## MadGraph5 Processes

Here we will describe two special ways PYTHIA can make use of MadGraph5 and MadGraph5_aMC@NLO [Alw11,Alw14], either by exporting Madgraph process code or by wrapping the MadGraph5_aMC@NLO generator as a PYTHIA Les Houches interface.

Of course, PYTHIA can also read in Les Houches Event Files (LHEF) generated by MadGraph. This is the most commonly used approach, and requires no further description here.

### MadGraph5 matrix-element plugins

Runtime plugin loading of matrix elements generated by Madgraph is available. A small set of pre-generated ones covering most Born-level SM processes and decays are included with the baseline Pythia distribution; see below for how to determine which ones are available and how to generate further ones.

#### Configuration and Build Procedure

MG5 ME plugin loading must first of all be enabled, by passing the flag `--with-mg5mes` to the Pythia `configure` script. This ensures that the MG5 ME plugin libraries are compiled during the `make` stage and thus that they will be available at runtime.

Optionally, a custom directory path, `--with-mg5mes=DIR`, can be provided to tell Pythia to look for user-generated matrix-element plugins in a non-standard location.

If no argument is supplied (normal usage), then Pythia will use the default location `DIR=plugins/mg5mes/` which contains the pre-generated MG5 ME libraries that are included with Pythia. You can do an `ls` in this directory to see which pre-generated libraries are available.

Each folder corresponds to a plugin, with the Madgraph configuration and commands used to generate it available in `PLUGIN.card` in the corresponding `PLUGIN` folder. At build time, each `PLUGIN` is compiled into a library of the form `libpythia8mg5PLUGIN.so` in the Pythia library folder.

#### Runtime Initialisation

Currently, the MG5 ME plugins are used for matrix-element corrections in Vincia, and to assign Born-level helicities for its helicity-dependent parton showers. The Pythia Settings word `Vincia:MEplugin` specify which plugin library to load. The libraries are named as `libpythia8mg5PLUGIN.so` where `PLUGIN` is one of the matrix-element folders specified by the path optionally passed to `--with-mg5mes=DIR`.

#### How to generate further MadGraph5 matrix-element plugins

Additional MG5 matrix-element libraries can be created by the user. Note however, that the runtime plugin loading relies on a dedicated MG5 output format which is not yet available in the public MG5 distribution. Instead, use the included `generate` script, located in `plugins/mg5mes`, to generate new plugin libraries for Pythia. This script relies on Docker, so note that you must have Docker installed on your system to use this.

As an example,

    ./generate --model=sm --output=example --process="p p > e+ e-"

will build all SM matrix elements for the process p p → e+ e-. The general usage requires three options as follows. Arguments to the options are indicated in caps, and default arguments are given in square brackets.

- `--model=MODEL` : Model to use, either internal or external `[sm]`. When external, specify either the relative, e.g. `./sm`, or absolute path.
- `--output=OUT`: Output directory for the generated matrix elements `[kernels]`.
- `--process=PROC`: Process or processes to generate `["p p > e+ e-"]`. Multiple processes can be passed, e.g. `./generate --process="p p > e+ e-" --process="p p > mu+ mu-"`.

Advanced usage is possible where the `--process` option is no longer used. The `--model` option, however, is still required if using any external models, and `--output` is required to specify the output directory.

- `--card=FILE`: Run a full MadGraph command card.
- `--interactive` : Run MadGraph in interactive mode.

### MadGraph5 code inside PYTHIA

By far the easiest way to implement new processes into PYTHIA 8 is by using the matrix-element generator MadGraph5. This program has an option to output the results of a matrix-element calculation as a set of PYTHIA 8 C++ classes (plus further auxiliary code), that can then be linked and used as semi-internal processes, meaning they are handled identically with normal internal ones. This way, MadGraph5 can be used to implement processes from any model that can be written in terms of a Lagrangian. Any 2 → 1, 2 → 2 and 2 → 3 processes can be implemented, the limit being set by the absence of efficient phase space generator algorithms for higher multiplicities in PYTHIA. Features such as s-channel resonances are automatically implemented in the process classes. Besides the process library and necessary model files, also an example main program is generated for each set of processes, which can be easily modified to perform the desired analyses.

