•πAγ

IsoVector[QuantumField[Particle[Vector[1], ___], ___], ___][_] := 0 ; <br /> QuantumField[Particle[Vector[1], ___], ___][_] := 0 ; IsoVector[QuantumField[Particle[Vector[0], ___], ___], ___][_] := 0 ; <br /> QuantumField[Particle[Vector[0], ___], ___][_] := 0 ; IsoVector[QuantumField[Particle[Scalar[2], ___], ___], ___][_] := 0 ; <br /> QuantumField[Particle[Scalar[2], ___], ___][_] := 0 ;

ll = ArgumentsSupply[Lagrangian[ChPTVirtualPhotons2[2]], x, RenormalizationState[0], ExpansionOrder -> 1, DropOrder -> 1, DiagonalToU -> True] ;

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

-1/12 i e^( ) f _ π^(ó  ) (< Overscript[π^( ), ->] · Overscript[σ, ->] '6 (÷¬öé - 3 σ^3) '6 Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] > + < Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 (÷¬öé - 3 σ^3) > - < Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] '6 (÷¬öé - 3 σ^3) '6 Overscript[π^( ), ->] · Overscript[σ, ->] > - < (÷¬öé - 3 σ^3) '6 Overscript[π^( ), ->] · Overscript[σ, ->] '6 Overscript[A^( ) _ μ, ->] · Overscript[σ, ->] >) γ^( ) _ μ

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

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

IsoIndicesCounter = 0 ;

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

e^( ) f _ π^(ó  ) f _ (3 k1 k2)^(2) γ^( ) _ μ (π^( )^k1 A^( ) _ μ^k2 - π^( )^k2 A^( ) _ μ^k1)

fields = {QuantumField[Particle[AxialVector[0], RenormalizationState[0]], LorentzIndex[μ1], SUNIndex[I1]][p1], QuantumField[Particle[Pion, RenormalizationState[0]], SUNIndex[I2]][p2], QuantumField[Particle[Photon, RenormalizationState[0]], LorentzIndex[μ3]][p3]}

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

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

-2 i e^( ) f _ π^(ó  ) g^(μ _ 1 μ _ 3) f _ (3 I _ 1 I _ 2)

mfa = FCToFA[melsimplified]

-2 i e^( ) f _ π^(ó  ) g^(μ _ 1 μ _ 3) f _ (3 I _ 1 I _ 2)

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

-2 i e^( ) f _ π^(ó  ) g^(μ _ 1 μ _ 3) f _ (3 I _ 1 I _ 2)

gencoup = GenericCoupling[mfacoll] ; gencoup

{e^( ) g^(μ _ 1 μ _ 3)}

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

{{-2 i DecayConstant[PseudoScalar[2], RenormalizationState[0]] SUNF[3, I1, I2]}}

$VeryVerbose = 2 ;

CheckF[gencoup, XName[VertexFields -> {AxialVector[0][0], PseudoScalar[2][0], Vector[1][0]}, PerturbationOrder -> 2, PhiModel -> ChPTVirtualPhotons2, XFileName -> Automatic] <> ".Gen"] ;

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\CouplingVectors\\ChPTVirtualPhotons2A00P20V10o2.Gen

File does not exist, evaluating

Saving

CheckF[classcoup, XName[VertexFields -> {AxialVector[0][0], PseudoScalar[2][0], Vector[1][0]}, PerturbationOrder -> 2, PhiModel -> ChPTVirtualPhotons2, XFileName -> Automatic] <> ".Mod"] ;

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\CouplingVectors\\ChPTVirtualPhotons2A00P20V10o2.Mod

File does not exist, evaluating

Saving

$VeryVerbose = 0 ;

Converted by Mathematica  (July 10, 2003)