two electroweak couplings). The additional strong couplings for multi-jet production are implicitly understood.

• The settings necessary for NLO accuracy are restricted to the 2->2,3,4 processes using the 2->2-4 key below the # set up NLO+PS ... comment. The example can be converted into a simple MENLOPS setup by using 2->2 instead, or into an MEPS setup by removing these lines altogether. Thus one can study the effect of incorporating higher-order matrix elements.

• The number of additional LO jets can be varied through changing the integer within the curly braces in the Process definition, which gives the maximum number of additional partons in the matrix elements.

• OpenLoops is used here as the provider of the one-loop matrix elements for the respective multiplicities.

• Tau leptons are set massive in order to exclude them from the massless lepton container (90).

• As both Comix and Amegic are specified as matrix element generators to be used, Amegic has to be specified to be used for all MC@NLO multiplicities using ME_Generator: Amegic. Additionally, we specify RS_ME_Generator: Comix such that the subtracted real-emission bit of the NLO matrix elements is calculated more efficiently with Comix instead of Amegic. This combination is currently the only one supported for NLO-matched/merged setups.

The jet criterion used to define the matrix element multiplicity in the context of multijet merging can be supplied by the user. As an example the source code file ./Examples/V_plus_Jets/LHC_WJets/My_JetCriterion.C provides such an alternative jet criterion. It can be compiled via executing cmake . in that directory. The newly created library is linked at run time using the SHERPA_LDADD flag. The new jet criterion is then evoked by JET_CRITERION.

8.1.2. Z production

This is a very basic example at Leading Order for Z production at the LHC. Most of the settings are kept at their default, please refer to the next section for a more sophisticated calculation at higher multiplicity and accuracy.

# Sherpa configuration for Z[ee]+Jets production

# set up beams for LHC run 2
BEAMS: 2212
BEAM_ENERGIES: 6500

# matrix-element calculation
ME_GENERATORS: [Comix]

## 7-point variations
SCALE_VARIATIONS: 4.0*

# pp -> Z[ee]
PROCESSES:
- 93 93 -> 11 -11:
    Order: {QCD: 0, EW: 2}

SELECTORS:
- [Mass, 11, -11, 66, E_CMS]

8.1.3. Z+jets production

This is an example setup for inclusive Z production at hadron colliders. The inclusive process is calculated at next-to-leading order accuracy matched to the parton shower using the MC@NLO prescription detailed in [HKSS12]. The next few higher jet multiplicities, calculated at next-to-leading order as well, are merged into the inclusive sample using the MEPS@NLO method – an extension of the CKKW method to NLO – as described in [HKSS13] and [GHK+13]. Finally, even higher multiplicities, calculated at leading order, are merged on top of that. A few things to note are detailed below the previous W+jets production example and apply also to this example.

# Sherpa configuration for Z[ee]+Jets production

# set up beams for LHC run 2
BEAMS: 2212
BEAM_ENERGIES: 6500

# matrix-element calculation
ME_GENERATORS:
  - Comix
  - Amegic
  - OpenLoops

## OTF variations
SCALE_VARIATIONS:
  - [0.25, 0.25]
  - [1.0,  0.25]
  - [0.25, 1.0]
  - [1.0,  1.0]
  - [4.0,  1.0]
  - [1.0,  4.0]
  - [4.0,  4.0]

PDF_VARIATIONS:
  - PDF4LHC21_40_pdfas*
  - NNPDF40_nnlo_as_01180
  - MSHT20nnlo_as118
  - CT18NNLO_as_0118

# EW setup and corrections
EW_SCHEME: alphamZsW
SIN2THETAW: 0.23113
ASSOCIATED_CONTRIBUTIONS_VARIATIONS:
  - [EW]
  - [EW, LO1]
  - [EW, LO1, LO2]
  - [EW, LO1, LO2, LO3]

# speed and neg weight fraction improvements
MC@NLO:
  PSMODE: 2
  RS_SCALE: METS{H_Tp2/4}

# pp -> Z[ee]+jets
PROCESSES:
- 93 93 -> 11 -11 93{5}:
    Order: {QCD: 0, EW: 2}
    CKKW: 20
    # set up NLO+PS final-state multiplicities
    2->2-4:
      NLO_Mode: MC@NLO
      NLO_Order: {QCD: 1, EW: 0}
      ME_Generator: Amegic
      RS_ME_Generator: Comix
      Loop_Generator: OpenLoops
      Associated_Contributions: [EW, LO1, LO2, LO3]
    # make integration of higher final-state multiplicities faster
    2->4-7:
      Integration_Error: 0.05
      Max_N_Quarks: 4
      Max_Epsilon: 0.01

SELECTORS:
- [Mass, 11, -11, 66, E_CMS]

8.1.4. W+bb production

This example is currently broken. Please contact the Authors for more information.

8.1.5. Zbb production

BEAMS: 2212
BEAM_ENERGIES: 6500

# general settings
EVENTS: 1M

# me generator settings
ME_GENERATORS: [Comix, Amegic, LHOLE]

HARD_DECAYS:
  Enabled: true
  Mass_Smearing: 0
  Channels:
    23,11,-11: {Status: 2}
    23,13,-13: {Status: 2}

PARTICLE_DATA:
  5:
    Massive: true
    Mass: 4.75  # consistent with MSTW 2008 nf 4 set
  23:
    Width: 0
    Stable: 0

MI_HANDLER: None
FRAGMENTATION: None
MEPS:
  CORE_SCALE: VAR{H_T2+sqr(91.188)}
PDF_LIBRARY: MSTW08Sherpa
PDF_SET: mstw2008nlo_nf4

PROCESSES:
- 93 93 -> 23 5 -5:
    NLO_Mode: MC@NLO
    NLO_Order: {QCD: 1, EW: 0}
    ME_Generator: Amegic
    RS_ME_Generator: Comix
    Loop_Generator: LHOLE
    Order: {QCD: 2, EW: 1}

SELECTORS:
- FastjetFinder:
    Algorithm: antikt
    N: 2
    PTMin: 5.0
    DR: 0.5
    EtaMax: 5
    Nb: 2

Things to notice:

• The matrix elements are interfaced via the Binoth Les Houches interface proposal [B+10], [A+b], External one-loop ME.

• The Z-boson is stable in the hard matrix elements. It is decayed using the internal decay module, indicated by the settings HARD_DECAYS:Enabled: true and PARTICLE_DATA:23:Stable: 0.

• fjcore from FastJet is used to regularize the hard cross section. We require two b-jets, indicated by Nb: 2 at the end of the FastjetFinder options.

• Four-flavour PDF are used to comply with the calculational setup.

8.2. Jet production

8.2.1. Jet production

To change any of the following LHC examples to production at the Tevatron simply change the beam settings to

BEAMS: [2212, -2212]
BEAM_ENERGIES: 980

8.2.1.1. MC@NLO setup for dijet and inclusive jet production

This is an example setup for dijet and inclusive jet production at hadron colliders at next-to-leading order precision matched to the parton shower using the MC@NLO prescription detailed in [HKSS12] and [HS12]. A few things to note are detailed below the example.

# collider setup
BEAMS: 2212
BEAM_ENERGIES: 6500

TAGS:
  LOOPGEN: <my-loop-gen>

# settings fot ME generators
ME_GENERATORS: [Amegic, Comix, $(LOOPGEN)]

# scale definitions
MEPS:
  CORE_SCALE: VAR{0.25*H_T2}

SCALE_VARIATIONS:
  - [0.25, 0.25]
  - [1.0,  0.25]
  - [0.25, 1.0]
  - [1.0,  1.0]
  - [4.0,  1.0]
  - [1.0,  4.0]
  - [4.0,  4.0]


PROCESSES:
- 93 93 -> 93 93:
    Order: {QCD: 2, EW: 0}
    NLO_Order: {QCD: 1, EW: 0}
    NLO_Mode: MC@NLO
    ME_Generator: Amegic
    Loop_Generator: $(LOOPGEN)
    RS_ME_Generator: Comix


SELECTORS:
- FastjetFinder:
    Algorithm: antikt
    N: 1
    PTMin: 20
    DR:    0.4
- FastjetFinder:
    Algorithm: antikt
    N: 2
    PTMin: 10
    DR:    0.4

Things to notice:

• Asymmetric cuts are implemented (relevant to the RS-piece of an MC@NLO calculation) by requiring at least two jets with pT > 10 GeV, one of which has to have pT > 20 GeV.