In order to create a PYTHIA 8 process library with MadGraph5, first download the MadGraph5 package from https://launchpad.net/mg5amcnlo, and untar the package. You can then specify the location of your `pythia81xx` directory in the file `input/mg5_configuration.txt`:
`pythia8_path = ./pythia81xx`
The location can be either relative (to the directory `MadGraph5_v_x_x_x/.`) or absolute.

For any model that is already implemented in the MadGraph5 package, you can directly use the model. Start the MadGraph5 interface `bin/mg5`, and do:

    import model model_name
    generate your_process_in_mg5_syntax
    add process your_next_process_in_mg5_syntax
    ...
    output pythia8 [path_to_pythia81xx_directory]

For examples of MG5 process syntax, please see http://madgraph.phys.ucl.ac.be/EXAMPLES/example_mg5.html or type `help generate`. If you specified the path to the `pythia81xx` directory in the `mg5_configuration` file, you do not need to enter it in the `output` command.

If your preferred model is found on the FeynRules model wiki page, http://feynrules.irmp.ucl.ac.be/wiki/ModelDatabaseMainPage, download the UFO (Universal FeynRules Output) tar file for the model, untar in the `models/` directory, and use as above.

If you want to implement a new model which has not yet been implemented, you can do this either using the Mathematica package FeynRules (see http://feynrules.irmp.ucl.ac.be/) or directly edit the UFO model files of the most similar model in the `models/` directory.

The resulting output from the `output pythia8` command is:

- A process directory `Processes_modelname` with the model information and the files needed for all processes defined for this model, placed in the `pythia81xx` main directory. The model files are `Parameters_modelname.h/cc` and `HelAmps_modelname.h/cc`, and the process files for each process class (with the same mass, spin and color of the initial/final state particles) are called `Sigma_modelname_processname.h/cc`. The directory also contains a `makefile` and a model parameter file `param_card_modelname.dat`.
- An example main program in the directory `examples/` (in the `pythia81xx` main directory) called `main_modelname_N.cc` and a corresponding makefile `Makefile_modelname_N`. This main program links in the process classes in the process directory described above. To run the example main program, just go to the `examples/` directory and run
  `make -f Makefile_modelname_N`
  or run `launch` directly inside the MadGraph5 command line interface.

Note that in order for PYTHIA 8 to be able to automatically decay any new particles, it is necessary to specify the branching ratios of the particles in the `param_card` file, see [Ska04,Alw07] for details.

For further technical details, please see the MadGraph5 release paper [Alw11] and the semi-internal processes page.

Currently the standard way of interfacing is to use the LHEF standard with an intermediate event file. The advantage is that then the MadGraph5 phase space generator can be used, which opens up for processes with more than three particles in the final state. The disadvantages are that it is less easy to mix and match with existing PYTHIA processes, and that one needs to regenerate and store large LHEF files for different kinematics cuts or parameter values.

Please cite the MadGraph5 release paper [Alw11] if you use MadGraph5 to generate process libraries for PYTHIA 8.

### MadGraph5_aMC@NLO executable inside PYTHIA

The `Pythia::setLHAupPtr(LHAup* lhaUpPtr)` method allows a Pythia generator to accept a pointer to an object derived from the `LHAup` base class. Such an object will be initialized from within Pythia, and be called repeatedly to generate the next parton-level event, using the LHA specification as a standard to transfer the relevant information back to Pythia. Properly constructed, the operation of an `LHAup` object thus is almost completely hidden from the user, and generates events almost like an ordinary internal Pythia process.

