Chapter 17 New External Physics Models
It is never possible to include all incarnations of physics models that can be described by the maybe weirdest form of a quantum field theory in a tailor-made implementation within a program like WHIZARD. Users clearly want to be able to use their own special type of model; in order to do so there are external tools to translate models described by their field content and Lagrangian densities into Feynman rules and make them available in an event generator like WHIZARD. In this chapter, we describe the interfaces to two such external models, SARAH and FeynRules. The FeynRules interface had been started already for the legacy version WHIZARD1 (where it had to be downloaded from https://whizard.hepforge.org as a separate package), but for the WHIZARDtwo release series it has been included in the FeynRules package (from their version v1.6.0 on). Note that there was a regression for the usage of external models (from either SARAH or FeynRules) in the first release of series v2.2, v2.2.0. This has been fixed in all upcoming versions. Besides using SARAH or FeynRules via their interfaces, there is now a much easier way to let those programs output model files in the "Universal FeynRules Output" (or UFO). This option does not have any principle limitations for models, and also does not rely on the never truly constant interfaces between two different tools. Their usage is described in Sec. 17.3. 17.1 New physics models via SARAHSARAH [75, 76, 77, 78, 79] is a Mathematica [80] package which derives for a given model the minimum conditions of the vacuum, the mass matrices, and vertices at tree-level as well as expressions for the one-loop corrections for all masses and the full two-loop renormalization group equations (RGEs). The vertices can be exported to be used with WHIZARD/O’Mega. All other information can be used to generate Fortran source code for the RGE solution tool and spectrum generator SPheno [81, 82] to get a spectrum generator for any model. The advantage is that SPheno calculates a consistent set of parameters (couplings, masses, rotation matrices, decay widths) which can be used as input for WHIZARD. SARAH and SPheno can be also downloaded from the HepForge server: 17.1.1 WHIZARD/O’Mega model files from SARAHGenerating the model filesHere we are giving only the information relevant to generate models for WHIZARD. For more details about the installation of SARAH and an exhaustion documentation about its usage, confer the SARAH manual. To generate the model files for WHIZARD/O’Mega with SARAH, a new Mathematica session has to be started. SARAH is loaded via
if SARAH has been stored in the applications directory of Mathematica. Otherwise, the full path has to be given
To get an overview which models are delivered with SARAH, the command
Finally, the output intended for WHIZARD/O’Mega is started via
The possible options of the
All options and the default values are also shown in the
Mathematica session via Using the generated model files with WHIZARDAfter the interface has completed evaluation, the generated files can
be found in the subdirectory
and run
By default, the last command installs the compiled model into
If the files are installed into the WHIZARD
installation prefix, the program will also pick them up automatically, while
WHIZARD’s
More information on the available options and their syntax can be obtained with
the
After the model is compiled it can be used in WHIZARD as
17.1.2 Linking SPheno and WHIZARD
As mentioned above, the user can also use SPheno to generate spectra
for its models. This is done by means of Fortran code for SPheno,
exported from SARAH. To do so, the user has to apply the command
Afterwards, SPheno returns not only the spectrum file in the
standard SUSY Les Houches accord (SLHA) format (for more details about
the SLHA and the WHIZARD SLHA interface cf. Sec. 10.2),
but also an additional file called
17.1.3 BSM ToolboxA convenient way to install SARAH together with WHIZARD, SPheno and some other codes are the BSM Toolbox scripts 2 [83]. These scripts are available at
The Toolbox provides two scripts. First, the
The After
The 17.2 New physics models via FeynRulesIn this section, we present the interface between the external tool FeynRules [84, 85, 86] and WHIZARD. FeynRules is a Mathematica [80] package that allows to derive Feynman rules from any perturbative quantum field theory-based Lagrangian in an automated way. It can be downloaded from The input provided by the user is threefold and consists of the Lagrangian defining the model, together with the definitions of all the particles and parameters that appear in the model. Once this information is provided, FeynRules can perform basic checks on the sanity of the implementation (e.g. hermiticity, normalization of the quadratic terms), and finally computes all the interaction vertices associated with the model and store them in an internal format for later processing. After the Feynman rules have been obtained, FeynRules can export the interaction vertices to WHIZARD via a dedicated interface [87]. The interface checks whether all the vertices are compliant with the structures supported by WHIZARD’s matrix element generator O’Mega, and discard them in the case they are not supported. The output of the interface consists of a set of files organized in a single directory which can be injected into WHIZARD/O’Mega and used as any other built-in models. Together with the model files, a framework is created which allows to communicate the new models to WHIZARD in a well defined way, after which step the model can be used exactly like the built-in ones. This specifically means that the user is not required to manually modify the code of WHIZARD/O’Mega, the models created by the interface can be used directly without any further user intervention. We first describe the installation and general usage of the interface, and then list the general properties like the supported particle types, color quantum numbers and Lorentz structures as well as types of gauge interactions. 