•ππππ

ll = ArgumentsSupply[Lagrangian[ChPTEM2[2]] /. {UMatrix[UChiralSpurionRight] -> UQuarkChargeMatrix[RenormalizationState[0], DiagonalToU -> True], UMatrix[UChiralSpurionLeft] -> UQuarkChargeMatrix[RenormalizationState[0], DiagonalToU -> True]}, x, RenormalizationState[0], DiagonalToU -> True, ExpansionOrder -> 4, DropOrder -> 4] ;

lll = DiscardTerms[ll, Retain -> {ParticleField[Pion , RenormalizationState[0]] -> 4}, CommutatorReduce -> True, Method -> Expand]

-(C^( ) < Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 σ^3 > (e^( ))^2)/(288 (f _ π^(ó  ))^4) + (C^( ) < Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] > (e^( ))^2)/(72 (f _ π^(ó  ))^4) - (C^( ) < Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] > (e^( ))^2)/(48 (f _ π^(ó  ))^4) + (C^( ) < Overscript[π^( ), ->] · Overscript[σ, ->] '6 σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] > (e^( ))^2)/(72 (f _ π^(ó  ))^4) - (C^( ) < σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] > (e^( ))^2)/(288 (f _ π^(ó  ))^4) + (C^( ) < σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 σ^3 > (e^( ))^2)/(96 (f _ π^(ó  ))^4) - (C^( ) < σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] > (e^( ))^2)/(24 (f _ π^(ó  ))^4) + (C^( ) < σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] > (e^( ))^2)/(16 (f _ π^(ó  ))^4) - (C^( ) < σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] > (e^( ))^2)/(24 (f _ π^(ó  ))^4) + (C^( ) < σ^3 '6 σ^3 '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] > (e^( ))^2)/(96 (f _ π^(ó  ))^4) + ((m _ π^(ó  ))^2 < Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] >)/(48 (f _ π^(ó  ))^2) - < Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] >/(24 (f _ π^(ó  ))^2) + < Overscript[π^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] >/(48 (f _ π^(ó  ))^2) + < Overscript[π^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] >/(16 (f _ π^(ó  ))^2) - < ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] >/(48 (f _ π^(ó  ))^2) + < ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] >/(48 (f _ π^(ó  ))^2) - < ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] >/(24 (f _ π^(ó  ))^2)

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

1/(48 (f _ π^(ó  ))^4) (C^( ) (Overscript[π^( ), ->] · Overscript[π^( ), ->] (-(Overscript[öõ(3), ->] · Overscript[π^( ), ->])^2 + 10 Overscript[öõ(3), ->] × Overscript[π^( ), ->] · Overscript[öõ(3), ->] × Overscript[π^( ), ->] + Overscript[π^( ), ->] · Overscript[π^( ), ->]) - 5 Overscript[öõ(3), ->] × Overscript[π^( ), ->] · Overscript[π^( ), ->] × Overscript[π^( ), ->] × Overscript[öõ(3), ->] × Overscript[π^( ), ->]) (e^( ))^2 + 2 (f _ π^(ó  ))^2 (4 (Overscript[π^( ), ->] · ∂ _ μ(Overscript[π^( ), ->]))^2 + Overscript[π^( ), ->] · Overscript[π^( ), ->] (Overscript[π^( ), ->] · Overscript[π^( ), ->] (m _ π^(ó  ))^2 - 4 ∂ _ μ(Overscript[π^( ), ->]) · ∂ _ μ(Overscript[π^( ), ->]))))

IsoIndicesCounter = 0 ;

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

-1/(48 (f _ π^(ó  ))^4) (π^( )^k1 (C^( ) (e^( ))^2 (π^( )^k1 (π^( )^3)^2 + π^( )^k2 (5 δ _ (3 k1)^(2) δ _ (3 k2)^(2) (π^( )^k3)^2 - 2 π^( )^k1 (8 π^( )^k2 - 5 δ _ (3 k2)^(2) δ _ (3 k3)^(2) π^( )^k3))) - 2 (f _ π^(ó  ))^2 ((m _ π^(ó  ))^2 π^( )^k1 (π^( )^k2)^2 + 4 ∂ _ τ1 π^( ) _ ó ^k2 (π^( )^k2 ∂ _ τ1 π^( ) _ ó ^k1 - π^( )^k1 ∂ _ τ1 π^( ) _ ó ^k2))))

