•3πA

ll = ArgumentsSupply[Lagrangian[ChPTVirtualPhotons2[2]], x, RenormalizationState[0], ExpansionOrder -> 4, DropOrder -> 3, DiagonalToU -> True] ;

lll = DiscardTerms[ll, Retain -> {Particle[AxialVector[0] , RenormalizationState[0]] -> 1, Particle[Pion , RenormalizationState[0]] -> 3}, CommutatorReduce -> True, Method -> Expand] /. $Substitutions // Simplify

-1/(24 f _ π^(ó    )) (-2 < Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] > - 3 < Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] > + < Overscript[π^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] > + 3 < Overscript[π^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] > + 3 < Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] > + 3 < Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] > - 2 < ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] > + 3 < ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] > - 3 < ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] > - 2 < Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] > + < Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] > - 2 < Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] >)

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

(3 Overscript[π^( ), ->] × ∂ _ μ(Overscript[π^( ), ->]) · Overscript[π^( ), ->] × Overscript[A^( ) _ μ, ->] - 3 Overscript[π^( ), ->] × ∂ _ μ(Overscript[π^( ), ->]) · Overscript[A^( ) _ μ, ->] × Overscript[π^( ), ->] - 10 Overscript[π^( ), ->] · ∂ _ μ(Overscript[π^( ), ->]) Overscript[π^( ), ->] · Overscript[A^( ) _ μ, ->] + 10 Overscript[π^( ), ->] · Overscript[π^( ), ->] ∂ _ μ(Overscript[π^( ), ->]) · Overscript[A^( ) _ μ, ->])/(12 f _ π^(ó    ))

IsoIndicesCounter = 0 ;

llll = llle // IsoIndicesSupply // IndicesCleanup // CommutatorReduce

(5 ∂ _ τ1 π^( ) _ ó ^k2 A^( ) _ τ1^k2 (π^( )^k1)^2)/(6 f _ π^(ó    )) - (5 π^( )^k2 ∂ _ τ1 π^( ) _ ó ^k1 A^( ) _ τ1^k2 π^( )^k1)/(6 f _ π^(ó    )) - (f _ (k1  k2  k5) f _ (k3  k4  k5) π^( )^k4 ∂ _ τ1 π^( ) _ ó ^k2 A^( ) _ τ1^k3 π^( )^k1)/(4 f _ π^(ó    )) + (f _ (k1  k2  k5) f _ (k3  k4  k5) π^( )^k3 ∂ _ τ1 π^( ) _ ó ^k2 A^( ) _ τ1^k4 π^( )^k1)/(4 f _ π^(ó    ))

fields = {QuantumField[Particle[AxialVector[0], RenormalizationState[0]], LorentzIndex[μ1], SUNIndex[I1]][p1], QuantumField[Particle[Pion, RenormalizationState[0]], SUNIndex[I2]][p2], QuantumField[Particle[Pion, RenormalizationState[0]], SUNIndex[I3]][p3], QuantumField[Particle[Pion, RenormalizationState[0]], SUNIndex[I4]][p4]}

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

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

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

mfa = FCToFA[melsimplified]

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

mfacoll = MomentaCollect[mfa, ParticlesNumber -> 1, PerturbationOrder -> 1]

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

gencoup = GenericCoupling[mfacoll] ; gencoup

{p _ 2 _ μ _ 1, p _ 3 _ μ _ 1, p _ 4 _ μ _ 1}

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

{{-(4 (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]])}, {-(4 (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]])}, {(4 (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]])}}

$VeryVerbose = 2 ;

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

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\CouplingVectors\\ChPTVirtualPhotons2A00P20P20P20o2.Gen

File does not exist, evaluating

Saving

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

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\CouplingVectors\\ChPTVirtualPhotons2A00P20P20P20o2.Mod

File does not exist, evaluating

Saving

$VeryVerbose = 0 ;


Converted by Mathematica  (July 10, 2003)