•ππππγγ

ll = ArgumentsSupply[Lagrangian[ChPTVirtualPhotons2[2]], x, RenormalizationState[0], DiagonalToU -> True, ExpansionOrder -> 4, DropOrder -> 4] ;

lll = DiscardTerms[ll, Retain -> {ParticleField[Pion , RenormalizationState[0]] -> 4, ParticleField[Photon, RenormalizationState[0]] -> 2}, CommutatorReduce -> True, Method -> Expand] /. $Substitutions // NMExpand // CycleUTraces // Expand ;

llle = ExpandU[lll, CommutatorReduce -> True] // Simplify

((e^( ))^2 (2 Overscript[öõ(3), ->] × Overscript[π^( ), ->] · Overscript[π^( ), ->] × Overscript[π^( ), ->] × Overscript[öõ(3), ->] × Overscript[π^( ), ->] + ((Overscript[öõ(3), ->] · Overscript[π^( ), ->])^2 - 5 Overscript[öõ(3), ->] × Overscript[π^( ), ->] · Overscript[öõ(3), ->] × Overscript[π^( ), ->] - Overscript[π^( ), ->] · Overscript[π^( ), ->]) Overscript[π^( ), ->] · Overscript[π^( ), ->]) γ^( ) _ μ^2)/(48 (f _ π^(ó  ))^2)

IsoIndicesCounter = 0 ;

llll = IsoIndicesSupply[llle] // SUNReduce[#, FullReduce -> True] & // IndicesCleanup // Simplify

((e^( ))^2 π^( )^k1 (π^( )^k1 (π^( )^3)^2 + π^( )^k2 (2 δ _ (3 k1)^(2) δ _ (3 k2)^(2) (π^( )^k3)^2 + π^( )^k1 (5 δ _ (3 k2)^(2) δ _ (3 k3)^(2) π^( )^k3 - 8 π^( )^k2))) γ^( ) _ ρ1^2)/(48 (f _ π^(ó  ))^2)

fields = {QuantumField[Particle[PseudoScalar[2], RenormalizationState[0]], SUNIndex[I1]][p1], QuantumField[Particle[PseudoScalar[2], RenormalizationState[0]], SUNIndex[I2]][p2], QuantumField[Particle[PseudoScalar[2], RenormalizationState[0]], SUNIndex[I3]][p3], QuantumField[Particle[PseudoScalar[2], RenormalizationState[0]], SUNIndex[I4]][p4], QuantumField[Particle[Vector[1], RenormalizationState[0]], LorentzIndex[μ5]][p5], QuantumField[Particle[Vector[1], RenormalizationState[0]], LorentzIndex[μ6]][p6]}

{π^( )^I _ 1, π^( )^I _ 2, π^( )^I _ 3, π^( )^I _ 4, γ^( ) _ μ _ 5, γ^( ) _ μ _ 6}

melsimplified = FeynRule[llll, fields] // SUNReduce[#, FullReduce -> True] & // IndicesCleanup // CommutatorReduce // Simplify

1/(3 (f _ π^(ó  ))^2) (4 i (e^( ))^2 g^(μ _ 5 μ _ 6) (δ _ (3 I _ 1)^(2) δ _ (3 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2) - 2 δ _ (I _ 1 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2) - 2 δ _ (I _ 1 I _ 3)^(2) δ _ (I _ 2 I _ 4)^(2) + δ _ (3 I _ 3)^(2) (δ _ (3 I _ 4)^(2) δ _ (I _ 1 I _ 2)^(2) + δ _ (3 I _ 2)^(2) δ _ (I _ 1 I _ 4)^(2) + δ _ (3 I _ 1)^(2) δ _ (I _ 2 I _ 4)^(2)) - 2 δ _ (I _ 1 I _ 2)^(2) δ _ (I _ 3 I _ 4)^(2) + δ _ (3 I _ 2)^(2) (δ _ (3 I _ 4)^(2) δ _ (I _ 1 I _ 3)^(2) + δ _ (3 I _ 1)^(2) δ _ (I _ 3 I _ 4)^(2))))

mfa = Simplify /@ MomentaCollect[melsimplified // Expand, PerturbationOrder -> 3]

1/(3 (f _ π^(ó  ))^2) (4 i (e^( ))^2 g^(μ _ 5 μ _ 6) (δ _ (3 I _ 1)^(2) δ _ (3 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2) - 2 δ _ (I _ 1 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2) - 2 δ _ (I _ 1 I _ 3)^(2) δ _ (I _ 2 I _ 4)^(2) + δ _ (3 I _ 3)^(2) (δ _ (3 I _ 4)^(2) δ _ (I _ 1 I _ 2)^(2) + δ _ (3 I _ 2)^(2) δ _ (I _ 1 I _ 4)^(2) + δ _ (3 I _ 1)^(2) δ _ (I _ 2 I _ 4)^(2)) - 2 δ _ (I _ 1 I _ 2)^(2) δ _ (I _ 3 I _ 4)^(2) + δ _ (3 I _ 2)^(2) (δ _ (3 I _ 4)^(2) δ _ (I _ 1 I _ 3)^(2) + δ _ (3 I _ 1)^(2) δ _ (I _ 3 I _ 4)^(2))))

gencoup = GenericCoupling[mfa]

{(e^( ))^2 g^(μ _ 5 μ _ 6)}

classcoup = ClassesCoupling[mfa] ; classcoup // StandardForm

{{(4 i (SUNDelta[3, I1] SUNDelta[3, I4] SUNDelta[I2, I3] - 2 SUNDelta[I1, I4] SUNDelta[I2, I3] - 2 SUNDelta[I1, I3] SUNDelta[I2, I4] + SUNDelta[3, I3] (SUNDelta[3, I4] SUNDelta[I1, I2] + SUNDelta[3, I2] SUNDelta[I1, I4] + SUNDelta[3, I1] SUNDelta[I2, I4]) - 2 SUNDelta[I1, I2] SUNDelta[I3, I4] + SUNDelta[3, I2] (SUNDelta[3, I4] SUNDelta[I1, I3] + SUNDelta[3, I1] SUNDelta[I3, I4])))/(3 DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}}

$VeryVerbose = 2 ;

CheckF[gencoup, XName[PhiModel -> ChPTVirtualPhotons2, VertexFields -> {PseudoScalar[2][0], PseudoScalar[2][0], PseudoScalar[2][0], PseudoScalar[2][0], Vector[1][0], Vector[1][0]}, MomentaOrder -> 2, XFileName -> Automatic] <> ".Gen"] ;

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\CouplingVectors\\ChPTVirtualPhotons2P20P20P20P20V10V10o2.Gen

File does not exist, evaluating

Saving

CheckF[classcoup, XName[PhiModel -> ChPTVirtualPhotons2, VertexFields -> {PseudoScalar[2][0], PseudoScalar[2][0], PseudoScalar[2][0], PseudoScalar[2][0], Vector[1][0], Vector[1][0]}, MomentaOrder -> 2, XFileName -> Automatic] <> ".Mod"] ;

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\CouplingVectors\\ChPTVirtualPhotons2P20P20P20P20V10V10o2.Mod

File does not exist, evaluating

Saving

$VeryVerbose = 0 ;

Converted by Mathematica  (July 10, 2003)