•ππγ

IsoVector[QuantumField[Particle[AxialVector[0 | 1], ___], ___], ___][_] := 0 ; QuantumField[Particle[AxialVector[0 | 1], ___], ___][_] := 0 ; IsoVector[QuantumField[Particle[Scalar[1 | 2], ___], ___], ___][_] := 0 ; QuantumField[Particle[Scalar[1 | 2], ___], ___][_] := 0 ; IsoVector[QuantumField[Particle[PseudoScalar[0], ___], ___], ___][_] := 0 ; QuantumField[Particle[PseudoScalar[0], ___], ___][_] := 0 ;

LoadLagrangian[ChPT2[4]] ;

lag = Lagrangian[ChPT2[4]] + Lagrangian[ChPTEM2[4]] /. {FST[LeftComponent[0], {μ}, {ν}] :> 2 FieldStrengthTensorFull[LorentzIndex[μ], UMatrix[UChiralSpurionLeft] QuantumField[Particle[LeftComponent[1]], LorentzIndex[ν]][x], x], FST[RightComponent[0], {μ}, {ν}] :> 2 FieldStrengthTensorFull[LorentzIndex[μ], UMatrix[UChiralSpurionRight] QuantumField[Particle[RightComponent[1]], LorentzIndex[ν]][x], x]}