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]}

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

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

-1/(3 (f _ π^(ó  ))^4) (i (4 C^( ) (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))) (e^( ))^2 + (f _ π^(ó  ))^2 (-δ _ (I _ 1 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2) (m _ π^(ó  ))^2 - δ _ (I _ 1 I _ 3)^(2) δ _ (I _ 2 I _ 4)^(2) (m _ π^(ó  ))^2 - δ _ (I _ 1 I _ 2)^(2) δ _ (I _ 3 I _ 4)^(2) (m _ π^(ó  ))^2 - 2 p _ 1 · p _ 4 δ _ (I _ 1 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2) - 2 p _ 2 · p _ 3 δ _ (I _ 1 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2) + p _ 2 · p _ 4 δ _ (I _ 1 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2) + p _ 3 · p _ 4 δ _ (I _ 1 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2) + p _ 1 · p _ 4 δ _ (I _ 1 I _ 3)^(2) δ _ (I _ 2 I _ 4)^(2) + p _ 2 · p _ 3 δ _ (I _ 1 I _ 3)^(2) δ _ (I _ 2 I _ 4)^(2) - 2 p _ 2 · p _ 4 δ _ (I _ 1 I _ 3)^(2) δ _ (I _ 2 I _ 4)^(2) + p _ 3 · p _ 4 δ _ (I _ 1 I _ 3)^(2) δ _ (I _ 2 I _ 4)^(2) + p _ 1 · p _ 4 δ _ (I _ 1 I _ 2)^(2) δ _ (I _ 3 I _ 4)^(2) + p _ 2 · p _ 3 δ _ (I _ 1 I _ 2)^(2) δ _ (I _ 3 I _ 4)^(2) + p _ 2 · p _ 4 δ _ (I _ 1 I _ 2)^(2) δ _ (I _ 3 I _ 4)^(2) - 2 p _ 3 · p _ 4 δ _ (I _ 1 I _ 2)^(2) δ _ (I _ 3 I _ 4)^(2) + p _ 1 · p _ 2 (δ _ (I _ 1 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2) + δ _ (I _ 1 I _ 3)^(2) δ _ (I _ 2 I _ 4)^(2) - 2 δ _ (I _ 1 I _ 2)^(2) δ _ (I _ 3 I _ 4)^(2)) + p _ 1 · p _ 3 (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 _ (I _ 1 I _ 2)^(2) δ _ (I _ 3 I _ 4)^(2)))))