17.2.1 Installation and Usage of the WHIZARD-FeynRules interfaceInstallation and basic usage:From FeynRules version 1.6.0 onward, the interface to WHIZARD is part of the FeynRules distribution3. In addition, the latest version of the interface can be downloaded from the WHIZARD homepage on HepForge. There you can also find an installer that can be used to inject the interface into an existing FeynRules installation (which allows to use the interface with the FeynRules release series1.4.x where it is not part of the package). Once installed, the interface can be called and used in the same way FeynRules’ other interfaces described in [84]. The details of how to install and use FeynRules itself can be found there, [84, 85, 86]. Here, we only describe how to use the interface to inject new models into WHIZARD. For example, once the FeynRules environment has been initialized and a model has been loaded, the command
will call the FeynmanRules command to extract the Feynman rules from the Lagrangian L, translate them together with the model data and finally write the files necessary for using the model within WHIZARD to an output directory (the name of which is inferred from the model name by default). Options can be added for further control over the translation process (see Sec. 17.2.2). Instead of using a Lagrangian, it is also possible to call the interface on a pure vertex list. For example, the following command
will directly translate the vertex list list. Note that this vertex list must be given in flavor-expanded form in order for the interface to process it correctly. The interface also supports the WriteWOExtParams command described in [84]. Issuing
will write a list of all the external parameters to filename. This is done in the form of a SINDARIN script. The only option accepted by the command above is the target version of WHIZARD, set by the option WOWhizardVersion. During execution, the interface will print out a series of messages. It is highly advised to carefully read through this output as it not only summarizes the settings and the location of the output files, but also contains information on any skipped vertices or potential incompatibilities of the model with WHIZARD. After the interface has run successfully and written the model files to the output directory, the model must be imported into WHIZARD. For doing so, the model files have to be compiled and can then be installed independently of WHIZARD. In the simplest scenario, assuming that the output directory is the current working directory and that the WHIZARD binaries can be found in the current ${PATH}, the installation is performed by simply executing
This will compile the model and install it into the directory ${HOME}/.whizard, making it fully available to WHIZARD without any further intervention. The build system can be adapted to more complicated cases through several options to the configure which are listed in the INSTALL file created in the output directory. A detailed explanation of all options can be found in Sec. 17.2.2. Supported fields and vertices:The following fields are currently supported by the interface: scalars, Dirac and Majorana fermions, vectors and symmetric tensors. The set of accepted operators, the full list of which can be found in Tab. 17.1, is a subset of all the operators supported by O’Mega. While still limited, this list is sufficient for a large number of BSM models. In addition, a future version of WHIZARD/O’Mega will support the definition of completely general Lorentz structures in the model, allowing the interface to translate all interactions handled by FeynRules. This will be done by means of a parser within O’Mega of the UFO file format for model files from FeynRules.
Color:Color is treated in O’Mega in the color flow decomposition, with the flow structure being implicitly determined from the representations of the particles present at the vertex. Therefore, the interface has to strip the color structure from the vertices derived by FeynRules before writing them out to the model files. While this process is straightforward for all color structures which correspond only to a single flow assignment, vertices with several possible flow configurations must be treated with care in order to avoid mismatches between the flows assigned by O’Mega and those actually encoded in the couplings. To this end, the interface derives the color flow decomposition from the color structure determined by FeynRules and rejects all vertices which would lead to a wrong flow assignment by O’Mega (these rejections are accompanied by warnings from the interface)4. At the moment, the SU(3)C representations supported by both WHIZARD and the interface are singlets (1), triplets (3), antitriplets (3) and octets (8). Tab. 17.2 shows all combinations of these representations which can form singlets together with the support status of the respective color structures in WHIZARD and the interface. Although the supported color structures do not comprise all possible singlets, the list is sufficient for a large number of SM extensions. Furthermore, a future revision of WHIZARD/O’Mega will allow for explicit color flow assignments, thus removing most of the current restrictions.
