FeynRules manual (development version)

QCD BGF model for FeynArts

Load FeynRules

FR$Parallel = False;
$FeynRulesPath = FileNameJoin[{$UserBaseDirectory, "Applications", "FeynRules"}];
<< FeynRules`;

\text{ - FeynRules - }

\text{Version: }\;\text{2.3.49}\;\text{ (} \;\text{29 September 2021}\;\text{).}

\text{Authors: A. Alloul, N. Christensen, C. Degrande, C. Duhr, B. Fuks}

$$$$

\text{Please cite:}

\text{ - Comput.Phys.Commun.185:2250-2300,2014 (arXiv:1310.1921);}

\text{ - Comput.Phys.Commun.180:1614-1641,2009 (arXiv:0806.4194).}

$$$$

\text{http://feynrules.phys.ucl.ac.be}

$$$$

\text{The FeynRules palette can be opened using the command FRPalette[].}

Load FeynRules model

If[$FrontEnd === Null, 
   nbDir = DirectoryName[$InputFileName], 
   nbDir = NotebookDirectory[] 
  ];

frModelPath = FileNameJoin[{nbDir, "QCDBGF.fr"}];
LoadModel[frModelPath];

\text{This model implementation was created by}

\text{Vladyslav Shtabovenko}

\text{Model Version: }0

\text{For more information, type ModelInformation[].}

\text{}

\text{ - Loading particle classes.}

\text{ - Loading gauge group classes.}

\text{ - Loading parameter classes.}

\text{$\backslash $nModel }\;\text{QCD in the background field formalism}\;\text{ loaded.}

Generate Feynman rules

fRules = FeynmanRules[LQCD]

\text{Starting Feynman rule calculation.}

\text{Expanding the Lagrangian...}

\text{Collecting the different structures that enter the vertex.}

17\text{ possible non-zero vertices have been found -$>$ starting the computation: }\;\text{FeynRules$\grave{ }$FR\$FeynmanRules}\;\text{ / }17.