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

(-(4 i C^( ) δ _ (3 I _ 3)^(2) δ _ (3 I _ 4)^(2) δ _ (I _ 1 I _ 2)^(2))/(3 (f _ π^(ó  ))^4) + (8 i C^( ) δ _ (I _ 3 I _ 4)^(2) δ _ (I _ 1 I _ 2)^(2))/(3 (f _ π^(ó  ))^4) - (4 i C^( ) δ _ (3 I _ 2)^(2) δ _ (3 I _ 4)^(2) δ _ (I _ 1 I _ 3)^(2))/(3 (f _ π^(ó  ))^4) - (4 i C^( ) δ _ (3 I _ 2)^(2) δ _ (3 I _ 3)^(2) δ _ (I _ 1 I _ 4)^(2))/(3 (f _ π^(ó  ))^4) - (4 i C^( ) δ _ (3 I _ 1)^(2) δ _ (3 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2))/(3 (f _ π^(ó  ))^4) + (8 i C^( ) δ _ (I _ 1 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2))/(3 (f _ π^(ó  ))^4) - (4 i C^( ) δ _ (3 I _ 1)^(2) δ _ (3 I _ 3)^(2) δ _ (I _ 2 I _ 4)^(2))/(3 (f _ π^(ó  ))^4) + (8 i C^( ) δ _ (I _ 1 I _ 3)^(2) δ _ (I _ 2 I _ 4)^(2))/(3 (f _ π^(ó  ))^4) - (4 i C^( ) δ _ (3 I _ 1)^(2) δ _ (3 I _ 2)^(2) δ _ (I _ 3 I _ 4)^(2))/(3 (f _ π^(ó  ))^4)) (e^( ))^2 + p _ 1 · p _ 4 ((2 i δ _ (I _ 1 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2))/(3 (f _ π^(ó  ))^2) - (i δ _ (I _ 1 I _ 3)^(2) δ _ (I _ 2 I _ 4)^(2))/(3 (f _ π^(ó  ))^2) - (i δ _ (I _ 1 I _ 2)^(2) δ _ (I _ 3 I _ 4)^(2))/(3 (f _ π^(ó  ))^2)) + p _ 2 · p _ 3 ((2 i δ _ (I _ 1 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2))/(3 (f _ π^(ó  ))^2) - (i δ _ (I _ 1 I _ 3)^(2) δ _ (I _ 2 I _ 4)^(2))/(3 (f _ π^(ó  ))^2) - (i δ _ (I _ 1 I _ 2)^(2) δ _ (I _ 3 I _ 4)^(2))/(3 (f _ π^(ó  ))^2)) + p _ 1 · p _ 3 (-(i δ _ (I _ 1 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2))/(3 (f _ π^(ó  ))^2) + (2 i δ _ (I _ 1 I _ 3)^(2) δ _ (I _ 2 I _ 4)^(2))/(3 (f _ π^(ó  ))^2) - (i δ _ (I _ 1 I _ 2)^(2) δ _ (I _ 3 I _ 4)^(2))/(3 (f _ π^(ó  ))^2)) + p _ 2 · p _ 4 (-(i δ _ (I _ 1 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2))/(3 (f _ π^(ó  ))^2) + (2 i δ _ (I _ 1 I _ 3)^(2) δ _ (I _ 2 I _ 4)^(2))/(3 (f _ π^(ó  ))^2) - (i δ _ (I _ 1 I _ 2)^(2) δ _ (I _ 3 I _ 4)^(2))/(3 (f _ π^(ó  ))^2)) + (m _ π^(ó  ))^2 ((i δ _ (I _ 1 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2))/(3 (f _ π^(ó  ))^2) + (i δ _ (I _ 1 I _ 3)^(2) δ _ (I _ 2 I _ 4)^(2))/(3 (f _ π^(ó  ))^2) + (i δ _ (I _ 1 I _ 2)^(2) δ _ (I _ 3 I _ 4)^(2))/(3 (f _ π^(ó  ))^2)) + p _ 1 · p _ 2 (-(i δ _ (I _ 1 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2))/(3 (f _ π^(ó  ))^2) - (i δ _ (I _ 1 I _ 3)^(2) δ _ (I _ 2 I _ 4)^(2))/(3 (f _ π^(ó  ))^2) + (2 i δ _ (I _ 1 I _ 2)^(2) δ _ (I _ 3 I _ 4)^(2))/(3 (f _ π^(ó  ))^2)) + p _ 3 · p _ 4 (-(i δ _ (I _ 1 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2))/(3 (f _ π^(ó  ))^2) - (i δ _ (I _ 1 I _ 3)^(2) δ _ (I _ 2 I _ 4)^(2))/(3 (f _ π^(ó  ))^2) + (2 i δ _ (I _ 1 I _ 2)^(2) δ _ (I _ 3 I _ 4)^(2))/(3 (f _ π^(ó  ))^2))

gencoup = GenericCoupling[mfa]

{(e^( ))^2, p _ 1 ° p _ 4, p _ 2 ° p _ 3, p _ 1 ° p _ 3, p _ 2 ° p _ 4, (m _ π^(ó  ))^2, p _ 1 ° p _ 2, p _ 3 ° p _ 4}

