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).