• Both the factorisation and renormalisation scales are set to the above defined scale factors times a quarter of the scalar sum of the transverse momenta of all anti-kt jets (R = 0.4, pT > 20 GeV) found on the ME-level before any parton shower emission. See SCALES for details on scale setters.

• The resummation scale, which sets the maximum scale of the additional emission to be resummed by the parton shower, is set to the above defined resummation scale factor times half of the transverse momentum of the softer of the two jets present at Born level.

• The external generator OpenLoops provides the one-loop matrix elements.

• The NLO_Mode is set to MC@NLO.

8.2.1.2. MEPS setup for jet production

BEAMS: 2212
BEAM_ENERGIES: 6500

PROCESSES:
- 93 93 -> 93 93 93{0}:
    Order: {QCD: 2, EW: 0}
    CKKW: 20
    Integration_Error: 0.02

SELECTORS:
- NJetFinder:
    N: 2
    PTMin: 20.0
    ETMin: 0.0
    R: 0.4
    Exp: -1

Things to notice:

• Order is set to {QCD: 2, EW: 0}. This ensures that all final state jets are produced via the strong interaction.

• An NJetFinder selector is used to set a resolution criterion for the two jets of the core process. This is necessary because the “CKKW” tag does not apply any cuts to the core process, but only to the extra-jet matrix elements, see Multijet merged event generation with Sherpa.

8.2.2. Jets at lepton colliders

This section contains two setups to describe jet production at LEP I, either through multijet merging at leading order accuracy or at next-to-leading order accuracy.

8.2.2.1. MEPS setup for ee->jets

This example shows a LEP set-up, with electrons and positrons colliding at a centre of mass energy of 91.2 GeV.

BEAMS: [11, -11]
BEAM_ENERGIES: 45.6

ALPHAS(MZ): 0.1188
ORDER_ALPHAS: 1

PROCESSES:
- 11 -11 -> 93 93 93{3}:
    CKKW: pow(10,-2.25/2.00)*E_CMS
    Order: {QCD: 0, EW: 2}

Things to notice:

• The running of alpha_s is set to leading order and the value of alpha_s at the Z-mass is set.

• Note that initial-state radiation is enabled by default. See ISR parameters on how to disable it if you want to evaluate the (unphysical) case where the energy for the incoming leptons is fixed.

8.2.2.2. MEPS@NLO setup for ee->jets

This example expands upon the above setup, elevating its description of hard jet production to next-to-leading order.

# collider setup
BEAMS: [11, -11]
BEAM_ENERGIES: 45.6

TAGS:
  # tags for process setup
  YCUT: 2.0
  # tags for ME generators
  LOOPGEN0: Internal
  LOOPGEN1: <my-loop-gen-for-3j>
  LOOPGEN2: <my-loop-gen-for-4j>
  LOOPMGEN: <my=loop-gen-for-massive-2j>

# settings for ME generators
ME_GENERATORS:
  - Comix
  - Amegic
  - $(LOOPGEN0)
  - $(LOOPGEN1)
  - $(LOOPGEN2)
  - $(LOOPMGEN)
AMEGIC: {INTEGRATOR: 4}

# model parameters
MODEL: SM
ALPHAS(MZ): 0.118
PARTICLE_DATA: {5: {Massive: true}}
HADRON_DECAYS:
  Max_Proper_Lifetime: 100

PROCESSES:
- 11 -11 -> 93 93 93{3}:
    CKKW: pow(10,-$(YCUT)/2.00)*E_CMS
    Order: {QCD: 0, EW: 2}
    RS_Enhance_Factor: 10
    2->2: { Loop_Generator: $(LOOPGEN0) }
    2->3: { Loop_Generator: $(LOOPGEN1) }
    2->4: { Loop_Generator: $(LOOPGEN2) }
    2->2-4:
      NLO_Mode: MC@NLO
      NLO_Order: {QCD: 1, EW: 0}
      ME_Generator: Amegic
      RS_ME_Generator: Comix
- 11 -11 -> 5 -5 93{3}:
    CKKW: pow(10,-$(YCUT)/2.00)*E_CMS
    Order: {QCD: 0, EW: 2}
    Loop_Generator: $(LOOPMGEN)
    RS_Enhance_Factor: 10
    2->2:
      NLO_Mode: MC@NLO
      NLO_Order: {QCD: 1, EW: 0}
      ME_Generator: Amegic
      RS_ME_Generator: Comix
- 11 -11 -> 5 5 -5 -5 93{1}:
    CKKW: pow(10,-$(YCUT)/2.00)*E_CMS
    Order: {QCD: 2, EW: 2}
    Cut_Core: 1

Things to notice:

• the b-quark mass has been enabled for the matrix element calculation (the default is massless) because it is not negligible for LEP energies

• the b b-bar and b b b-bar b-bar processes are specified separately because the 93 particle container contains only partons set massless in the matrix element calculation, see Particle containers.

• model parameters can be modified in the config file; in this example, the value of alpha_s at the Z mass is set.

8.3. Higgs boson + jets production

8.3.1. H production in gluon fusion with interference effects

This is a setup for inclusive Higgs production through gluon fusion at hadron colliders. The inclusive process is calculated at next-to-leading order accuracy, including all interference effects between Higgs-boson production and the SM gg->yy background. The corresponding matrix elements are taken from [BDS02] and [DL].

# collider parameters
BEAMS: 2212
BEAM_ENERGIES: 6500

# generator parameters
EVENTS: 1M
EVENT_GENERATION_MODE: Weighted
AMEGIC: {ALLOW_MAPPING: 0}
ME_GENERATORS: [Amegic, Higgs]
SCALES: VAR{Abs2(p[2]+p[3])}

# physics parameters
PARTICLE_DATA:
  4:  {Yukawa: 1.42}
  5:  {Yukawa: 4.92}
  15: {Yukawa: 1.777}
EW_SCHEME: 3
RUN_MASS_BELOW_POLE: 1

PROCESSES:
- 93 93 -> 22 22:
    NLO_Mode: Fixed_Order
    Order: {QCD: 2, EW: 2}
    NLO_Order: {QCD: 1, EW: 0}
    Enable_MHV: 12
    Loop_Generator: Higgs
    Integrator: PS2
    RS_Integrator: PS3

SELECTORS:
- HiggsFinder:
    PT1: 40
    PT2: 30
    Eta: 2.5
    MassRange: [100, 150]
- [IsolationCut, 22, 0.4, 2, 0.025]

Things to notice:

• This calculation is at fixed-order NLO.

• All scales, i.e. the factorisation, renormalisation and resummation scales are set to the invariant mass of the di-photon pair.

• Dedicated phase space generators are used by setting Integrator: PS2 and RS_Integrator: PS3, cf. Integrator.

To compute the interference contribution only, as was done in [DL], one can set HIGGS_INTERFERENCE_ONLY: 1. By default, all partonic processes are included in this simulation, however, it is sensible to disable quark initial states at the leading order. This is achieved by setting HIGGS_INTERFERENCE_MODE: 3.

One can also simulate the production of a spin-2 massive graviton in Sherpa using the same input card by setting HIGGS_INTERFERENCE_SPIN: 2. Only the massive graviton case is implemented, specifically the scenario where k_q=k_g. NLO corrections are approximated, as the gg->X->yy and qq->X->yy loop amplitudes have not been computed so far.

8.3.2. H+jets production in gluon fusion

This is an example setup for inclusive Higgs production through gluon fusion at hadron colliders used in [HKS]. The inclusive process is calculated at next-to-leading order accuracy matched to the parton shower using the MC@NLO prescription detailed in [HKSS12]. The next few higher jet multiplicities, calculated at next-to-leading order as well, are merged into the inclusive sample using the MEPS@NLO method – an extension of the CKKW method to NLO – as described in [HKSS13] and [GHK+13]. Finally, even higher multiplicities, calculated at leading order, are merged on top of that. A few things to note are detailed below the example.