17\text{ vertices obtained.}

\left( \begin{array}{cc} \left( \begin{array}{cc} B & 1 \\ B & 2 \\ B & 3 \\ \end{array} \right) & -\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _1,\mu _2} \;\text{p}_1^{\mu _3}+\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _1,\mu _2} \;\text{p}_2^{\mu _3}+\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _1,\mu _3} \;\text{p}_1^{\mu _2}-\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _1,\mu _3} \;\text{p}_3^{\mu _2}-\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _2,\mu _3} \;\text{p}_2^{\mu _1}+\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _2,\mu _3} \;\text{p}_3^{\mu _1} \\ \left( \begin{array}{cc} B & 1 \\ B & 2 \\ G & 3 \\ \end{array} \right) & \frac{\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _1,\mu _3} \;\text{p}_2^{\mu _2}}{\text{GaugeXi}(G)}-\frac{\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _2,\mu _3} \;\text{p}_1^{\mu _1}}{\text{GaugeXi}(G)}-\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _1,\mu _2} \;\text{p}_1^{\mu _3}+\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _1,\mu _2} \;\text{p}_2^{\mu _3}+\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _1,\mu _3} \;\text{p}_1^{\mu _2}-\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _1,\mu _3} \;\text{p}_3^{\mu _2}-\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _2,\mu _3} \;\text{p}_2^{\mu _1}+\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _2,\mu _3} \;\text{p}_3^{\mu _1} \\ \left( \begin{array}{cc} \;\text{ghG}^{\dagger } & 1 \\ \;\text{ghG} & 2 \\ B & 3 \\ \end{array} \right) & \;\text{gs} f_{\text{a}_3,\text{a}_1,\text{a}_2} \;\text{p}_1^{\mu _3}-\text{gs} f_{\text{a}_3,\text{a}_1,\text{a}_2} \;\text{p}_2^{\mu _3} \\ \left( \begin{array}{cc} B & 1 \\ B & 2 \\ B & 3 \\ B & 4 \\ \end{array} \right) & i \;\text{gs}^2 \eta _{\mu _1,\mu _4} \eta _{\mu _2,\mu _3} f_{\text{a}_1,\text{a}_3,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_4,\text{Gluon\$1}}+i \;\text{gs}^2 \eta _{\mu _1,\mu _4} \eta _{\mu _2,\mu _3} f_{\text{a}_1,\text{a}_2,\text{Gluon\$1}} f_{\text{a}_3,\text{a}_4,\text{Gluon\$1}}+i \;\text{gs}^2 \eta _{\mu _1,\mu _3} \eta _{\mu _2,\mu _4} f_{\text{a}_1,\text{a}_4,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_3,\text{Gluon\$1}}-i \;\text{gs}^2 \eta _{\mu _1,\mu _3} \eta _{\mu _2,\mu _4} f_{\text{a}_1,\text{a}_2,\text{Gluon\$1}} f_{\text{a}_3,\text{a}_4,\text{Gluon\$1}}-i \;\text{gs}^2 \eta _{\mu _1,\mu _2} \eta _{\mu _3,\mu _4} f_{\text{a}_1,\text{a}_4,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_3,\text{Gluon\$1}}-i \;\text{gs}^2 \eta _{\mu _1,\mu _2} \eta _{\mu _3,\mu _4} f_{\text{a}_1,\text{a}_3,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_4,\text{Gluon\$1}} \\ \left( \begin{array}{cc} \;\text{ghG}^{\dagger } & 1 \\ \;\text{ghG} & 2 \\ B & 3 \\ B & 4 \\ \end{array} \right) & i \;\text{gs}^2 \eta _{\mu _3,\mu _4} f_{\text{a}_3,\text{a}_2,\text{Gluon\$1}} f_{\text{a}_4,\text{a}_1,\text{Gluon\$1}}+i \;\text{gs}^2 \eta _{\mu _3,\mu _4} f_{\text{a}_3,\text{a}_1,\text{Gluon\$1}} f_{\text{a}_4,\text{a}_2,\text{Gluon\$1}} \\ \left( \begin{array}{cc} B & 1 \\ G & 2 \\ G & 3 \\ \end{array} \right) & \frac{\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _1,\mu _2} \;\text{p}_3^{\mu _3}}{\text{GaugeXi}(G)}-\frac{\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _1,\mu _3} \;\text{p}_2^{\mu _2}}{\text{GaugeXi}(G)}-\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _1,\mu _2} \;\text{p}_1^{\mu _3}+\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _1,\mu _2} \;\text{p}_2^{\mu _3}+\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _1,\mu _3} \;\text{p}_1^{\mu _2}-\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _1,\mu _3} \;\text{p}_3^{\mu _2}-\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _2,\mu _3} \;\text{p}_2^{\mu _1}+\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _2,\mu _3} \;\text{p}_3^{\mu _1} \\ \left( \begin{array}{cc} B & 1 \\ B & 2 \\ B & 3 \\ G & 4 \\ \end{array} \right) & i \;\text{gs}^2 \eta _{\mu _1,\mu _4} \eta _{\mu _2,\mu _3} f_{\text{a}_1,\text{a}_3,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_4,\text{Gluon\$1}}+i \;\text{gs}^2 \eta _{\mu _1,\mu _4} \eta _{\mu _2,\mu _3} f_{\text{a}_1,\text{a}_2,\text{Gluon\$1}} f_{\text{a}_3,\text{a}_4,\text{Gluon\$1}}+i \;\text{gs}^2 \eta _{\mu _1,\mu _3} \eta _{\mu _2,\mu _4} f_{\text{a}_1,\text{a}_4,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_3,\text{Gluon\$1}}-i \;\text{gs}^2 \eta _{\mu _1,\mu _3} \eta _{\mu _2,\mu _4} f_{\text{a}_1,\text{a}_2,\text{Gluon\$1}} f_{\text{a}_3,\text{a}_4,\text{Gluon\$1}}-i \;\text{gs}^2 \eta _{\mu _1,\mu _2} \eta _{\mu _3,\mu _4} f_{\text{a}_1,\text{a}_4,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_3,\text{Gluon\$1}}-i \;\text{gs}^2 \eta _{\mu _1,\mu _2} \eta _{\mu _3,\mu _4} f_{\text{a}_1,\text{a}_3,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_4,\text{Gluon\$1}} \\ \left( \begin{array}{cc} \;\text{ghG}^{\dagger } & 1 \\ \;\text{ghG} & 2 \\ G & 3 \\ \end{array} \right) & \;\text{gs} f_{\text{a}_3,\text{a}_1,\text{a}_2} \;\text{p}_1^{\mu _3} \\ \left( \begin{array}{cc} \;\text{ghG}^{\dagger } & 1 \\ \;\text{ghG} & 2 \\ B & 3 \\ G & 4 \\ \end{array} \right) & i \;\text{gs}^2 \eta _{\mu _3,\mu _4} f_{\text{a}_3,\text{a}_1,\text{Gluon\$1}} f_{\text{a}_4,\text{a}_2,\text{Gluon\$1}} \\ \left( \begin{array}{cc} B & 1 \\ B & 2 \\ G & 3 \\ G & 4 \\ \end{array} \right) & -\frac{i \;\text{gs}^2 \eta _{\mu _1,\mu _4} \eta _{\mu _2,\mu _3} f_{\text{a}_1,\text{a}_4,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_3,\text{Gluon\$1}}}{\text{GaugeXi}(G)}-\frac{i \;\text{gs}^2 \eta _{\mu _1,\mu _3} \eta _{\mu _2,\mu _4} f_{\text{a}_1,\text{a}_3,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_4,\text{Gluon\$1}}}{\text{GaugeXi}(G)}+i \;\text{gs}^2 \eta _{\mu _1,\mu _4} \eta _{\mu _2,\mu _3} f_{\text{a}_1,\text{a}_3,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_4,\text{Gluon\$1}}+i \;\text{gs}^2 \eta _{\mu _1,\mu _4} \eta _{\mu _2,\mu _3} f_{\text{a}_1,\text{a}_2,\text{Gluon\$1}} f_{\text{a}_3,\text{a}_4,\text{Gluon\$1}}+i \;\text{gs}^2 \eta _{\mu _1,\mu _3} \eta _{\mu _2,\mu _4} f_{\text{a}_1,\text{a}_4,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_3,\text{Gluon\$1}}-i \;\text{gs}^2 \eta _{\mu _1,\mu _3} \eta _{\mu _2,\mu _4} f_{\text{a}_1,\text{a}_2,\text{Gluon\$1}} f_{\text{a}_3,\text{a}_4,\text{Gluon\$1}}-i \;\text{gs}^2 \eta _{\mu _1,\mu _2} \eta _{\mu _3,\mu _4} f_{\text{a}_1,\text{a}_4,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_3,\text{Gluon\$1}}-i \;\text{gs}^2 \eta _{\mu _1,\mu _2} \eta _{\mu _3,\mu _4} f_{\text{a}_1,\text{a}_3,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_4,\text{Gluon\$1}} \\ \left( \begin{array}{cc} G & 1 \\ G & 2 \\ G & 3 \\ \end{array} \right) & -\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _1,\mu _2} \;\text{p}_1^{\mu _3}+\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _1,\mu _2} \;\text{p}_2^{\mu _3}+\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _1,\mu _3} \;\text{p}_1^{\mu _2}-\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _1,\mu _3} \;\text{p}_3^{\mu _2}-\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _2,\mu _3} \;\text{p}_2^{\mu _1}+\text{gs} f_{\text{a}_1,\text{a}_2,\text{a}_3} \eta _{\mu _2,\mu _3} \;\text{p}_3^{\mu _1} \\ \left( \begin{array}{cc} B & 1 \\ G & 2 \\ G & 3 \\ G & 4 \\ \end{array} \right) & i \;\text{gs}^2 \eta _{\mu _1,\mu _4} \eta _{\mu _2,\mu _3} f_{\text{a}_1,\text{a}_3,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_4,\text{Gluon\$1}}+i \;\text{gs}^2 \eta _{\mu _1,\mu _4} \eta _{\mu _2,\mu _3} f_{\text{a}_1,\text{a}_2,\text{Gluon\$1}} f_{\text{a}_3,\text{a}_4,\text{Gluon\$1}}+i \;\text{gs}^2 \eta _{\mu _1,\mu _3} \eta _{\mu _2,\mu _4} f_{\text{a}_1,\text{a}_4,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_3,\text{Gluon\$1}}-i \;\text{gs}^2 \eta _{\mu _1,\mu _3} \eta _{\mu _2,\mu _4} f_{\text{a}_1,\text{a}_2,\text{Gluon\$1}} f_{\text{a}_3,\text{a}_4,\text{Gluon\$1}}-i \;\text{gs}^2 \eta _{\mu _1,\mu _2} \eta _{\mu _3,\mu _4} f_{\text{a}_1,\text{a}_4,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_3,\text{Gluon\$1}}-i \;\text{gs}^2 \eta _{\mu _1,\mu _2} \eta _{\mu _3,\mu _4} f_{\text{a}_1,\text{a}_3,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_4,\text{Gluon\$1}} \\ \left( \begin{array}{cc} G & 1 \\ G & 2 \\ G & 3 \\ G & 4 \\ \end{array} \right) & i \;\text{gs}^2 \eta _{\mu _1,\mu _4} \eta _{\mu _2,\mu _3} f_{\text{a}_1,\text{a}_3,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_4,\text{Gluon\$1}}+i \;\text{gs}^2 \eta _{\mu _1,\mu _4} \eta _{\mu _2,\mu _3} f_{\text{a}_1,\text{a}_2,\text{Gluon\$1}} f_{\text{a}_3,\text{a}_4,\text{Gluon\$1}}+i \;\text{gs}^2 \eta _{\mu _1,\mu _3} \eta _{\mu _2,\mu _4} f_{\text{a}_1,\text{a}_4,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_3,\text{Gluon\$1}}-i \;\text{gs}^2 \eta _{\mu _1,\mu _3} \eta _{\mu _2,\mu _4} f_{\text{a}_1,\text{a}_2,\text{Gluon\$1}} f_{\text{a}_3,\text{a}_4,\text{Gluon\$1}}-i \;\text{gs}^2 \eta _{\mu _1,\mu _2} \eta _{\mu _3,\mu _4} f_{\text{a}_1,\text{a}_4,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_3,\text{Gluon\$1}}-i \;\text{gs}^2 \eta _{\mu _1,\mu _2} \eta _{\mu _3,\mu _4} f_{\text{a}_1,\text{a}_3,\text{Gluon\$1}} f_{\text{a}_2,\text{a}_4,\text{Gluon\$1}} \\ \left( \begin{array}{cc} \overset{-}{\text{dq}} & 1 \\ \;\text{dq} & 2 \\ B & 3 \\ \end{array} \right) & -i \;\text{gs} \delta _{\text{f}_1,\text{f}_2} T_{\text{m}_1,\text{m}_2}^{\text{a}_3} \gamma _{\text{s}_1,\text{s}_2}{}^{\mu _3} \\ \left( \begin{array}{cc} \overset{-}{\text{uq}} & 1 \\ \;\text{uq} & 2 \\ B & 3 \\ \end{array} \right) & -i \;\text{gs} \delta _{\text{f}_1,\text{f}_2} T_{\text{m}_1,\text{m}_2}^{\text{a}_3} \gamma _{\text{s}_1,\text{s}_2}{}^{\mu _3} \\ \left( \begin{array}{cc} \overset{-}{\text{dq}} & 1 \\ \;\text{dq} & 2 \\ G & 3 \\ \end{array} \right) & -i \;\text{gs} \delta _{\text{f}_1,\text{f}_2} T_{\text{m}_1,\text{m}_2}^{\text{a}_3} \gamma _{\text{s}_1,\text{s}_2}{}^{\mu _3} \\ \left( \begin{array}{cc} \overset{-}{\text{uq}} & 1 \\ \;\text{uq} & 2 \\ G & 3 \\ \end{array} \right) & -i \;\text{gs} \delta _{\text{f}_1,\text{f}_2} T_{\text{m}_1,\text{m}_2}^{\text{a}_3} \gamma _{\text{s}_1,\text{s}_2}{}^{\mu _3} \\ \end{array} \right)