The `LHAupMadgraph` is precisely such a class, derived from `LHAup`, that contains the code needed to wrap a MadGraph5_aMC@NLO executable. Thereby the generation of Madgraph processes from within Pythia becomes straightforward. An explicit example is provided in `main153.cc`. We describe some of the key elements used there and in the general case.

LHAupMadgraph::LHAupMadgraph(Pythia* pythia, bool match = true, string dir = "madgraphrun", string exe = "mg5_aMC")
creates an instance of the `LHAupMadgraph` class.
`argument` pythia : pointer to the `Pythia` instance, such that some of its facilities can be used inside the interface.
`argument` match (`default = on`) : should be true if jet matching is requested. For tree-level generation MLM matching is used, while FxFx matching is used for aMC@NLO generation. This is set up in `LHAupMadgraph::setInit()`, which could be modified to represent other matching strategies or parameter values.
`argument` dir (`default = madgraphrun`) : the name of the run directory, into which MadGraph puts its (intermediate) results.
`argument` exe (`default = mg5_aMC`) : the name of the MadGraph5_aMC@NLO executable that `LHAupMadgraph` is meant to wrap. In additon it may be necessary to prepend the full pathname of the executable: `"(something)/MG5_aMC_v2_3_3/bin/mg5_aMC"`.

bool LHAupMadgraph::readString(string line, Stage stage = Auto)
allows the user to send commands to MadGraph.
`argument` line : the command to be sent to MadGraph. Any string begining with `"configure "` is used for the initial MadGraph configuration with `"configure "` stripped from the begining. In general, only the process and run settings need to be provided. Run settings must begin with `" set"`; note the leading space. The output and launch commands, random seed, and shower choice are automatically handled. For example, the following will produce di-muon events from 13 TeV proton proton collisions at NLO in QCD:
`readString("generate p p > mu+ mu- [QCD]");`
`argument` stage (`default = Auto`) : if the stage is set to Auto, commands beginning with `" set"` are used in the launch stage, commands begining with `"configure"` are used in the configuration stage, and all remaining commands (excluding `output` and `launch`) are used in the generate stage. Output, launch, seed, and shower commands are automatically handled. If the user wishes to override commands, then the stage can be specified. This will prevent any automatically generated commands from being used for that stage. This should only be done if the user understands what additional commands are needed.

void LHAupMadgraph::setEvents(int events)
the number of events to generate per MadGraph run. Normally does not need to be set, but defaults to 10000.

void LHAupMadgraph::setSeed(int seed, int runs = 30081)
the random seed (sequence), normally not needed to be set explicitly. If the random seed is negative (default of -1), then the MadGraph seed is taken as the Pythia parameter `"Random:seed"`, which must be greater than 0. If the maximum number of allowed runs is exceeded (default of 30081) an error is thrown. The seed for a MadGraph run is set as:
(random seed - 1) * (maximum runs) + (number of runs) + 1.
MadGraph can only handle random seeds up to 30081 * 30081. So, with this strategy, one can generate Pythia jobs with seeds from 1 to 30081, with each job running MadGraph less than 30081 times, and ensure a fully statistically independent sample. If more than 30081 jobs are needed, then the maximum allowed runs can be lowered accordingly, and if need be, setEvents can be used to increase the number of events generated per run.

void LHAupMadgraph::setJets(int jets)
Set the number maximum number of jets generated by MadGraph. If negative (default of -1) then the number of jets is determined automatically, to be the maximum number of jets produced at leading order.

Note that GZIP support must be enabled in the Pythia executable, so use the `--with-gzip` option in the `configure` step before Pythia compilation.

Events are generated with MadGraph utilizing the gridpack method for MadGraph5 and an equivalent method for aMC@NLO. Consequently the run directory, `"madgraphrun"` by default, does not need to be deleted between independent runs with the same configuration (excluding random seeds). Indeed, keeping the directory significantly speeds the generation process, particularly for NLO generation with aMC@NLO as the grid initialization can be skipped after the initial run.