# collider parameters
BEAMS: 2212
BEAM_ENERGIES: 6500

# settings for ME generators
ME_GENERATORS: [Comix, Amegic, Internal, OpenLoops]

# settings for hard decays
HARD_DECAYS:
  Enabled: true
  Channels:
    25,22,22: {Status: 2}
  Apply_Branching_Ratios: false
  Use_HO_SM_Widths: false

# model parameters
MODEL: HEFT
PARTICLE_DATA:
  25: {Mass: 125, Width: 0}

PROCESSES:
- 93 93 -> 25 93{2}:
    Order: {QCD: 2, EW: 0, HEFT: 1}
    CKKW: 30
    2->1-2: { Loop_Generator: Internal }
    2->3: { Loop_Generator: OpenLoops }
    2->1-3:
      NLO_Mode: MC@NLO
      NLO_Order: {QCD: 1, EW: 0}
      ME_Generator: Amegic
      RS_ME_Generator: Comix

Things to notice:

• The example can be converted into a simple MENLOPS setup by replacing 2->1-3 with 2->1, or into an MEPS setup with 2->0, to study the effect of incorporating higher-order matrix elements.

• Providers of the one-loop matrix elements for the respective multiplicities are set using Loop_Generator. For the two simplest cases Sherpa can provide it internally. Additionally, MCFM is interfaced for the H+2jet process, cf. MCFM interface.

• To enable the Higgs to decay to a pair of photons, for example, the hard decays are invoked. For details on the hard decay handling and how to enable specific decay modes see Hard decays.

8.3.3. H+jets production in gluon fusion with finite top mass effects

This is example is similar to H+jets production in gluon fusion but with finite top quark mass taken into account as described in [B+15] for all merged jet multiplicities. Mass effects in the virtual corrections are treated in an approximate way. In case of the tree-level contributions, including real emission corrections, no approximations are made concerning the mass effects.

# collider parameters
BEAMS: 2212
BEAM_ENERGIES: 6500

# settings for ME generators
ME_GENERATORS: [Amegic, Internal, OpenLoops]

# settings for hard decays
HARD_DECAYS:
  Enabled: true
  Channels:
    25,22,22: {Status: 2}
  Apply_Branching_Ratios: false
  Use_HO_SM_Widths: false

# model parameters
MODEL: HEFT
PARTICLE_DATA:
  25: {Mass: 125, Width: 0}

# finite top mass effects
KFACTOR: GGH
OL_IGNORE_MODEL: true
OL_PARAMETERS:
  preset: 2
  allowed_libs: pph2,pphj2,pphjj2
  psp_tolerance: 1.0e-7

PROCESSES:
- 93 93 -> 25 93{1}:
    Order: {QCD: 2, EW: 0, HEFT: 1}
    CKKW: 30
    Loop_Generator: Internal
    2->1-2:
      NLO_Mode: MC@NLO
      NLO_Order: {QCD: 1, EW: 0}

Things to notice:

• One-loop matrix elements from OpenLoops [CMP12] are used in order to correct for top mass effects. Sherpa must therefore be compiled with OpenLoops support to run this example. Also, the OpenLoops process libraries listed in the run card must be installed.

• The maximum jet multiplicities that can be merged in this setup are limited by the availability of loop matrix elements used to correct for finite top mass effects.

• The comments in H+jets production in gluon fusion apply here as well.

8.3.4. H+jets production in associated production

This section collects example setups for Higgs boson production in association with vector bosons

8.3.4.1. Higgs production in association with W bosons and jets

This is an example setup for Higgs boson production in association with a W boson and jets, as used in [HKP+]. It uses the MEPS@NLO method to merge pp->WH and pp->WHj at next-to-leading order accuracy and adds pp->WHjj at leading order. The Higgs boson is decayed to W-pairs and all W decay channels resulting in electrons or muons are accounted for, including those with intermediate taus.

# collider setup
BEAMS: 2212
BEAM_ENERGIES: 6500

ME_GENERATORS: [Comix, Amegic, OpenLoops]

# define custom particle container for easy process declaration
PARTICLE_CONTAINERS:
  900: {Name: W, Flavs: [24, -24]}
  901: {Name: lightflavs, Flavs: [1, -1, 2, -2, 3, -3, 4, -4, 21]}
MC@NLO:
  DISALLOW_FLAVOUR: 5

# particle properties (ME widths need to be zero if external)
PARTICLE_DATA:
  24: {Width: 0}
  25: {Mass: 125.5, Width: 0}
  15: {Stable: 0, Massive: true}


# hard decays setup, specify allowed decay channels, ie.:
# h->Wenu, h->Wmunu, h->Wtaunu, W->enu, W->munu, W->taunu, tau->enunu, tau->mununu + cc
HARD_DECAYS:
  Enabled: true
  Channels:
    25,24,-12,11: {Status: 2}
    25,24,-14,13: {Status: 2}
    25,24,-16,15: {Status: 2}
    25,-24,12,-11: {Status: 2}
    25,-24,14,-13: {Status: 2}
    25,-24,16,-15: {Status: 2}
    24,12,-11: {Status: 2}
    24,14,-13: {Status: 2}
    24,16,-15: {Status: 2}
    -24,-12,11: {Status: 2}
    -24,-14,13: {Status: 2}
    -24,-16,15: {Status: 2}
    15,16,-12,11: {Status: 2}
    15,16,-14,13: {Status: 2}
    -15,-16,12,-11: {Status: 2}
    -15,-16,14,-13: {Status: 2}
  Decay_Tau: 1
  Apply_Branching_Ratios: 0

PROCESSES:
- 901 901 -> 900 25 901{2}:
    Order: {QCD: 0, EW: 2}
    CKKW: 30
    2->2-3:
      NLO_Mode: MC@NLO
      NLO_Order: {QCD: 1, EW: 0}
      ME_Generator: Amegic
      RS_ME_Generator: Comix
      Loop_Generator: OpenLoops

Things to notice:

• Two custom particle container, cf. Particle containers, have been declared, facilitating the process declaration.

• As the bottom quark is treated as being massless by default, a five flavour calculation is performed. The particle container ensures that no external bottom quarks, however, are considered to resolve the overlap with single top and top pair processes.

• OpenLoops [CMP12] is used as the provider of the one-loop matrix elements.

• To enable the decays of the Higgs, W boson and tau lepton the hard decay handler is invoked. For details on the hard decay handling and how to enable specific decay modes see Hard decays.

8.3.4.2. Higgs production in association with Z bosons and jets

This is an example setup for Higgs boson production in association with a Z boson and jets, as used in [HKP+]. It uses the MEPS@NLO method to merge pp->ZH and pp->ZHj at next-to-leading order accuracy and adds pp->ZHjj at leading order. The Higgs boson is decayed to W-pairs. All W and Z bosons are allowed to decay into electrons, muons or tau leptons. The tau leptons are then allowed to decay into all possible partonic channels, leptonic and hadronic, to allow for all possible trilepton signatures, unavoidably producing two and four lepton events as well.

# collider setup
BEAMS: 2212
BEAM_ENERGIES: 6500

ME_GENERATORS: [Comix, Amegic, OpenLoops]

# define custom particle container for easy process declaration
PARTICLE_CONTAINERS:
  901: {Name: lightflavs, Flavs: [1, -1, 2, -2, 3, -3, 4, -4, 21]}
MC@NLO:
  DISALLOW_FLAVOUR: 5

# particle properties (ME widths need to be zero if external)
PARTICLE_DATA:
  23: {Width: 0}
  25: {Mass: 125.5, Width: 0}
  15: {Stable: 0, Massive: true}


# hard decays setup, specify allowed decay channels
# h->Wenu, h->Wmunu, h->Wtaunu, W->enu, W->munu, W->taunu,
# Z->ee, Z->mumu, Z->tautau, tau->any + cc
HARD_DECAYS:
  Enabled: true
  Channels:
    25,24,-12,11: {Status: 2}
    25,24,-14,13: {Status: 2}
    25,24,-16,15: {Status: 2}
    25,-24,12,-11: {Status: 2}
    25,-24,14,-13: {Status: 2}
    25,-24,16,-15: {Status: 2}
    24,12,-11: {Status: 2}
    24,14,-13: {Status: 2}
    24,16,-15: {Status: 2}
    23,15,-15: {Status: 2}
    -24,-12,11: {Status: 2}
    -24,-14,13: {Status: 2}
    -24,-16,15: {Status: 2}
    15,16,-12,11: {Status: 2}
    15,16,-14,13: {Status: 2}
    -15,-16,12,-11: {Status: 2}
    -15,-16,14,-13: {Status: 2}
    15,16,-2,1: {Status: 2}
    15,16,-4,3: {Status: 2}
    -15,-16,2,-1: {Status: 2}
    -15,-16,4,-3: {Status: 2}
  Decay_Tau: 1
  Apply_Branching_Ratios: 0

PROCESSES:
- 901 901 -> 23 25 901{2}:
    Order: {QCD: 0, EW: 2}
    CKKW: 30
    2->2-3:
      NLO_Mode: MC@NLO
      NLO_Order: {QCD: 1, EW: 0}
      ME_Generator: Amegic
      RS_ME_Generator: Comix
      Loop_Generator: OpenLoops

Things to notice:

• A custom particle container, cf. Particle containers, has been declared, facilitating the process declaration.

