•ππγγ

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

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

1/8 (e^( ))^2 < Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 σ^3 '6 σ^3 > γ^( ) _ μ^2 - 1/8 (e^( ))^2 < Overscript[π^( ), ->] · Overscript[σ, ->] '6 σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 σ^3 > γ^( ) _ μ^2

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

1/4 (e^( ))^2 (-(Overscript[φυ(3), ->] · Overscript[π^( ), ->])^2 + Overscript[φυ(3), ->] × Overscript[π^( ), ->] · Overscript[φυ(3), ->] × Overscript[π^( ), ->] + Overscript[π^( ), ->] · Overscript[π^( ), ->]) γ^( ) _ μ^2

IsoIndicesCounter = 0 ;

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

-1/4 (e^( ))^2 ((π^( )^3)^2 + π^( )^k1 (δ _ (3 k1)^(2) δ _ (3 k2)^(2) π^( )^k2 - 2 π^( )^k1)) γ^( ) _ ρ1^2

fields = {QuantumField[Particle[PseudoScalar[2], RenormalizationState[0]], SUNIndex[I1]][p1], QuantumField[Particle[PseudoScalar[2], RenormalizationState[0]], SUNIndex[I2]][p2], QuantumField[Particle[Vector[1], RenormalizationState[0]], LorentzIndex[μ3]][p3], QuantumField[Particle[Vector[1], RenormalizationState[0]], LorentzIndex[μ4]][p4]}

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

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

-2 i (e^( ))^2 g^(μ _ 3 μ _ 4) (δ _ (3 I _ 1)^(2) δ _ (3 I _ 2)^(2) - δ _ (I _ 1 I _ 2)^(2))

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

(e^( ))^2 g^(μ _ 3 μ _ 4) (2 i δ _ (I _ 1 I _ 2)^(2) - 2 i δ _ (3 I _ 1)^(2) δ _ (3 I _ 2)^(2))

gencoup = GenericCoupling[mfa]

{(e^( ))^2 g^(μ _ 3 μ _ 4)}

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

{{-2 i (SUNDelta[3, I1] SUNDelta[3, I2] - SUNDelta[I1, I2])}}

$VeryVerbose = 2 ;

CheckF[gencoup, XName[PhiModel -> ChPTVirtualPhotons2, VertexFields -> {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\\ChPTVirtualPhotons2P20P20V10V10o2.Gen

File does not exist, evaluating

Saving

CheckF[classcoup, XName[PhiModel -> ChPTVirtualPhotons2, VertexFields -> {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\\ChPTVirtualPhotons2P20P20V10V10o2.Mod

File does not exist, evaluating

Saving

$VeryVerbose = 0 ;

Converted by Mathematica  (July 10, 2003)