k _ 13^( ) (< Q '6 Q > '6 < Q '6 Q >) (f _ π^(ó  ))^4 + k _ 9^( ) (< Q '6 Q > '6 < Q '6 ÷„ '6 Q '6 ÷„^† >) (f _ π^(ó  ))^4 + k _ 1^( ) (< Q '6 ÷„ '6 Q '6 ÷„^† > '6 < Q '6 ÷„ '6 Q '6 ÷„^† >) (f _ π^(ó  ))^4 + k _ 14^( ) ((< (÷„ '6 χ^† + χ '6 ÷„^†) '6 Q > + < (÷„^† '6 χ + χ^† '6 ÷„) '6 Q >) '6 < Q >) (f _ π^(ó  ))^2 + k _ 11^( ) (< Q '6 Q > '6 (< ÷„ '6 χ^† > + < χ '6 ÷„^† >)) (f _ π^(ó  ))^2 + k _ 10^( ) (< Q '6 Q > '6 < ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† >) (f _ π^(ó  ))^2 + k _ 4^( ) (< ÷„^† '6 ÷s _ μ(÷„) '6 Q > '6 < ÷s _ μ(÷„) '6 ÷„^† '6 Q >) (f _ π^(ó  ))^2 + k _ 3^( ) (< ÷„^† '6 ÷s _ μ(÷„) '6 Q > '6 < ÷„^† '6 ÷s _ μ(÷„) '6 Q > + < ÷s _ μ(÷„) '6 ÷„^† '6 Q > '6 < ÷s _ μ(÷„) '6 ÷„^† '6 Q >) (f _ π^(ó  ))^2 + k _ 7^( ) (< Q '6 ÷„ '6 Q '6 ÷„^† > '6 (< χ '6 ÷„^† > + < χ^† '6 ÷„ >)) (f _ π^(ó  ))^2 + k _ 2^( ) (< Q '6 ÷„ '6 Q '6 ÷„^† > '6 < ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† >) (f _ π^(ó  ))^2 + k _ 12^( ) (< ÷s _ μ(Q _ L) '6 ÷s _ μ(Q _ L) > + < ÷s _ μ(Q _ R) '6 ÷s _ μ(Q _ R) >) (f _ π^(ó  ))^2 + k _ 8^( ) < (÷„^† '6 χ - χ^† '6 ÷„) '6 (÷„^† '6 Q '6 ÷„ '6 Q - Q '6 ÷„^† '6 Q '6 ÷„) > (f _ π^(ó  ))^2 + k _ 5^( ) (< (Q '6 ÷s _ μ(Q) - ÷s _ μ(Q) '6 Q) '6 ÷„^† '6 ÷s _ μ(÷„) > - < (Q '6 ÷s _ μ(Q) - ÷s _ μ(Q) '6 Q) '6 ÷s _ μ(÷„) '6 ÷„^† >) (f _ π^(ó  ))^2 + k _ 6^( ) < ÷s _ μ(Q) '6 ÷„ '6 ÷s _ μ(Q) '6 ÷„^† > (f _ π^(ó  ))^2 + L _ 7^( ) ((< χ '6 ÷„^† > - < ÷„ '6 χ^† >) '6 (< χ '6 ÷„^† > - < ÷„ '6 χ^† >)) + L _ 6^( ) ((< ÷„ '6 χ^† > + < χ '6 ÷„^† >) '6 (< ÷„ '6 χ^† > + < χ '6 ÷„^† >)) + L _ 4^( ) (< ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† > '6 (< ÷„ '6 χ^† > + < χ '6 ÷„^† >)) + L _ 1^( ) (< ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† > '6 < ÷s _ ν(÷„) '6 ÷s _ ν(÷„)^† >) + L _ 2^( ) (< ÷s _ μ(÷„) '6 ÷s _ ν(÷„)^† > '6 < ÷s _ μ(÷„) '6 ÷s _ ν(÷„)^† >) + H _ 2^( ) < χ^† '6 χ > + k _ 15^( ) (γ^( ) _ (μ ν) '6 γ^( ) _ (μ ν)) < Q '6 Q > + H _ 1^( ) (< (i (Q _ L '6 γ^( ) _ μ '6 Q _ L '6 γ^( ) _ ν - Q _ L '6 γ^( ) _ ν '6 Q _ L '6 γ^( ) _ μ) + Q _ L ∂ _ μ γ^( ) _ ν^ó  - Q _ L ∂ _ ν γ^( ) _ μ^ó ) '6 (i (Q _ L '6 γ^( ) _ μ '6 Q _ L '6 γ^( ) _ ν - Q _ L '6 γ^( ) _ ν '6 Q _ L '6 γ^( ) _ μ) + Q _ L ∂ _ μ γ^( ) _ ν^ó  - Q _ L ∂ _ ν γ^( ) _ μ^ó ) > + < (i (Q _ R '6 γ^( ) _ μ '6 Q _ R '6 γ^( ) _ ν - Q _ R '6 γ^( ) _ ν '6 Q _ R '6 γ^( ) _ μ) + Q _ R ∂ _ μ γ^( ) _ ν^ó  - Q _ R ∂ _ ν γ^( ) _ μ^ó ) '6 (i (Q _ R '6 γ^( ) _ μ '6 Q _ R '6 γ^( ) _ ν - Q _ R '6 γ^( ) _ ν '6 Q _ R '6 γ^( ) _ μ) + Q _ R ∂ _ μ γ^( ) _ ν^ó  - Q _ R ∂ _ ν γ^( ) _ μ^ó ) >) + L _ 5^( ) < ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† '6 (÷„ '6 χ^† + χ '6 ÷„^†) > + i L _ 9^( ) (< (i (Q _ L '6 γ^( ) _ μ '6 Q _ L '6 γ^( ) _ ν - Q _ L '6 γ^( ) _ ν '6 Q _ L '6 γ^( ) _ μ) + Q _ L ∂ _ μ γ^( ) _ ν^ó  - Q _ L ∂ _ ν γ^( ) _ μ^ó ) '6 ÷s _ μ(÷„) '6 ÷s _ ν(÷„)^† > + < (i (Q _ R '6 γ^( ) _ μ '6 Q _ R '6 γ^( ) _ ν - Q _ R '6 γ^( ) _ ν '6 Q _ R '6 γ^( ) _ μ) + Q _ R ∂ _ μ γ^( ) _ ν^ó  - Q _ R ∂ _ ν γ^( ) _ μ^ó ) '6 ÷s _ μ(÷„)^† '6 ÷s _ ν(÷„) >) + L _ 8^( ) (< ÷„ '6 χ^† '6 ÷„ '6 χ^† > + < χ '6 ÷„^† '6 χ '6 ÷„^† >) + L _ 3^( ) < ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† '6 ÷s _ ν(÷„) '6 ÷s _ ν(÷„)^† > + L _ 10^( ) < (i (Q _ L '6 γ^( ) _ μ '6 Q _ L '6 γ^( ) _ ν - Q _ L '6 γ^( ) _ ν '6 Q _ L '6 γ^( ) _ μ) + Q _ L ∂ _ μ γ^( ) _ ν^ó  - Q _ L ∂ _ ν γ^( ) _ μ^ó ) '6 ÷„ '6 (i (Q _ R '6 γ^( ) _ μ '6 Q _ R '6 γ^( ) _ ν - Q _ R '6 γ^( ) _ ν '6 Q _ R '6 γ^( ) _ μ) + Q _ R ∂ _ μ γ^( ) _ ν^ó  - Q _ R ∂ _ ν γ^( ) _ μ^ó ) '6 ÷„^† >

IsoVector[QuantumField[Particle[Vector[0], ___], ___], ___][_] := 0 ; QuantumField[Particle[Vector[0], ___], ___][_] := 0 ;

ll = CheckF[(WriteString["stdout", "."] ; UNMSplit[#, x, DropOrder -> 2]) & /@ lag, "llV2piEM"] ;

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

ArgumentsSupply :: argxpr : Warning : The argument x is already in the expression.

llld = DiscardTerms[lll, Retain -> {ParticleField[Pion , RenormalizationState[0]] -> 2, ParticleField[Photon, RenormalizationState[0]] -> 1}, CommutatorReduce -> True, Method -> Expand] ;

llle = (WriteString["stdout", "."] ; ExpandU[#] // CommutatorReduce // Simplify) & /@ llld ;

....................................

llll = ($IsoIndicesCounter = 0 ; WriteString["stdout", "."] ; # // IsoIndicesSupply // SUNReduce[#, FullReduce -> True] & // IndicesCleanup // CommutatorReduce[#, FullReduce -> True] & // Simplify) & /@ llle ;