• As the bottom quark is treated as being massless by default, a five flavour calculation is performed. The particle container ensures that no external bottom quarks, however, are considered to resolve the overlap with single top and top pair processes.

• OpenLoops [CMP12] is used as the provider of the one-loop matrix elements.

• To enable the decays of the Higgs, W and Z bosons and tau lepton the hard decay handler is invoked. For details on the hard decay handling and how to enable specific decay modes see Hard decays.

8.3.4.3. Higgs production in association with lepton pairs

This is an example setup for Higgs boson production in association with an electron-positron pair using the MC@NLO technique. The Higgs boson is decayed to b-quark pairs. Contrary to the previous examples this setup does not use on-shell intermediate vector bosons in its matrix element calculation.

BEAMS: 2212
BEAM_ENERGIES: 6500

ME_GENERATORS: [Comix, Amegic, OpenLoops]

MEPS:
  CORE_SCALE: VAR{Abs2(p[2]+p[3]+p[4])}

PARTICLE_DATA:
  5: {Massive: true}
  15: {Massive: true}
  25: {Stable: 0, Width: 0.0}

# hard decays setup, specify allowed decay channels h->bb
HARD_DECAYS:
  Enabled: true
  Channels:
    25 -> 5 -5: {Status: 2}
  Apply_Branching_Ratios: false

PROCESSES:
- 93 93 -> 11 -11 25:
    Order: {QCD: 0, EW: 3}
    NLO_Mode: MC@NLO
    NLO_Order: {QCD: 1, EW: 0}
    Loop_Generator: OpenLoops
    ME_Generator: Amegic
    RS_ME_Generator: Comix
    Integration_Error: 0.1

Things to notice:

• The central scale is set to the invariant mass of the Higgs boson and the lepton pair.

• As the bottom quark is set to be treated massively, a four flavour calculation is performed.

• OpenLoops [CMP12] is used as the provider of the one-loop matrix elements.

• To enable the decays of the Higgs the hard decay handler is invoked. For details on the hard decay handling and how to enable specific decay modes see Hard decays.

8.3.5. Associated t anti-t H production at the LHC

This set-up illustrates the interface to an external loop matrix element generator as well as the possibility of specifying hard decays for particles emerging from the hard interaction. The process generated is the production of a Higgs boson in association with a top quark pair from two light partons in the initial state. Each top quark decays into an (anti-)bottom quark and a W boson. The W bosons in turn decay to either quarks or leptons.

BEAMS: 2212
BEAM_ENERGIES: 6500

ME_GENERATORS: [Comix, Amegic, OpenLoops]

MEPS:
  CORE_SCALE: VAR{sqr(175+125/2)}

PARTICLE_DATA:
  5: {Yukawa: 4.92}
  6: {Stable: 0, Width: 0.0}
  24: {Stable: 0}
  25: {Stable: 0, Width: 0.0}

# hard decays setup, specify allowed decay channels h->bb
HARD_DECAYS:
  Enabled: true
  Channels:
    25,5,-5: {Status: 2}
  Apply_Branching_Ratios: false

PROCESSES:
- 93 93 -> 25 6 -6:
    Order: {QCD: 2, EW: 1}
    NLO_Mode: MC@NLO
    NLO_Order: {QCD: 1, EW: 0}
    Loop_Generator: OpenLoops
    ME_Generator: Amegic
    RS_ME_Generator: Comix
    Integration_Error: 0.1

Things to notice:

• The virtual matrix elements is interfaced from OpenLoops.

• The top quarks are stable in the hard matrix elements. They are decayed using the internal decay module, indicated by the settings in the HARD_DECAYS and PARTICLE_DATA blocks.

• Widths of top and Higgs are set to 0 for the matrix element calculation. A kinematical Breit-Wigner distribution will be imposed a-posteriori in the decay module.

• The Yukawa coupling of the b-quark has been set to a non-zero value to allow the H->bb decay channel even despite keeping the b-quark massless for a five-flavour-scheme calculation.

• Higgs BRs are not included in the cross section (Apply_Branching_Ratios: false) as they will be LO only and not include loop-induced decays

8.4. Top quark (pair) + jets production

8.4.1. Top quark pair production

# collider setup
BEAMS: 2212
BEAM_ENERGIES: 6500

# scales
EXCLUSIVE_CLUSTER_MODE: 1
MEPS:
  CORE_SCALE: TTBar

# me generator settings
ME_GENERATORS: [Comix, Amegic, OpenLoops]

# decays
HARD_DECAYS:
  Enabled: true
  Channels:
    24,2,-1: {Status: 0}
    24,4,-3: {Status: 0}
    -24,-2,1: {Status: 0}
    -24,-4,3: {Status: 0}

# particle properties (width of external particles of the MEs must be zero)
PARTICLE_DATA:
  6: {Width: 0}

# on-the-fly variations
SCALE_VARIATIONS: 4.0*  # 7-point scale variations

PROCESSES:
- 93 93 -> 6 -6 93{3}:
    Order: {QCD: 2, EW: 0}
    CKKW: 20
    2->2-3:
      NLO_Mode: MC@NLO
      NLO_Order: {QCD: 1, EW: 0}
      ME_Generator: Amegic
      RS_ME_Generator: Comix
      Loop_Generator: OpenLoops
    2->5-8:
      Max_N_Quarks: 6
      Integration_Error: 0.05

Things to notice:

• We use OpenLoops to compute the virtual corrections [CMP12].

• We match matrix elements and parton showers using the MC@NLO technique for massive particles, as described in [HHL+13].

• A non-default METS core scale setter is used, cf. Scale setting in multi-parton processes (METS)

• We enable top decays through the internal decay module using HARD_DECAYS:Enabled: true

• We calculate on-the-fly a 7-point scale variation, cf. On-the-fly event weight variations.

8.4.2. Top quark pair production incuding approximate EW corrections

# collider setup
BEAMS: 2212
BEAM_ENERGIES: 6500

# scales
EXCLUSIVE_CLUSTER_MODE: 1
MEPS:
  CORE_SCALE: TTBar

# me generator settings
ME_GENERATORS: [Comix, Amegic, OpenLoops]

# decays
HARD_DECAYS:
  Enabled: true
  Channels:
    24,2,-1: {Status: 0}
    24,4,-3: {Status: 0}
    -24,-2,1: {Status: 0}
    -24,-4,3: {Status: 0}

# particle properties (width of external particles of the MEs must be zero)
PARTICLE_DATA:
  6: {Width: 0}

# on-the-fly variations (QCD)
SCALE_VARIATIONS: 4.0*  # 7-point scale variations

# on-the-fly variations (EWapprox)
ASSOCIATED_CONTRIBUTIONS_VARIATIONS:
- [EW]
- [EW, LO1]
- [EW, LO1, LO2]
- [EW, LO1, LO2, LO3]

OL_PARAMETERS:
  ew_renorm_scheme: 1

PROCESSES:
- 93 93 -> 6 -6 93{3}:
    Order: {QCD: 2, EW: 0}
    CKKW: 20
    2->2-3:
      NLO_Mode: MC@NLO
      NLO_Order: {QCD: 1, EW: 0}
      ME_Generator: Amegic
      RS_ME_Generator: Comix
      Loop_Generator: OpenLoops
      Associated_Contributions: [EW, LO1, LO2, LO3]
    2->5-8:
      Max_N_Quarks: 6
      Integration_Error: 0.05

Things to notice:

• In addition to the setup in Top quark pair production we add approximate EW corrections, cf. [GLS18].

• Please note: this setup only works with OpenLoops v.2 or later.

• The approximate EW corrections are added as additional variations on the event weight.