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

{{-(4 i (CouplingConstant[ChPTEM2[2], RenormalizationState[0]] SUNDelta[3, I3] SUNDelta[3, I4] SUNDelta[I1, I2] + CouplingConstant[ChPTEM2[2], RenormalizationState[0]] SUNDelta[3, I2] SUNDelta[3, I4] SUNDelta[I1, I3] + CouplingConstant[ChPTEM2[2], RenormalizationState[0]] SUNDelta[3, I2] SUNDelta[3, I3] SUNDelta[I1, I4] + CouplingConstant[ChPTEM2[2], RenormalizationState[0]] SUNDelta[3, I1] SUNDelta[3, I4] SUNDelta[I2, I3] - 2 CouplingConstant[ChPTEM2[2], RenormalizationState[0]] SUNDelta[I1, I4] SUNDelta[I2, I3] + CouplingConstant[ChPTEM2[2], RenormalizationState[0]] SUNDelta[3, I1] SUNDelta[3, I3] SUNDelta[I2, I4] - 2 CouplingConstant[ChPTEM2[2], RenormalizationState[0]] SUNDelta[I1, I3] SUNDelta[I2, I4] + CouplingConstant[ChPTEM2[2], RenormalizationState[0]] SUNDelta[3, I1] SUNDelta[3, I2] SUNDelta[I3, I4] - 2 CouplingConstant[ChPTEM2[2], RenormalizationState[0]] SUNDelta[I1, I2] SUNDelta[I3, I4]))/(3 DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4)}, {(i (2 SUNDelta[I1, I4] SUNDelta[I2, I3] - SUNDelta[I1, I3] SUNDelta[I2, I4] - SUNDelta[I1, I2] SUNDelta[I3, I4]))/(3 DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}, {(i (2 SUNDelta[I1, I4] SUNDelta[I2, I3] - SUNDelta[I1, I3] SUNDelta[I2, I4] - SUNDelta[I1, I2] SUNDelta[I3, I4]))/(3 DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}, {-(i (SUNDelta[I1, I4] SUNDelta[I2, I3] - 2 SUNDelta[I1, I3] SUNDelta[I2, I4] + SUNDelta[I1, I2] SUNDelta[I3, I4]))/(3 DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}, {-(i (SUNDelta[I1, I4] SUNDelta[I2, I3] - 2 SUNDelta[I1, I3] SUNDelta[I2, I4] + SUNDelta[I1, I2] SUNDelta[I3, I4]))/(3 DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}, {(i (SUNDelta[I1, I4] SUNDelta[I2, I3] + SUNDelta[I1, I3] SUNDelta[I2, I4] + SUNDelta[I1, I2] SUNDelta[I3, I4]))/(3 DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}, {-(i (SUNDelta[I1, I4] SUNDelta[I2, I3] + SUNDelta[I1, I3] SUNDelta[I2, I4] - 2 SUNDelta[I1, I2] SUNDelta[I3, I4]))/(3 DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}, {-(i (SUNDelta[I1, I4] SUNDelta[I2, I3] + SUNDelta[I1, I3] SUNDelta[I2, I4] - 2 SUNDelta[I1, I2] SUNDelta[I3, I4]))/(3 DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}}

$VeryVerbose = 2 ;

CheckF[gencoup, XName[PhiModel -> ChPTEM2, VertexFields -> {PseudoScalar[2][0], PseudoScalar[2][0], PseudoScalar[2][0], PseudoScalar[2][0]}, MomentaOrder -> 2, XFileName -> Automatic] <> ".Gen"] ;

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\CouplingVectors\\ChPTEM2P20P20P20P20o2.Gen

File exists, loading

CheckF[classcoup, XName[PhiModel -> ChPTEM2, VertexFields -> {PseudoScalar[2][0], PseudoScalar[2][0], PseudoScalar[2][0], PseudoScalar[2][0]}, MomentaOrder -> 2, XFileName -> Automatic] <> ".Mod"] ;

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\CouplingVectors\\ChPTEM2P20P20P20P20o2.Mod

File exists, loading

$VeryVerbose = 0 ;

Converted by Mathematica  (July 10, 2003)