............

lala = Simplify /@ Collect[llll /. NM -> Times, CouplingConstant[_[4], __]] ;

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]}

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

mel = ((WriteString["stdout", "."] ; I * FunctionalD[PhiToFC[#], fields]) & /@ lala) ;

.....

melsimplified = Collect[mel // SUNReduce[#, FullReduce -> True] &, {_DecayConstant, _CouplingConstant, _Pair}] // Contract // FullSimplify

(4 e^( ) (5 (e^( ))^2 (k _ 2^( ) + k _ 10^( )) (p _ 1^μ _ 3 - p _ 2^μ _ 3) (f _ π^(ó  ))^2 + 18 (2 L _ 4^( ) + L _ 5^( )) (p _ 1^μ _ 3 - p _ 2^μ _ 3) (m _ π^(ó  ))^2 + L _ 9^( ) (9 p _ 1^μ _ 3 p _ 2 · p _ 3 - 9 p _ 2^μ _ 3 p _ 1 · p _ 3)) f _ (3 I _ 1 I _ 2)^(2))/(9 (f _ π^(ó  ))^2)

facoll = MomentaCollect[melsimplified // FCToFA // Expand, ParticlesNumber -> 2, PerturbationOrder -> 4, MetricTensor -> None]

p _ 1 _ μ _ 3 (20/9 k _ 2^( ) f _ (3 I _ 1 I _ 2)^(2) + 20/9 k _ 10^( ) f _ (3 I _ 1 I _ 2)^(2)) (e^( ))^3 - p _ 2 _ μ _ 3 (20/9 k _ 2^( ) f _ (3 I _ 1 I _ 2)^(2) + 20/9 k _ 10^( ) f _ (3 I _ 1 I _ 2)^(2)) (e^( ))^3 - (4 L _ 9^( ) p _ 2 _ μ _ 3 (p _ 1 ° p _ 3) f _ (3 I _ 1 I _ 2)^(2) e^( ))/(f _ π^(ó  ))^2 + (4 L _ 9^( ) p _ 1 _ μ _ 3 (p _ 2 ° p _ 3) f _ (3 I _ 1 I _ 2)^(2) e^( ))/(f _ π^(ó  ))^2 + p _ 1 _ μ _ 3 (m _ π^(ó  ))^2 ((16 L _ 4^( ) f _ (3 I _ 1 I _ 2)^(2))/(f _ π^(ó  ))^2 + (8 L _ 5^( ) f _ (3 I _ 1 I _ 2)^(2))/(f _ π^(ó  ))^2) e^( ) - p _ 2 _ μ _ 3 (m _ π^(ó  ))^2 ((16 L _ 4^( ) f _ (3 I _ 1 I _ 2)^(2))/(f _ π^(ó  ))^2 + (8 L _ 5^( ) f _ (3 I _ 1 I _ 2)^(2))/(f _ π^(ó  ))^2) e^( )

gencoup = GenericCoupling[facoll] ; gencoup

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

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

{{-(4 CouplingConstant[ChPT2[4], 9, RenormalizationState[0]] SU2F[3, I1, I2])/DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, {(4 CouplingConstant[ChPT2[4], 9, RenormalizationState[0]] SU2F[3, I1, I2])/DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, {20/9 (CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]] SU2F[3, I1, I2] + CouplingConstant[ChPTEM2[4], 10, RenormalizationState[0]] SU2F[3, I1, I2])}, {-20/9 (CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]] SU2F[3, I1, I2] + CouplingConstant[ChPTEM2[4], 10, RenormalizationState[0]] SU2F[3, I1, I2])}, {(8 (2 CouplingConstant[ChPT2[4], 4, RenormalizationState[0]] SU2F[3, I1, I2] + CouplingConstant[ChPT2[4], 5, RenormalizationState[0]] SU2F[3, I1, I2]))/DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, {-(8 (2 CouplingConstant[ChPT2[4], 4, RenormalizationState[0]] SU2F[3, I1, I2] + CouplingConstant[ChPT2[4], 5, RenormalizationState[0]] SU2F[3, I1, I2]))/DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}}

$VeryVerbose = 2 ;

CheckF[gencoup, XName[VertexFields -> {PseudoScalar[2][0], PseudoScalar[2][0], Vector[1][0]}, PerturbationOrder -> 4, PhiModel -> ChPTEM2, XFileName -> Automatic] <> ".Gen"] ;

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\CouplingVectors\\ChPTEM2P20P20V10o4.Gen

File exists, loading

CheckF[classcoup, XName[VertexFields -> {PseudoScalar[2][0], PseudoScalar[2][0], Vector[1][0]}, PerturbationOrder -> 4, PhiModel -> ChPTEM2, XFileName -> Automatic] <> ".Mod"] ;

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\CouplingVectors\\ChPTEM2P20P20V10o4.Mod

File exists, loading

$VeryVerbose = 0 ;

Converted by Mathematica  (July 10, 2003)