8.4.3. Production of a top quark pair in association with a W-boson

# collider setup
BEAMS: 2212
BEAM_ENERGIES: 6500

# me generator settings
ME_GENERATORS: [Comix, Amegic, OpenLoops]

# settings for hard decays
HARD_DECAYS:
  Enabled: true
  Channels:
    24,2,-1: {Status: 0}
    24,4,-3: {Status: 0}
    24,16,-15: {Status: 0}

# model parameters
PARTICLE_DATA:
  6: {Width: 0}
  24: {Width: 0}

# technical parameters
EXCLUSIVE_CLUSTER_MODE: 1

PROCESSES:
- 93 93 -> 6 -6 24:
    NLO_Mode: MC@NLO
    NLO_Order: {QCD: 1, EW: 0}
    Order: {QCD: 2, EW: 1}
    ME_Generator: Amegic
    RS_ME_Generator: Comix
    Loop_Generator: OpenLoops

Things to notice:

• Hard decays are enabled through HARD_DECAYS:Enabled: true.

• Top quarks and W bosons are final states in the hard matrix elements, so their widths are set to zero using Width: 0 in their PARTICLE_DATA settings.

• Certain decay channels are disabled using Status: 0 in the Channels sub-settings of the HARD_DECAYS setting.

8.5. Single-top production in the s, t and tW channel

In this section, examples for single-top production in three different channels are described. For the channel definitions and a validation of these setups, see [BSK].

8.5.1. t-channel single-top production

# SHERPA run card for t-channel single top-quark production at MC@NLO
# and N_f = 5

# collider setup
BEAMS: 2212
BEAM_ENERGIES: 6500

# me generator settings
ME_GENERATORS: [Comix, Amegic, OpenLoops]

# scales
# CORESCALE SingleTop:
#   use Mandelstam \hat{t} for s-channel 2->2 core process
MEPS:
  CORE_SCALE: SingleTop

# disable hadronic W decays
HARD_DECAYS:
  Enabled: true
  Channels:
    24,2,-1: {Status: 0}
    24,4,-3: {Status: 0}
    -24,-2,1: {Status: 0}
    -24,-4,3: {Status: 0}

# choose EW Gmu input scheme
EW_SCHEME: 3

# required for using top-quark in ME
PARTICLE_DATA: { 6: {Width: 0} }

PROCESSES:
- 93 93 -> 6 93:
    NLO_Mode: MC@NLO
    NLO_Order: {QCD: 1, EW: 0}
    Order: {QCD: 0, EW: 2}
    ME_Generator: Amegic
    RS_ME_Generator: Comix
    Loop_Generator: OpenLoops
    Min_N_TChannels: 1  # require t-channel W

Things to notice:

• We use OpenLoops to compute the virtual corrections [CMP12].

• We match matrix elements and parton showers using the MC@NLO technique for massive particles, as described in [HHL+13].

• A non-default METS core scale setter is used, cf. Scale setting in multi-parton processes (METS)

• We enable top and W decays through the internal decay module using HARD_DECAYS:Enabled: true. The W is restricted to its leptonic decay channels.

• By setting Min_N_TChannels: 1, only t-channel diagrams are used for the calculation

8.5.2. t-channel single-top production with N_f=4

# SHERPA run card for t-channel single top-quark production at MC@NLO
# and N_f = 4

# collider setup
BEAMS: 2212
BEAM_ENERGIES: 6500

# me generator settings
ME_GENERATORS: [Comix, Amegic, OpenLoops]

# scales
#   muR = transverse momentum of the bottom
#   muF = muQ = transverse momentum of the top
MEPS:
  CORE_SCALE: VAR{MPerp2(p[2])}{MPerp2(p[3])}{MPerp2(p[2])}

# disable hadronic W decays
HARD_DECAYS:
  Enabled: true
  Channels:
    24,2,-1: {Status: 0}
    24,4,-3: {Status: 0}
    -24,-2,1: {Status: 0}
    -24,-4,3: {Status: 0}

# choose EW Gmu input scheme
EW_SCHEME: 3

PARTICLE_DATA:
  6: {Width: 0}  # required for using top-quark in ME
  5: {Massive: true, Mass: 4.18}  # mass as in NNPDF30_nlo_as_0118_nf_4

# configure for N_f = 4
PDF_LIBRARY: LHAPDFSherpa
PDF_SET: NNPDF30_nlo_as_0118_nf_4
ALPHAS: {USE_PDF: 1}

PROCESSES:
- 93 93 -> 6 -5 93:
    NLO_Mode: MC@NLO
    NLO_Order: {QCD: 1, EW: 0}
    Order: {QCD: 1, EW: 2}
    ME_Generator: Amegic
    RS_ME_Generator: Comix
    Loop_Generator: OpenLoops
    Min_N_TChannels: 1  # require t-channel W

Things to notice:

• We use an Nf4 PDF and use its definition of the bottom mass

• See t-channel single-top production for more comments

8.5.3. s-channel single-top production

# SHERPA run card for s-channel single top-quark production at MC@NLO
# and N_f = 5

# collider setup
BEAMS: 2212
BEAM_ENERGIES: 6500

# me generator settings
ME_GENERATORS: [Comix, Amegic, OpenLoops]

# scales
# CORESCALE SingleTop:
#   use Mandelstam \hat{s} for s-channel 2->2 core process
MEPS:
  CORE_SCALE: SingleTop

# disable hadronic W decays
HARD_DECAYS:
  Enabled: true
  Channels:
    24,2,-1: {Status: 0}
    24,4,-3: {Status: 0}
    -24,-2,1: {Status: 0}
    -24,-4,3: {Status: 0}

# choose EW Gmu input scheme
EW_SCHEME: 3

# required for using top-quark in ME
PARTICLE_DATA: { 6: {Width: 0} }

# there is no bottom in the initial-state in s-channel production
PARTICLE_CONTAINERS:
  900: {Name: lj, Flavs: [1, -1, 2, -2, 3, -3, 4, -4, 21]}

PROCESSES:
- 900 900 -> 6 93:
    NLO_Mode: MC@NLO
    NLO_Order: {QCD: 1, EW: 0}
    Order: {QCD: 0, EW: 2}
    ME_Generator: Amegic
    RS_ME_Generator: Comix
    Loop_Generator: OpenLoops
    Max_N_TChannels: 0  # require s-channel W

Things to notice:

• By excluding the bottom quark from the initial-state at Born level using PARTICLE_CONTAINERS, and by setting Max_N_TChannels: 0, only s-channel diagrams are used for the calculation

• See t-channel single-top production for more comments

8.5.4. tW-channel single-top production

# SHERPA run card for tW-channel single top-quark production at MC@NLO
# and N_f = 5

# collider setup
BEAMS: 2212
BEAM_ENERGIES: 6500

# me generator settings
ME_GENERATORS: [Comix, Amegic, OpenLoops]

# scales
# mu = transverse momentum of the top
MEPS:
  CORE_SCALE: VAR{MPerp2(p[3])}{MPerp2(p[3])}{MPerp2(p[3])}

# disable hadronic W decays
HARD_DECAYS:
  Enabled: true
  Channels:
    24,2,-1: {Status: 0}
    24,4,-3: {Status: 0}
    -24,-2,1: {Status: 0}
    -24,-4,3: {Status: 0}

# choose EW Gmu input scheme
EW_SCHEME: 3

# required for using top-quark/W-boson in ME
PARTICLE_DATA:
  6: {Width: 0}
  24: {Width: 0}

PROCESSES:
- 93 93 -> 6 -24:
    No_Decay: -6  # remove ttbar diagrams
    NLO_Mode: MC@NLO
    NLO_Order: {QCD: 1, EW: 0}
    Order: {QCD: 1, EW: 1}
    ME_Generator: Amegic
    RS_ME_Generator: Comix
    Loop_Generator: OpenLoops

Things to notice:

• By setting No_Decay: -6, the doubly-resonant TTbar diagrams are removed. Only the singly-resonant diagrams remain as required by the definition of the channel.