Create FeynArts model

SetDirectory[FileNameJoin[{$UserBaseDirectory, "Applications", "FeynCalc", "FeynArts", "Models"}]];
WriteFeynArtsOutput[LQCD, Output -> "QCDBGF", CouplingRename -> False,SelectParticles -> {
     {ghG, ghGbar, B}, {ghG, ghGbar, B, B}, {B, G, G}, 
     {ghG, ghGbar, G}, {ghG, ghGbar, B, G}, {B, B, G, G}, 
     {G, G, G}, {B, G, G, G}, {G, G, G, G}, {uqbar, uq, G}, {dqbar, dq, G}, 
     {uqbar, uq, B}, {dqbar, dq, B}}];

\text{ - - - FeynRules interface to FeynArts - - -}

\text{ C. Degrande C. Duhr, 2013}

\text{ Counterterms: B. Fuks, 2012}

\text{Calculating Feynman rules for }\;\text{L1}

\text{Starting Feynman rules calculation for L1.}

\text{Expanding the Lagrangian...}

\text{Selecting specified field content. Warning! Only mass eigenstates should be selected!}

\text{Neglecting all terms with more than }4\text{ particles.}

\text{Neglecting all terms with less than }3\text{ particles.}

\text{Collecting the different structures that enter the vertex.}

13\text{ possible non-zero vertices have been found -$>$ starting the computation: }\;\text{FeynRules$\grave{ }$FR\$FeynmanRules}\;\text{ / }13.

13\text{ vertices obtained.}

\text{mytimecheck,after LGC}

\text{Writing FeynArts model file into directory }\;\text{QCDBGF}

\text{Writing FeynArts generic file on }\;\text{QCDBGF.gen}.