Running αS:While a running strong coupling is fully supported by the interface, a choice has to be made which quantities are to be reevaluated when the strong coupling is evolved. By default aS, G (see Ref. [84] for the nomenclature regarding the QCD coupling) and any vertex factors depending on them are evolved. The list of internal parameters that are to be recalculated (together with the vertex factors depending on them) can be extended (beyond aS and G) by using the option WORunParameters when calling the interface 6. Gauge choices:The interface supports the unitarity, Feynman and Rξ gauges. The choice of gauge must be communicated to the interface via the option WOGauge. Note that massless gauge bosons are always treated in Feynman gauge. If the selected gauge is Feynman or Rξ, the interface can automatically assign the proper masses to the Goldstone bosons. This behavior is requested by using the WOAutoGauge option. In the Rξ gauges, the symbol representing the gauge ξ must be communicated to the interface by using the WOGaugeSymbol option (the symbol is automatically introduced into the list of external parameters if WOAutoGauge is selected at the same time). This feature can be used to automatically extend models implemented in Feynman gauge to the Rξ gauges. Since WHIZARD (at least until the release series 2.3) is a tree-level tool working with helicity amplitudes, the ghost sector is irrelevant for WHIZARD and hence dropped by the interface. 17.2.2 Options of the WHIZARD-FeynRules interfaceIn the following we present a comprehensive list of all the options accepted by WriteWOOutput. Additionally, we note that all options of the FeynRules command FeynmanRules are accepted by WriteWOOutput, which passes them on to FeynmanRules.
17.2.3 Validation of the interfaceThe output of the interface has been extensively validated. Specifically, the integrated cross sections for all possible 2→ 2 processes in the FeynRules SM, the MSSM and the Three-Site Higgsless Model have been compared between WHIZARD, MadGraph, and CalcHep, using the respective FeynRules interfaces as well as the in-house implementations of these models (the Three-Site Higgsless model not being available in MadGraph). Also, different gauges have been checked for WHIZARD and CalcHep. In all comparisons, excellent agreement within the Monte Carlo errors was achieved. The detailed comparison including examples of the comparison tables can be found in [87]. 17.2.4 Examples for the WHIZARD-/FeynRules interfaceHere, we will use the Standard Model, the MSSM and the Three-Site Higgsless Model as prime examples to explain the usage of the interface. Those are the models that have been used in the validation of the interface in [87]. The examples are constructed to show the application of the different options of the interface and to serve as a starting point for the generation of the user’s own WHIZARD versions of other FeynRules models. WHIZARD-FeynRules example: Standard ModelTo start off, we will create Whizard 2 versions of the Standard Model as implemented in FeynRules for different gauge choices. SM: Unitarity GaugeIn order to invoke FeynRules, we change to the corresponding directory and load the program in Mathematica via
The model is loaded by
Note that the second line is required to switch the Standard Model to Unitarity gauge as opposed to Feynman gauge (which is the default). Generating a WHIZARD model is now simply done by
After invokation, the interface first gives a short summary of the setup
Note that, as we have not changed any options, those settings represent the
defaults. The output proceeds with the calculation of the Feynman rules from the
Standard Model Lagrangian
The last line of the above output is particularily interesting, as it informs us that everything worked out correctly: the interface was able to match all vertices, and the only discarded vertex was the QCD ghost interaction. After the interface has finished running, the model files in the output directory are ready to use and can be compiled using the procedure described in the previous section. SM: Feynman and Rξ gaugesAs the Standard Model as implemented in FeynRules also supports Feynman gauge, we can use the program to generate a Feynman gauge version of the model. Loading FeynRules and the model proceeds as above, with the only difference being the change
In order to inform the interface about the modified gauge, we have to
add the option
The modified gauge is reflected in the output of the interface
The summary of the vertex identification now takes the following form
Again, this line tells us that there were no problems — the only discarded interactions involved the ghost sector which is irrelevant for the tree-level part of WHIZARD. For a tree-level calculation, the only difference between the different gauges from the perspective of the interface are the gauge boson propagators and the Goldstone boson masses. Therefore, the interface can automatically convert a model in Feynman gauge to a model in Rξ gauge. To this end, the call to the interface must be changed to
The
The modified setup is again reflected in the interface output
Note the default choice While the Compilation and usageIn order to compile and use the freshly generated model files, change to the
output directory which can be determined from the interface output (in this
example, it is
The model is now ready and can be used similarly to the builtin WHIZARD models. For example, a minimal WHIZARD input file for calculating the e+e− —→ W+W− scattering cross section in the freshly generated model would look like
WHIZARD/FeynRules example: MSSMIn this Section, we illustrate the usage of the interface between FeynRules and Whizard in the context of the MSSM. All the parameters of the model are then ordered in Les Houches blocks and counters following the SUSY Les Houches Accord (SLHA) [52, 53, 54] (cf. also Sec. 10.2). After having downloaded the model
from the FeynRules website, we store it in a new directory, labelled
We are again adopting unitarity gauge. The number of vertices associated to supersymmetric Lagrangians is in general
very large (several thousands). For such models with many interactions,
it is recommended to first extract all the Feynman rules of the theory before
calling the interface between WHIZARD and FeynRules.
