WallGo/ WallGoMatrix

(1.0.0) current version: 1.1.0 »

Computes 2-to-2 scattering matrix amplitudes for arbitrary quantum field theories

Contributed by: Andreas Ekstedt
Oliver Gould
Joonas Hirvonen
Benoit Laurent
Lauri Niemi
Philipp Schicho
Jorinde van de Vis

Computes 2-to-2 scattering matrix amplitudes for arbitrary quantum field theories.

Installation Instructions

To install this paclet in your Wolfram Language environment, evaluate this code:
PacletInstall["WallGo/WallGoMatrix"]

To load the code after installation, evaluate this code:
Needs["WallGo`WallGoMatrix`"]

Details

WallGoMatrix is a Mathematica package for computing 2-to-2 scattering matrix elements for arbitrary quantum field theories. It is part of the WallGo project for computing the bubble wall speed for cosmological phase transitions. Users can implement their own models. For WallGoMatrix, the model building routines are taken from DRalgo and involve constructing coupling tensors. The WallGoMatrix routines then contract these coupling tensors with the appropriate kinematic factors to yield the 2-to-2 scattering matrix elements.

Examples

Basic Example of QCD

Model (4)

Using SU(3) in the adjoint representation with Dynkin index {1,1} and representation R= 8.

In[1]:=

Group = {"SU3"};
RepAdjoint = {{1, 1}};
CouplingName = {gs};

No scalars are present in the theory:

In[2]:=

Fermions are implemented as Weyl spinors. Therefore, to create one Dirac fermion, one left-handed and one right-handed fermion is needed:

In[3]:=

Rep1 = {{{1, 0}}, "L"};
Rep2 = {{{1, 0}}, "R"};
RepFermion1Gen = {Rep1, Rep2};

For QCD, Nf=6 fermions are needed:

In[4]:=

RepFermion3Gen = {RepFermion1Gen, RepFermion1Gen, RepFermion1Gen, RepFermion1Gen, RepFermion1Gen, RepFermion1Gen} // Flatten[#, 1] &;

The input for the gauge interactions to DRalgo are then given by

In[5]:=

${gvvv, gvff, gvss, \[Lambda]1, \[Lambda]3, \[Lambda]4, \[Mu]ij, \[Mu]IJ, \[Mu]IJC, Ysff, YsffC} = AllocateTensors[Group, RepAdjoint, CouplingName, RepFermion3Gen, RepScalar];$