•ππγ

Lagrangian[ChPTVirtualPhotons2[2]]

1/4 (< χ '6 ÷„^† > + < χ^† '6 ÷„ > + < ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† >) (f _ π^(ó  ))^2 - 1/2 λ ∂ _ μ(γ^( ) _ μ) ∂ _ ν(γ^( ) _ ν) - 1/4 (γ^( ) _ (μ ν) '6 γ^( ) _ (μ ν)) + C^( ) < Q _ R '6 ÷„ '6 Q _ L '6 ÷„^† >

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

1/4 i e^( ) < Overscript[π^( ), ->] · Overscript[σ, ->] '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] '6 σ^3 > γ^( ) _ μ - 1/4 i e^( ) < Overscript[π^( ), ->] · Overscript[σ, ->] '6 σ^3 '6 ∂ _ μ(Overscript[π^( ), ->]) · Overscript[σ, ->] > γ^( ) _ μ

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

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

IsoIndicesCounter = 0 ;

llll = IsoIndicesSupply[llle] // SUNReduce // IndicesCleanup // CommutatorReduce // Simplify

-e^( ) f _ (3 k1 k2)^(2) π^( )^k1 γ^( ) _ τ1 ∂ _ τ1 π^( ) _ ó ^k2

fields = {QuantumField[Particle[Pion, RenormalizationState[0]], SUNIndex[I1]][p1], QuantumField[Particle[Pion, RenormalizationState[0]], SUNIndex[I2]][p2], QuantumField[Particle[Photon, RenormalizationState[0]], LorentzIndex[μ3]][p3]}

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

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

e^( ) (p _ 1^μ _ 3 - p _ 2^μ _ 3) f _ (3 I _ 1 I _ 2)^(2)

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

e^( ) p _ 1^μ _ 3 f _ (3 I _ 1 I _ 2)^(2) - e^( ) p _ 2^μ _ 3 f _ (3 I _ 1 I _ 2)^(2)

gencoup = GenericCoupling[mfa]

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

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

{{SU2F[3, I1, I2]}, {-SU2F[3, I1, I2]}}

$VeryVerbose = 2 ;

CheckF[gencoup, XName[PhiModel -> ChPTVirtualPhotons2, VertexFields -> {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\\ChPTVirtualPhotons2P20P20V10o2.Gen

File does not exist, evaluating

Saving

CheckF[classcoup, XName[PhiModel -> ChPTVirtualPhotons2, VertexFields -> {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\\ChPTVirtualPhotons2P20P20V10o2.Mod

File does not exist, evaluating

Saving

$VeryVerbose = 0 ;

Converted by Mathematica  (July 10, 2003)