• See t-channel single-top production for more comments

8.6. Vector boson pairs + jets production

8.6.1. Dilepton, missing energy and jets production

# collider setup
BEAMS: 2212
BEAM_ENERGIES: 6500

# me generator settings
ME_GENERATORS: [Comix, Amegic, OpenLoops]
METS: { CLUSTER_MODE: 16 }

# define parton container without b-quarks to
# remove 0 processes with top contributions
PARTICLE_CONTAINERS:
  901: {Name: lightflavs, Flavs: [1, -1, 2, -2, 3, -3, 4, -4, 21]}
MC@NLO:
  DISALLOW_FLAVOUR: 5

PROCESSES:
- 901 901 -> 90 91 90 91 901{3}:
    Order: {QCD: 0, EW: 4}
    CKKW: 30
    2->4-5:
      NLO_Mode: MC@NLO
      NLO_Order: {QCD: 1, EW: 0}
      ME_Generator: Amegic
      RS_ME_Generator: Comix
      Loop_Generator: OpenLoops
    2->5-7:
      Integration_Error: 0.05

SELECTORS:
- VariableSelector:
    Variable: PT
    Flavs: 90
    Ranges: [[5.0, E_CMS], [5.0, E_CMS]]
    Ordering: [PT_UP]
- [Mass, 11, -11, 10.0, E_CMS]
- [Mass, 13, -13, 10.0, E_CMS]
- [Mass, 15, -15, 10.0, E_CMS]

8.6.2. Dilepton, missing energy and jets production (gluon initiated)

# collider setup
BEAMS: 2212
BEAM_ENERGIES: 6500

# scales
MEPS:
  CORE_SCALE: VAR{Abs2(p[2]+p[3]+p[4]+p[5])/4.0}

# me generator settings
ME_GENERATORS: [Amegic, OpenLoops]
AMEGIC: { ALLOW_MAPPING: 0 }
# the following phase space libraries have to be generated with the
# corresponding qq->llvv setup (Sherpa.tree.yaml) first;
# they will appear in Process/Amegic/lib/libProc_fsrchannels*.so
SHERPA_LDADD: [Proc_fsrchannels4, Proc_fsrchannels5]

PROCESSES:
- 93 93 -> 90 90 91 91 93{1}:
    CKKW: $(QCUT)
    Enable_MHV: 10
    Loop_Generator: OpenLoops
    2->4:
      Order: {QCD: 2, EW: 4}
      Integrator: fsrchannels4
    2->5:
      Order: {QCD: 3, EW: 4}
      Integrator: fsrchannels5
      Integration_Error: 0.02

SELECTORS:
- [Mass, 11, -11, 10.0, E_CMS]
- [Mass, 13, -13, 10.0, E_CMS]
- [Mass, 15, -15, 10.0, E_CMS]

8.6.3. Four lepton and jets production

# collider setup
BEAMS: 2212
BEAM_ENERGIES: 6500

# me generator settings
ME_GENERATORS: [Comix, Amegic, OpenLoops]
METS: { CLUSTER_MODE: 16 }

PROCESSES:
- 93 93 -> 90 90 90 90 93{3}:
    Order: {QCD: 0, EW: 4}
    CKKW: 30
    2->4-5:
      NLO_Mode: MC@NLO
      NLO_Order: {QCD: 1, EW: 0}
      ME_Generator: Amegic
      RS_ME_Generator: Comix
      Loop_Generator: OpenLoops
    2->5-7:
      Integration_Error: 0.05

SELECTORS:
- VariableSelector:
    Variable: PT
    Flavs: 90
    Ranges: [[5.0, E_CMS], [5.0, E_CMS]]
    Ordering: [PT_UP]
- [Mass, 11, -11, 10.0, E_CMS]
- [Mass, 13, -13, 10.0, E_CMS]
- [Mass, 15, -15, 10.0, E_CMS]

8.6.4. Four lepton and jets production (gluon initiated)

# collider setup
BEAMS: 2212
BEAM_ENERGIES: 6500

# scales
MEPS:
  CORE_SCALE: VAR{Abs2(p[2]+p[3]+p[4]+p[5])/4.0}

# me generator settings
ME_GENERATORS: [Amegic, OpenLoops]
AMEGIC: { ALLOW_MAPPING: 0 }
# the following phase space libraries have to be generated with the
# corresponding qq->llll setup (Sherpa.tree.yaml) first;
# they will appear in Process/Amegic/lib/libProc_fsrchannels*.so
SHERPA_LDADD: [Proc_fsrchannels4, Proc_fsrchannels5]

PROCESSES:
- 93 93 -> 90 90 90 90 93{1}:
    CKKW: $(QCUT)
    Enable_MHV: 10
    Loop_Generator: OpenLoops
    2->4:
      Order: {QCD: 2, EW: 4}
      Integrator: fsrchannels4
    2->5:
      Order: {QCD: 3, EW: 4}
      Integrator: fsrchannels5
      Integration_Error: 0.02

SELECTORS:
- [Mass, 11, -11, 10.0, E_CMS]
- [Mass, 13, -13, 10.0, E_CMS]
- [Mass, 15, -15, 10.0, E_CMS]

8.6.5. WZ production with jets production

# collider setup
BEAMS: 2212
BEAM_ENERGIES: 6500

# scales
MEPS:
  CORE_SCALE: VAR{Abs2(p[2]+p[3])/4.0}

# me generator settings
ME_GENERATORS: [Comix, Amegic, OpenLoops]

HARD_DECAYS:
  Enabled: true
  Channels:
    24,2,-1: {Status: 2}
    24,4,-3: {Status: 2}
    -24,-2,1: {Status: 2}
    -24,-4,3: {Status: 2}
    23,12,-12: {Status: 2}
    23,14,-14: {Status: 2}
    23,16,-16: {Status: 2}

PARTICLE_DATA:
  23: {Width: 0}
  24: {Width: 0}

PROCESSES:
- 93 93 -> 24 23 93{3}:
    Order: {QCD: 0, EW: 2}
    CKKW: 30
    2->2-3:
      NLO_Mode: MC@NLO
      NLO_Order: {QCD: 1, EW: 0}
      ME_Generator: Amegic
      RS_ME_Generator: Comix
      Loop_Generator: OpenLoops
    2->3-7:
      Integration_Error: 0.05
- 93 93 -> -24 23 93{3}:
    Order: {QCD: 0, EW: 2}
    CKKW: 30
    2->2-3:
      NLO_Mode: MC@NLO
      NLO_Order: {QCD: 1, EW: 0}
      ME_Generator: Amegic
      RS_ME_Generator: Comix
      Loop_Generator: OpenLoops
    2->3-7:
      Integration_Error: 0.05

8.6.6. Same sign dilepton, missing energy and jets production

# collider setup
BEAMS: 2212
BEAM_ENERGIES: 6500

# choose EW Gmu input scheme
EW_SCHEME: 3

# tags for process setup
TAGS:
  NJET: 1
  QCUT: 30

# scales
MEPS:
  CORE_SCALE: VAR{Abs2(p[2]+p[3]+p[4]+p[5])}
EXCLUSIVE_CLUSTER_MODE: 1

# solves problem with dipole QED modeling
ME_QED: { CLUSTERING_THRESHOLD: 10 }

# improve integration performance
PSI: { ITMIN: 25000 }
INTEGRATION_ERROR: 0.05

PROCESSES:
- 93 93 -> 11 11 -12 -12 93 93 93{$(NJET)}:
    Order: {QCD: 0, EW: 6}
    CKKW: $(QCUT)
- 93 93 -> 13 13 -14 -14 93 93 93{$(NJET)}:
    Order: {QCD: 0, EW: 6}
    CKKW: $(QCUT)
- 93 93 -> 15 15 -16 -16 93 93 93{$(NJET)}:
    Order: {QCD: 0, EW: 6}
    CKKW: $(QCUT)
- 93 93 -> 11 13 -12 -14 93 93 93{$(NJET)}:
    Order: {QCD: 0, EW: 6}
    CKKW: $(QCUT)
- 93 93 -> 11 15 -12 -16 93 93 93{$(NJET)}:
    Order: {QCD: 0, EW: 6}
    CKKW: $(QCUT)
- 93 93 -> 13 15 -14 -16 93 93 93{$(NJET)}:
    Order: {QCD: 0, EW: 6}
    CKKW: $(QCUT)
- 93 93 -> -11 -11 12 12 93 93 93{$(NJET)}:
    Order: {QCD: 0, EW: 6}
    CKKW: $(QCUT)
- 93 93 -> -13 -13 14 14 93 93 93{$(NJET)}:
    Order: {QCD: 0, EW: 6}
    CKKW: $(QCUT)
- 93 93 -> -15 -15 16 16 93 93 93{$(NJET)}:
    Order: {QCD: 0, EW: 6}
    CKKW: $(QCUT)
- 93 93 -> -11 -13 12 14 93 93 93{$(NJET)}:
    Order: {QCD: 0, EW: 6}
    CKKW: $(QCUT)
- 93 93 -> -11 -15 12 16 93 93 93{$(NJET)}:
    Order: {QCD: 0, EW: 6}
    CKKW: $(QCUT)
- 93 93 -> -13 -15 14 16 93 93 93{$(NJET)}:
    Order: {QCD: 0, EW: 6}
    CKKW: $(QCUT)

SELECTORS:
- [PT, 90, 5.0, E_CMS]
- NJetFinder:
    N: 2
    PTMin: 15.0
    ETMin: 0.0
    R: 0.4
    Exp: -1

8.6.7. Polarized same-sign \(\mathrm{W}^+\) boson pair production in association with two jets at LO+PS

This is an example for the simulation of polarized cross sections for pure electroweak same-sign \(\mathrm{W}^+\) boson pair production in association with two jets at LO+PS.

