# 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].

Please note: AMEGIC can only be used for the built-in models (SM and HEFT). For anything else, please use Comix.

## 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 electro-weak 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 alphamZ. 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.

To account for quark mixing the CKM matrix elements have to be assigned. For this purpose the Wolfenstein parametrization [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 parametrizes 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 parametrisation. 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. If 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. Similarily, 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],:cite:Christensen2009jx, 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 --enable-ufo option of the configure script, as described in Installation. This requires Python version 2.6 or later and an installation of SCons. The above command generates source code for the UFO model, compiles it, and installs the corresponding library, making it available for event generation. Python, SCons, 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 durin 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 relevan command line arguments.

An example configuration file 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, 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 (hadronization, 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. For more details on the Sherpa interface to FeynRules please consult [CdAD+11],:cite:Hoeche2014kca.

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.