•ππγγ

ll = ArgumentsSupply[Lagrangian[ChPTEM2[2]], x, RenormalizationState[0], DiagonalToU -> True, ExpansionOrder -> 2, DropOrder -> 2]

1/4 (< (-((Overscript[π^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] + ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->]) ℵ^2)/(2 (f _ π^(ó  ))^2) + (i ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] ℵ)/f _ π^(ó  ) + i ((-((Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->]) ℵ^2)/(2 (f _ π^(ó  ))^2) + (i Overscript[π^( ), ->] · Overscript[σ, ->] ℵ)/f _ π^(ó  ) + ÷¬öé) '6 (1/6 e^( ) ÷¬öé - 1/2 e^( ) σ^3) '6 γ^( ) _ μ) - i ((1/6 e^( ) ÷¬öé - 1/2 e^( ) σ^3) '6 γ^( ) _ μ '6 (-((Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->]) ℵ^2)/(2 (f _ π^(ó  ))^2) + (i Overscript[π^( ), ->] · Overscript[σ, ->] ℵ)/f _ π^(ó  ) + ÷¬öé))) '6 (-((Overscript[π^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] + ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->]) ℵ^2)/(2 (f _ π^(ó  ))^2) - (i ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] ℵ)/f _ π^(ó  ) + i ((-((Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->]) ℵ^2)/(2 (f _ π^(ó  ))^2) - (i Overscript[π^( ), ->] · Overscript[σ, ->] ℵ)/f _ π^(ó  ) + ÷¬öé) '6 γ^( ) _ μ '6 (1/6 e^( ) ÷¬öé - 1/2 e^( ) σ^3)) - i (γ^( ) _ μ '6 (1/6 e^( ) ÷¬öé - 1/2 e^( ) σ^3) '6 (-((Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->]) ℵ^2)/(2 (f _ π^(ó  ))^2) - (i Overscript[π^( ), ->] · Overscript[σ, ->] ℵ)/f _ π^(ó  ) + ÷¬öé))) > + 2 !, _ 0^( ) < (((÷¬öé/2 - σ^3/2) (m _ π^(ó  ))^2)/(2 !, _ 0^( )) + ((÷¬öé/2 + σ^3/2) (m _ π^(ó  ))^2)/(2 !, _ 0^( ))) '6 (-((Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->]) ℵ^2)/(2 (f _ π^(ó  ))^2) - (i Overscript[π^( ), ->] · Overscript[σ, ->] ℵ)/f _ π^(ó  ) + ÷¬öé) > + 2 !, _ 0^( ) < (((÷¬öé/2 - σ^3/2) (m _ π^(ó  ))^2)/(2 !, _ 0^( )) + ((÷¬öé/2 + σ^3/2) (m _ π^(ó  ))^2)/(2 !, _ 0^( ))) '6 (-((Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->]) ℵ^2)/(2 (f _ π^(ó  ))^2) + (i Overscript[π^( ), ->] · Overscript[σ, ->] ℵ)/f _ π^(ó  ) + ÷¬öé) >) (f _ π^(ó  ))^2 - 1/4 ((∂ _ μ γ^( ) _ ν^ó  - ∂ _ ν γ^( ) _ μ^ó ) '6 (∂ _ μ γ^( ) _ ν^ó  - ∂ _ ν γ^( ) _ μ^ó )) + C^( ) < Q _ R '6 (-((Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->]) ℵ^2)/(2 (f _ π^(ó  ))^2) + (i Overscript[π^( ), ->] · Overscript[σ, ->] ℵ)/f _ π^(ó  ) + ÷¬öé) '6 Q _ L '6 (-((Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->]) ℵ^2)/(2 (f _ π^(ó  ))^2) - (i Overscript[π^( ), ->] · Overscript[σ, ->] ℵ)/f _ π^(ó  ) + ÷¬öé) > - 1/2 λ ∂ _ μ γ^( ) _ μ^ó  ∂ _ ν γ^( ) _ ν^ó 

lll = DiscardTerms[ll, Retain -> {ParticleField[Pion , RenormalizationState[0]] -> 2, ParticleField[Photon, RenormalizationState[0]] -> 2}, CommutatorReduce -> True, Method -> Expand]

-1/16 (e^( ))^2 < Overscript[π^( ), ->] · Overscript[σ, ->] '6 σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 σ^3 > γ^( ) _ μ^2 + 1/16 (e^( ))^2 < Overscript[π^( ), ->] · Overscript[σ, ->] '6 σ^3 '6 σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] > γ^( ) _ μ^2 + 1/16 (e^( ))^2 < σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 σ^3 > γ^( ) _ μ^2 - 1/16 (e^( ))^2 < σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] > γ^( ) _ μ^2

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

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

IsoIndicesCounter = 0 ;

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

1/2 (e^( ))^2 π^( )^k1 (π^( )^k1 - δ _ (3 k1)^(2) δ _ (3 k2)^(2) π^( )^k2) 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 // 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 -> ChPTEM2, 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\\ChPTEM2P20P20V10V10o2.Gen

File exists, loading

CheckF[classcoup, XName[PhiModel -> ChPTEM2, 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\\ChPTEM2P20P20V10V10o2.Mod

File exists, loading

$VeryVerbose = 0 ;

Converted by Mathematica  (July 10, 2003)