The main idea behind the FeynHelpers interface to KIRA is to
facilitate the generation of KIRA config files for reducing the given
sets of loop integrals written in the FeynCalc notation (i.e. as
GLIs with the corresponding lists of
FCTopology symbols) to masters.
If needed, the reduction can be done by running the corresponding scripts from a Mathematica notebook, although we do not recommend using this approach for complicated calculations.
Let us assume that upon simplifying some amplitude we have a list of topologies and the corresponding loop integrals that need to be reduced.
topos = {FCTopology["fctopology1", {SFAD[{{q2, 0}, {0, 1}, 1}], SFAD[{{q1, 0}, {0, 1}, 1}], SFAD[{{q1 + q2, 0}, {0, 1}, 1}], SFAD[{{p + q1, 0}, {0, 1}, 1}], SFAD[{{p - q2, 0}, {0, 1}, 1}]}, {q1, q2}, {p}, {Hold[Pair][Momentum[p, D], Momentum[p, D]] -> pp}, {}]};ints = {GLI["fctopology1", {-2, 1, 1, 2, 1}], GLI["fctopology1", {-1, 0, 1, 2, 1}], GLI["fctopology1", {-1, 1, 0, 2, 1}],
GLI["fctopology1", {-1, 1, 1, 1, 1}], GLI["fctopology1", {-1, 1, 1, 2, 0}], GLI["fctopology1", {-1, 1, 1, 2, 1}],
GLI["fctopology1", {0, -1, 1, 2, 1}], GLI["fctopology1", {0, 0, 0, 2, 1}], GLI["fctopology1", {0, 0, 1, 1, 1}],
GLI["fctopology1", {0, 0, 1, 2, 0}], GLI["fctopology1", {0, 0, 1, 2, 1}], GLI["fctopology1", {0, 1, -1, 2, 1}],
GLI["fctopology1", {0, 1, 0, 1, 1}], GLI["fctopology1", {0, 1, 0, 2, 0}], GLI["fctopology1", {0, 1, 0, 2, 1}],
GLI["fctopology1", {0, 1, 1, 0, 1}], GLI["fctopology1", {0, 1, 1, 1, 0}], GLI["fctopology1", {0, 1, 1, 1, 1}],
GLI["fctopology1", {0, 1, 1, 2, -1}], GLI["fctopology1", {0, 1, 1, 2, 0}], GLI["fctopology1", {0, 1, 1, 2, 1}],
GLI["fctopology1", {1, -1, 1, 1, 1}], GLI["fctopology1", {1, 0, 0, 1, 1}], GLI["fctopology1", {1, 0, 1, 0, 1}],
GLI["fctopology1", {1, 0, 1, 1, 0}], GLI["fctopology1", {1, 0, 1, 1, 1}], GLI["fctopology1", {1, 1, -1, 1, 1}],
GLI["fctopology1", {1, 1, 0, 0, 1}], GLI["fctopology1", {1, 1, 0, 1, 0}], GLI["fctopology1", {1, 1, 0, 1, 1}],
GLI["fctopology1", {1, 1, 1, -1, 1}], GLI["fctopology1", {1, 1, 1, 0, 0}], GLI["fctopology1", {1, 1, 1, 0, 1}],
GLI["fctopology1", {1, 1, 1, 1, -1}], GLI["fctopology1", {1, 1, 1, 1, 0}], GLI["fctopology1", {1, 1, 1, 1, 1}]}The first step is to generate the job file.
KiraCreateJobFile[topos, ints, NotebookDirectory[]]Notice that it is crucial to provide the list of integrals to be reduced, as the code will need some of their properties (top sectors) when writing the job file.
The next steps are to create a file containing the list of integrals
and a configuration file for the reduction. Notice that we must specify
the mass dimension of all kinematic invariants appearing in the topology
using the option KiraMassDimensions
KiraCreateIntegralFile[ints, topos, NotebookDirectory[]]
KiraCreateConfigFiles[topos, ints, NotebookDirectory[],
KiraMassDimensions -> {pp -> 1}]In the case of complicated topologies the reduction must be done on a powerful workstation or computer cluster and can take hours, days or even weeks. But as long as everything is simple enough, there should be no harm running it directly from the notebook via
KiraRunReduction[NotebookDirectory[], topos,
KiraBinaryPath -> FileNameJoin[{$HomeDirectory, "bin", "kira"}],
KiraFermatPath -> FileNameJoin[{$HomeDirectory, "bin", "ferl64", "fer64"}]]Here it is important not only to specify the correct path to the KIRA
binary (KiraBinaryPath) but also the one pointing to a
suitable FERMAT binary (KiraFermatPath). The latter will be
set via the shell environment variable FERMATPATH.
Finally, in order to load the reduction tables into Mathematica it is convenient to use
tables=KiraImportResults[topos, NotebookDirectory[]]which returns a list of replacement rules that can be directly applied to the given amplitude or perhaps exported to FORM.