MadSymbolic

MadSymbolic (or MadSym in short), is MadGraph5_aMC@NLO (MG5aMC) plugin designed to help export MG5aMC tree and loop amplitudes to gammaLoop where it can be further manipulated.

In particular, the amplitude expressions can be processed symbolically using gammaLoop and the computer algebra system Symbolica.

Installation

MadSymbolic has two core dependencies:

• MadGraph5_aMC@NLO.

• gammaLoop which you can install from source or with pip install gammaloop.

Then you can install madsymbolic by placing the git clone into the PLUGIN directory of your MG5aMC installation.

Usage

The MadSymbolic plugin offers additional commands to the MG5aMC command line interface, which you can access by running mg5_aMC as follows:

./bin/mg5_aMC --mode=madsymbolic

Commands available

The following new commands become available when running MG5aMC with the MadSymbolic plugin:

• set_madsymbolic_option <OPTION_NAME> <OPTION_VALUE>

  Specifies a particular option for the MadSymbolic plugin.

  e.g: set_madsymbolic_option gammaloop_path /path/to/gammaloop/directory

• force_loop_model

  Because MadSymbolic only considers bare symbolic amplitudes, it is useful to make it possible for MG5aMC to generate loop amplitudes from any UFO model, even those without the necessary additional Feynman rules encoding renormalisation and so-called R2 counterterms.

  This command thus forces MG5aMC to allow the generation of loop amplitudes irrespectively of the nature of the UFO model already imported.

• write_graphs <OUTPUT_DIR_NAME> <OPTIONS>

  This command is meant to be ran after having run a generate or add process command of MG5aMC but before running its output command. You can specify the option --help to get more information on the available options. The graphs contained in all tree and loop amplitudes generated by MG5aMC will be written to the specified directory, in a YAML format that can be read by gammaLoop. The set of graphs for the amplitude of each individual partonic channel will be written to separate files.

  e.g.: write_graphs test_output --format yaml --file_name test

• gL <GAMMALOOP_COMMAND>

  This command gL acts as a prefix for running any gammaLoop command. It will typically be used to further process the graphs written by write_graphs and to perform symbolic manipulations on the amplitude expressions. Note that MadSymbolic already automatically makes sure that gammaLoop has loaded the same UFO model that is currently active in MG5aMC.

  e.g.: gL help

Example

Here is a simple example run of MadSymbolic with MG5aMC to generate all diagrams making up the tree and loop amplitudes of the process $q \bar{q} \to d \bar{d}g$. You can write a card test.madsym with the following content:

```bash

Only necessary if you the gammaloop Python library is not in your PYTHONPATH

setmadsymbolicoption gammalooppath PATH/TO/YOUR/GAMMALOOP/INSTALLATION import model sm-nowidths forceloopmodel define q = u u~ d d~ generate q q > d d~ g [virt=QCD] writegraphs testmadsymbolicoutput --format yaml gL importgraphs testmadsymbolicoutput/loopamplitude0ddxddxg.yaml --format yaml gL output testgammaloopoutput -mr -exp -ef mathematica ```

and run it with ./bin/mg5_aMC --mode=madsymbolic test.madsym. You will find the graphs processed by gammaLoop in the directory test_gammaloop_output. For example you can see the diagram renderings with:

bash cd test_gammaloop_output/sources/amplitudes/loop_amplitude_0_ddx_ddxg/drawings make -j 16 open feynman_diagrams.pdf

And the numerator expressions in test_gammaloop_output/sources/amplitudes/loop_amplitude_0_ddx_ddxg/numerator.