The reason is related to the efficiency of the interface which takes
a lot of time in the extraction of the interaction vertices. In the
case one wishes to study the phenomenology of several benchmark
scenarios, this procedure, which is illustrated below,
allows to use the interface in the best way. The Feynman rules
are derived from the Lagrangian once and for all and then reused by the
interface for each set of WHIZARD model files to be produced,
considerably speeding up the generation of multiple model files
issued from a single Lagrangian. In addition, the scalar potential of
supersymmetric theories contains a large set of four scalar
interactions, in general irrelevant for collider phenomenology. These
vertices can be neglected with the help of the
where By default, all the parameters of the model are set to the value of 1. A complete parameter <slha_params>.dat file must therefore be loaded. Such a parameter file can be downloaded from the FeynRules website or created by hand by the user, and loaded into FeynRules as
This command does not reduce the size of the model output by removing vertices with vanishing couplings. However, if desired, this task could be done with the LoadRestriction command (see Ref. [90] for details). The vertices are exported to WHIZARD by the command
Note that the numerical values of the parameters of the model can be modified directly from WHIZARD, without having to generate a second time the WHIZARD model files from FeynRules. A SINDARIN script is created by the interface with the help of the instruction
and can be further modified according to the needs of the user. WHIZARD-FeynRules example: Three-Site Higgsless ModelThe Three-Site Higgsless model or Minimal Higgsless model (MHM) has
been implemented into LanHEP [91], FeynRules
and independently into WHIZARD [39],
and the collider phenomenology has been studied by making use of these
implementations [91, 50, 39].
Furthermore, the independent implementations in FeynRules and
directly into Whizard have been compared and found to
agree [87]. After the discovery of a Higgs boson
at the LHC in 2012, such a model is not in good agreement with
experimental data any more. Here, we simply use it as a guinea pig to
describe the handling of a model with non-renormalizable interactions
with the FeynRules interface, and discuss how to generate WHIZARD
model files for it. The model has been implemented in Feynman gauge as
well as unitarity gauge and contains the variable Since this model makes use of a nonlinear sigma field of the form
many higher dimensional operators are included in the model which are
not currently not supported by WHIZARD. Even for a future release of
WHIZARD containing general Lorentz structures in interaction
vertices, the user would be forced to expand the series only up to a
certain order. Although WHIZARD can reject these vertices
and print a warning message to the user, it is preferable to remove
the vertices right away in the interface by the option
As the use of different gauges was already illustrated in the SM example, we discuss the model only in Feynman gauge here. We load FeynRules:
The MHM model itself is then loaded by
where
where we have also made use of the option
After calculating the Feynman rules and processing the vertices, the interface gives a summary:
showing that no vertices were missed. The files are stored in the
directory 17.3 New physics models via the UFO file formatIn this section, we describe how to use the Universal FeynRules Output (UFO, [88]) format for physics models inside WHIZARD. Please refer the manuals of e.g. FeynRules manual for details on how to generate a UFO file for your favorite physics model. UFO files are a collection of Python scripts that encode the particles, the couplings, the Lorentz structures, the decays, as well as parameters, vertices and propagators of the corresponding model. They reside in a directory of the exact name of the model they have been created from. If the user wants to generate events for processes from a physics model from a UFO file, then this directory of scripts generated by FeynRules is immediately available if it is a subdirectory of the working directory of WHIZARD. The directory name will be taken as the model name. (The UFO-model file name must not start with a non-letter character, i.e. especially not a number. In case such a file name wants to be used at all costs, the model name in the SINDARIN script has to put in quotation marks, but this is not guaranteed to always work.) Then, a UFO model named, e.g., test_model is accessed by an extra ufo tag in the model assignment:
If desired, WHIZARD can access a directory of UFO files elsewhere on the file system. For instance, if FeynRules output resides in the subdirectory MyMdl of /home/users/john/ufo, WHIZARD can use the model named MyMdl as follows
that is, the SINDARIN keyword ufo can take an argument. Note however, that the latter approach can backfire — in case just the working directory is packed and archived for future reference.
|