# collider setup
BEAMS: 2212
BEAM_ENERGIES: 6500

# ME-Generator settings
ME_GENERATORS:
- Comix
COMIX_DEFAULT_GAUGE: 0

# scales
MEPS:
  CORE_SCALE: VAR{0.5*Abs2(p[2]+p[3])} 

# width 0 for the stable W bosons in the hard matrix element
# width 0 for Z boson to preserve SU(2) Ward Identities
PARTICLE_DATA:
  24: {Width: 0}
  23: {Width: 0}
WIDTH_SCHEME: Fixed

# decay channels & polarization settings
HARD_DECAYS:
  Enabled: true
  Channels:
    24,12,-11: {Status: 2}
    24,14,-13: {Status: 2}
  Pol_Cross_Section: 
   Enabled: true
   Reference_System: [Lab, COM]

# vector boson production process
PROCESSES:
- 93 93 -> 24 24 93 93:
    Order: {QCD: 0, EW: 4} 

# cuts on PROCESSES final state particles
SELECTORS:
- FastjetSelector:
    Expression: Mass(p[4]+p[5])>500 
    Algorithm: antikt
    N: 2
    PTMin: 20.0
    EtaMax: 5.0
- FastjetSelector:
    Expression: abs(Eta(p[4])-Eta(p[5]))>2.5
    Algorithm: antikt
    N: 2
    PTMin: 20.0
    EtaMax: 5.0

Things to notice:

• The COMIX_DEFAULT_GAUGE is set to a special value to get the polarization vectors mentioned in section Simulation of polarized cross sections for intermediate particles .

• The width of the \(\mathrm{W}^\pm\) boson is set to zero to retain gauge invariance since it is considered as stable during the hard scattering process (PROCESSES). To preserve SU(2) Ward Identities also the width of the Z boson need to be set to zero then.

• The process is divided into the production of the vector bosons (PROCESSES) and their decays (HARD_DECAYS), all matrix elements are calculated with on-shell vector bosons (narrow-width approximation). Mass_Smearing and SPIN_CORRELATIONS are enabled per default.

8.6.8. Polarized \(\mathrm{W}^+\) Z boson pair production -pair production at nLO+PS

This is an example for the simulation of polarized cross sections for pure electroweak \(\mathrm{W}^+\) Z boson pair production at nLO+PS. The resulting unpolarized cross section contains all NLO QCD corrections while for polarized cross sections the effect of virtual corrections on the polarization fractions is neglected.

# collider setup
BEAMS: 2212
BEAM_ENERGIES: 6500

# settings matrix-element generation
ME_GENERATORS:
  - Comix
  - Amegic
  - OpenLoops
COMIX_DEFAULT_GAUGE: 0

# scale setting
SCALES: METS{0.25*sqr(80.352+91.153)}

# width 0 for the stable vector bosons in the hard matrix element
PARTICLE_DATA:
  24: 
    Width: 0
  23:
    Width: 0
WIDTH_SCHEME: Fixed

# speed and neg weight fraction improvements
MC@NLO:
  PSMODE: 2

# vector boson production part pp -> WZ
PROCESSES:
# leading order
- 93 93 -> 24 23:
    Order: {QCD: 0, EW: 2}
# NLO QCD corrections
    NLO_Mode: MC@NLO
    NLO_Order: {QCD: 1, EW: 0}
    ME_Generator: Amegic
    RS_ME_Generator: Comix
    Loop_Generator: OpenLoops

# vector boson decays
HARD_DECAYS:
  Enabled: true
  Channels:
    24,12,-11: {Status: 2}
    23,13,-13: {Status: 2}
# settings for polarized cross sections 
  Pol_Cross_Section:
    Enabled: true
    Reference_System: [Lab, COM]

8.7. Event generation in the MSSM using UFO

This is an example for event generation in the MSSM using Sherpa’s UFO support. In the corresponding Example directory <prefix>/share/SHERPA-MC/Examples/BSM/UFO_MSSM/, you will find a directory MSSM that contains the UFO output for the MSSM (https://feynrules.irmp.ucl.ac.be/wiki/MSSM). To run the example, generate the model as described in UFO Model Interface by executing

$ cd <prefix>/share/SHERPA-MC/Examples/BSM/UFO_MSSM/
$ <prefix>/bin/Sherpa-generate-model MSSM

An example run card will be written to the working directory. Use this run card as a template to generate events.

8.8. Deep-inelastic scattering

8.8.1. DIS at HERA

This is an example of a setup for hadronic final states in deep-inelastic lepton-nucleon scattering at a centre-of-mass energy of 300 GeV. Corresponding measurements were carried out by the H1 and ZEUS collaborations at the HERA collider at DESY Hamburg.

# collider setup
BEAMS: [-11, 2212]
BEAM_ENERGIES: [27.5, 820]
PDF_SET: [None, Default]

# technical parameters
TAGS:
  QCUT: 5
  SDIS: 1.0
  LGEN: BlackHat
ME_GENERATORS:
  - Comix
  - Amegic
  - $(LGEN)
RESPECT_MASSIVE_FLAG: true
SHOWER:
  KIN_SCHEME: 1

# hadronization tune
PARJ:
  - [21, 0.432]
  - [41, 1.05]
  - [42, 1.0]
  - [47, 0.65]
MSTJ:
  - [11, 5]
FRAGMENTATION: Lund
DECAYMODEL: Lund

PROCESSES:
- -11 93 -> -11 93 93{4}:
    CKKW: $(QCUT)/sqrt(1.0+sqr($(QCUT)/$(SDIS))/Abs2(p[2]-p[0]))
    Order: {QCD: 0, EW: 2}
    Max_N_Quarks: 6
    Loop_Generator: $(LGEN)
    2->2-3:
      NLO_Mode: MC@NLO
      NLO_Order: {QCD: 1, EW: 0}
      ME_Generator: Amegic
      RS_ME_Generator: Comix
    2->3:
      PSI_ItMin: 25000
      Integration_Error: 0.03

SELECTORS:
- [Q2, -11, -11, 4, 1e12]

Things to notice:

• the beams are asymmetric with the positrons at an energy of 27.5 GeV, while the protons carry 820 GeV of energy.

• the multi-jet merging cut is set dynamically for each event, depending on the photon virtuality, see [CGH10].

• there is a selector cut on the photon virtuality. This cut implements the experimental requirements for identifying the deep-inelastic scattering process.

8.9. Fixed-order next-to-leading order calculations

8.9.1. Production of NTuples

Root NTuples are a convenient way to store the result of cumbersome fixed-order calculations in order to perform multiple analyses. This example shows how to generate such NTuples and reweighted them in order to change factorisation and renormalisation scales. Note that in order to use this setup, Sherpa must be configured with option -DSHERPA_ENABLE_ROOT=ON, see Event output formats. If Sherpa has not been configured with Rivet analysis support, please disable the analysis using -a0 on the command line, see Command Line Options.

When using NTuples, one needs to bear in mind that every calculation involving jets in the final state is exclusive in the sense that a lower cut-off on the jet transverse momenta must be imposed. It is therefore necessary to check whether the event sample stored in the NTuple is sufficiently inclusive before using it. Similar remarks apply when photons are present in the NLO calculation or when cuts on leptons have been applied at generation level to increase efficiency. Every NTuple should therefore be accompanied by an appropriate documentation.

NTuple compression can be customized using the parameter ROOTNTUPLE_COMPRESSION, which is used to call TFile::SetCompressionSettings. For a detailed documentation of available options, see http://root.cern.ch

This example will generate NTuples for the process pp->lvj, where l is an electron or positron, and v is an electron (anti-)neutrino. We identify parton-level jets using the anti-k_T algorithm with R=0.4 [CSS08]. We require the transverse momentum of these jets to be larger than 20 GeV. No other cuts are applied at generation level.

