•ππππγ

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]] -> 1}, CommutatorReduce -> True, Method -> Expand] /. $Substitutions // NMExpand // CycleUTraces // Expand

(i e^( ) < ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 σ^3 > γ^( ) _ μ)/(48 (f _ π^(ó  ))^2) - (i e^( ) < ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] > γ^( ) _ μ)/(16 (f _ π^(ó  ))^2) + (i e^( ) < ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] > γ^( ) _ μ)/(16 (f _ π^(ó  ))^2) - (i e^( ) < ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] > γ^( ) _ μ)/(48 (f _ π^(ó  ))^2)

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

-(e^( ) (Overscript[öõ(3), ->] × Overscript[π^( ), ->] × ∂ _ μ(Overscript[π^( ), ->]) × Overscript[π^( ), ->] · Overscript[π^( ), ->] + Overscript[öõ(3), ->] × ∂ _ μ(Overscript[π^( ), ->]) · Overscript[π^( ), ->] Overscript[π^( ), ->] · Overscript[π^( ), ->]) γ^( ) _ μ)/(6 (f _ π^(ó  ))^2)

IsoIndicesCounter = 0 ;

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

(e^( ) π^( )^k1 (f _ (3 k1 k3)^(2) π^( )^k2 - 2 f _ (3 k2 k3)^(2) π^( )^k1) π^( )^k3 γ^( ) _ τ1 ∂ _ τ1 π^( ) _ ó ^k2)/(6 (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]}

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

melsimplified = FeynRule[llll, fields] // SUNReduce // IndicesCleanup // CommutatorReduce // Simplify

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

mfa = MomentaCollect[melsimplified // Expand, PerturbationOrder -> 2]

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

gencoup = GenericCoupling[mfa]

{e^( ) p _ 4 _ μ _ 5, e^( ) p _ 3 _ μ _ 5, e^( ) p _ 2 _ μ _ 5, e^( ) p _ 1 _ μ _ 5}

classcoup = ClassesCoupling[mfa] // Together ; classcoup // StandardForm

{{(2 (SU2F[3, I3, I4] SUNDelta[I1, I2] + SU2F[3, I2, I4] SUNDelta[I1, I3] + SU2F[3, I1, I4] SUNDelta[I2, I3]))/(3 DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}, {-(2 (SU2F[3, I3, I4] SUNDelta[I1, I2] - SU2F[3, I2, I3] SUNDelta[I1, I4] - SU2F[3, I1, I3] SUNDelta[I2, I4]))/(3 DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}, {-(2 (SU2F[3, I2, I4] SUNDelta[I1, I3] + SU2F[3, I2, I3] SUNDelta[I1, I4] - SU2F[3, I1, I2] SUNDelta[I3, I4]))/(3 DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}, {-(2 (SU2F[3, I1, I4] SUNDelta[I2, I3] + SU2F[3, I1, I3] SUNDelta[I2, I4] + SU2F[3, I1, I2] 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]}, MomentaOrder -> 2, XFileName -> Automatic] <> ".Gen"] ;

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\CouplingVectors\\ChPTVirtualPhotons2P20P20P20P20V10o2.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]}, MomentaOrder -> 2, XFileName -> Automatic] <> ".Mod"] ;

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\CouplingVectors\\ChPTVirtualPhotons2P20P20P20P20V10o2.Mod

File does not exist, evaluating

Saving

$VeryVerbose = 0 ;

Converted by Mathematica  (July 10, 2003)