EVENTS: 100k
EVENT_GENERATION_MODE: Weighted
TAGS:
  LGEN: BlackHat
ME_GENERATORS: [Amegic, $(LGEN)]
# Analysis (please configure with -DSHERPA_ENABLE_RIVET=ON & -DSHERPA_ENABLE_HEPMC3=ON)
ANALYSIS: Rivet
ANALYSIS_OUTPUT: Analysis/HTp/BVI/
# NTuple output (please configure with '-DSHERPA_ENABLE_ROOT=ON')
EVENT_OUTPUT: EDRoot[NTuple_B-like]
BEAMS: 2212
BEAM_ENERGIES: 3500
SCALES: VAR{sqr(sqrt(H_T2)-PPerp(p[2])-PPerp(p[3])+MPerp(p[2]+p[3]))/4}
EW_SCHEME: 0
WIDTH_SCHEME: Fixed  # sin\theta_w -> 0.23
DIPOLES: {ALPHA: 0.03}
PARTICLE_DATA:
  13: {Massive: true}
  15: {Massive: true}
PROCESSES:
# The Born piece
- 93 93 -> 90 91 93:
    Order: {QCD: 1, EW: 2}
    NLO_Order: {QCD: 1, EW: 0}
    NLO_Mode: Fixed_Order
    NLO_Part: B
# The virtual piece
- 93 93 -> 90 91 93:
    Order: {QCD: 1, EW: 2}
    NLO_Order: {QCD: 1, EW: 0}
    NLO_Mode: Fixed_Order
    NLO_Part: V
    Loop_Generator: $(LGEN)
# The integrated subtraction piece
- 93 93 -> 90 91 93:
    Order: {QCD: 1, EW: 2}
    NLO_Order: {QCD: 1, EW: 0}
    NLO_Mode: Fixed_Order
    NLO_Part: I
SELECTORS:
- FastjetFinder:
    Algorithm: antikt
    N: 1
    PTMin: 20
    ETMin: 0
    DR: 0.4
RIVET:
  --analyses: ATLAS_2012_I1083318
  USE_HEPMC_SHORT: 1
  --ignore-beams: 1

Things to notice:

• NTuple production is enabled by EVENT_OUTPUT: Root[NTuple_B-like], see Event output formats.

• The scale used is defined as in [BBD+09].

• EW_SCHEME: 0 and WIDTH_SCHEME: Fixed are used to set the value of the weak mixing angle to 0.23, consistent with EW precision measurements.

• DIPOLES:ALPHA: 0.03 is used to limit the active phase space of dipole subtractions.

• 13:Massive: true and 15:Massive: 1 are used to limit the number of active lepton flavours to electron and positron.

• The option USE_HEPMC_SHORT: 1 is used in the Rivet analysis section as the events produced by Sherpa are not at particle level.

8.9.1.1. NTuple production

Start Sherpa using the command line

$ Sherpa Sherpa.B-like.yaml

Sherpa will first create source code for its matrix-element calculations. This process will stop with a message instructing you to compile. Do so by running

$ ./makelibs -j4

Launch Sherpa again, using

$ Sherpa Sherpa.B-like.yaml

Sherpa will then compute the Born, virtual and integrated subtraction contribution to the NLO cross section and generate events. These events are analysed using the Rivet library and stored in a Root NTuple file called NTuple_B-like.root. We will use this NTuple later to compute an NLO uncertainty band.

The real-emission contribution, including subtraction terms, to the NLO cross section is computed using

$ Sherpa Sherpa.R-like.yaml

Events are generated, analysed by Rivet and stored in the Root NTuple file NTuple_R-like.root.

The two analyses of events with Born-like and real-emission-like kinematics need to be merged, which can be achieved using scripts like yodamerge. The result can then be plotted and displayed.

8.9.1.2. Usage of NTuples in Sherpa

Next we will compute the NLO uncertainty band using Sherpa. To this end, we make use of the Root NTuples generated in the previous steps. Note that the setup files for reweighting are almost identical to those for generating the NTuples. We have simply replaced EVENT_OUTPUT by EVENT_INPUT.

We re-evaluate the events with the scale variation as defined in the Reweight configuration files:

$ Sherpa Sherpa.Reweight.B-like.yaml
$ Sherpa Sherpa.Reweight.R-like.yaml

The contributions can again be combined using yodamerge.

8.9.2. MINLO

The following configuration file shows how to implement the MINLO procedure from [HNZ]. A few things to note are detailed below. MINLO can also be applied when reading NTuples, see Production of NTuples. In this case, the scale and K factor must be defined, see SCALES and KFACTOR.

BEAMS: 2212
BEAM_ENERGIES: 6500

EVENT_GENERATION_MODE: W
MEPS:
  CORE_SCALE: VAR{Abs2(p[2]+p[3])+0.25*sqr(sqrt(H_T2)-PPerp(p[2])-PPerp(p[3])+PPerp(p[2]+p[3]))}

PROCESSES:
- 93 93 -> 11 -12 93:
    Scales: MINLO
    KFactor: MINLO
    ME_Generator: Amegic
    Loop_Generator: BlackHat
    Order: {QCD: 1, EW: 2}

SELECTORS:
- [Mass, 11, -12, 2, E_CMS]
- FastjetFinder:
    Algorithm: antikt
    N: 1
    PTMin: 1.0
    ETMin: 1.0
    DR: 0.4

Things to notice:

• The R parameter of the flavour-based kT clustering algorithm can be changed using MINLO:DELTA_R.

• Setting MINLO: {SUDAKOV_MODE: 0} defines whether to include power corrections stemming from the finite parts in the integral over branching probabilities. It defaults to 1.

• The parameter MINLO:SUDAKOV_PRECISION defines the precision target for integration of the Sudakov exponent. It defaults to 1e-4.

8.10. Soft QCD: Minimum Bias and Cross Sections

8.10.1. Calculation of inclusive cross sections

Note that this example is not yet updated to the new YAML input format. Contact the Authors for more information.

(run){
  OUTPUT              = 2
  EVENT_TYPE          = MinimumBias
  SOFT_COLLISIONS     = Shrimps
  Shrimps_Mode        = Xsecs

  deltaY    =  1.5;
  Lambda2   =  1.7;
  beta_0^2  =  20.0;
  kappa     =  0.6;
  xi        =  0.2;
  lambda    =  0.3;
  Delta     =  0.4;
}(run)

(beam){
  BEAM_1 =  2212; BEAM_ENERGY_1 = 450.;
  BEAM_2 =  2212; BEAM_ENERGY_2 = 450.;
}(beam)

(me){
  ME_SIGNAL_GENERATOR = None
}(me)

Things to notice:

• Inclusive cross sections (total, inelastic, low-mass single-diffractive, low-mass double-diffractive, elastic) and the elastic slope are calculated for varying centre-of-mass energies in pp collisions

• The results are written to the file InclusiveQuantities/xsecs_total.dat and to the screen. The directory will automatically be created in the path from where Sherpa is run.

• The parameters of the model are not very well tuned.

8.10.2. Simulation of Minimum Bias events

Contact the Authors for more information.

BEAMS: 2212
BEAM_ENERGIES: 3500

EVENT_TYPE:          MinimumBias
ME_GENERATORS:       None
SOFT_COLLISIONS:     Shrimps
Shrimps_Mode:        Inelastic
FRAGMENTATION:       Ahadic
YFS:
  MODE:              None

ANALYSIS: Rivet
ANALYSIS_OUTPUT: Shrimps

RIVET:
  --analyses: [ATLAS_2010_S8918562, ATLAS_2010_S8894728, ATLAS_2011_S8994773, ATLAS_2012_I1084540, TOTEM_2012_I1115294, CMS_2011_S8978280, CMS_2011_S9120041, CMS_2011_S9215166]

Things to notice:

• The SHRiMPS model is not properly tuned yet – all parameters are set to very natural values, such as for example 1.0 GeV for infrared parameters.

• Elastic scattering and low-mass diffraction are not included.

• A large number of Minimum Bias-type analyses is enabled.

8.11. Setups for event production at B-factories

8.11.1. QCD continuum

Example setup for QCD continuum production at the Belle/KEK collider. Please note, it does not include any hadronic resonance.

# collider setup
BEAMS:  [