•ππγ

IsoVector[QuantumField[Particle[AxialVector[0], ___], ___], ___][_] := 0 ; IsoVector[QuantumField[Particle[Vector[0], ___], ___], ___][_] := 0 ; QuantumField[Particle[Vector[0], ___], ___][_] := 0 ; IsoVector[QuantumField[Particle[Scalar[1], ___], ___], ___][_] := 0 ; QuantumField[Particle[Scalar[1], ___], ___][_] := 0 ;

lag = Lagrangian[ChPTVirtualPhotons2[4]] /. QuantumField[Particle[(LeftComponent | RightComponent)[0], ___], ___, SUNIndex[0], ___] -> 0

(k _ 12^( ) (< Q '6 Q > '6 < Q '6 Q >) + k _ 13^( ) (< Q '6 ÷„ '6 Q '6 ÷„^† > '6 < Q '6 Q >) + k _ 14^( ) (< Q '6 ÷„ '6 Q '6 ÷„^† > '6 < Q '6 ÷„ '6 Q '6 ÷„^† >)) (f _ π^(ó  ))^4 + (k _ 5^( ) ((< ÷„^† '6 χ > + < χ^† '6 ÷„ >) '6 < Q '6 Q >) + k _ 6^( ) ((< ÷„^† '6 χ > + < χ^† '6 ÷„ >) '6 < Q '6 ÷„ '6 Q '6 ÷„^† >) + k _ 1^( ) (< ÷s _ μ(÷„)^† '6 ÷s _ μ(÷„) > '6 < Q '6 Q >) + k _ 2^( ) (< ÷s _ μ(÷„)^† '6 ÷s _ μ(÷„) > '6 < Q '6 ÷„ '6 Q '6 ÷„^† >) + k _ 7^( ) ((< (÷„ '6 χ^† + χ '6 ÷„^†) '6 Q > + < (÷„^† '6 χ + χ^† '6 ÷„) '6 Q >) '6 < Q >) + k _ 4^( ) (< ÷s _ μ(÷„)^† '6 Q '6 ÷„ > '6 < ÷s _ μ(÷„) '6 Q '6 ÷„^† >) + k _ 3^( ) (< ÷s _ μ(÷„)^† '6 Q '6 ÷„ > '6 < ÷s _ μ(÷„)^† '6 Q '6 ÷„ > + < ÷s _ μ(÷„) '6 Q '6 ÷„^† > '6 < ÷s _ μ(÷„) '6 Q '6 ÷„^† >) + k _ 11^( ) (< c _ μ^L Q _ L '6 c _ μ^L Q _ L > + < c _ μ^R Q _ R '6 c _ μ^R Q _ R >) + k _ 9^( ) (< ÷s _ μ(÷„)^† '6 (c _ μ^R Q _ R '6 Q - Q '6 c _ μ^R Q _ R) '6 ÷„ > + < ÷s _ μ(÷„) '6 (c _ μ^L Q _ L '6 Q - Q '6 c _ μ^L Q _ L) '6 ÷„^† >) + k _ 10^( ) < c _ μ^R Q _ R '6 ÷„ '6 c _ μ^L Q _ L '6 ÷„^† > + k _ 8^( ) (< (χ '6 ÷„^† - ÷„ '6 χ^†) '6 Q '6 ÷„ '6 Q '6 ÷„^† > + < (χ^† '6 ÷„ - ÷„^† '6 χ) '6 Q '6 ÷„^† '6 Q '6 ÷„ >)) (f _ π^(ó  ))^2 - 1/16 l _ 7^( ) ((< χ^† '6 ÷„ > - < ÷„^† '6 χ >) '6 (< χ^† '6 ÷„ > - < ÷„^† '6 χ >)) + 1/16 l _ 3^( ) ((< ÷„^† '6 χ > + < χ^† '6 ÷„ >) '6 (< ÷„^† '6 χ > + < χ^† '6 ÷„ >)) + 1/4 l _ 1^( ) (< ÷s _ μ(÷„)^† '6 ÷s _ μ(÷„) > '6 < ÷s _ ν(÷„)^† '6 ÷s _ ν(÷„) >) + 1/4 l _ 2^( ) (< ÷s _ μ(÷„)^† '6 ÷s _ ν(÷„) > '6 < ÷s _ μ(÷„)^† '6 ÷s _ ν(÷„) >) + 1/2 (h _ 1^( ) - h _ 3^( )) Re({χ}) + k _ 15^( ) (γ^( ) _ (μ ν) '6 γ^( ) _ (μ ν)) < Q '6 Q > + 1/4 (h _ 1^( ) + h _ 3^( )) < χ^† '6 χ > + 1/4 l _ 4^( ) (< ÷s _ μ(÷„)^† '6 ÷s _ μ(χ) > + < ÷s _ μ(χ)^† '6 ÷s _ μ(÷„) >) + l _ 5^( ) < G _ (μ ν)^R '6 G _ (μ ν)^L^† > - h _ 2^( ) (< G _ (μ ν)^L '6 G _ (μ ν)^L > + < G _ (μ ν)^R '6 G _ (μ ν)^R >) + 1/2 i l _ 6^( ) (< G _ (μ ν)^L '6 ÷s _ μ(÷„)^† '6 ÷s _ ν(÷„) > + < G _ (μ ν)^R '6 ÷s _ μ(÷„) '6 ÷s _ ν(÷„)^† >)

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

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

LeafCount /@ List @@ ll

{23, 23, 497, 499, 579, 21825, 21825, 30, 1174, 4762, 4761, 48368, 39475}

lll = ArgumentsSupply[ll, x, RenormalizationState[0], DiagonalToU -> True, ExpansionOrder -> 2, DropOrder -> 2] /. $Substitutions // CycleUTraces ;

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

LeafCount /@ List @@ lll

{117, 962, 9661, 9661, 114, 202, 228, 323, 2932, 47553, 5418, 5417, 22759}

llld = (WriteString["stdout", "."] ; DiscardTerms[#, Retain -> {ParticleField[Pion , RenormalizationState[0]] -> 2, ParticleField[Photon, RenormalizationState[0]] -> 1}, CommutatorReduce -> True, Method -> Expand]) & /@ lll ;

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

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)

...

i (20/9 i (e^( ))^3 k _ 1^( ) p _ 2^μ _ 3 f _ (3 I _ 1 I _ 2) - 20/9 i (e^( ))^3 k _ 1^( ) p _ 1^μ _ 3 f _ (3 I _ 1 I _ 2)) + i (20/9 i (e^( ))^3 k _ 2^( ) p _ 2^μ _ 3 f _ (3 I _ 1 I _ 2) - 20/9 i (e^( ))^3 k _ 2^( ) p _ 1^μ _ 3 f _ (3 I _ 1 I _ 2)) + i (-(i e^( ) l _ 6^( ) p _ 2^τ1 (i g^(μ _ 3 τ1) p _ 3^τ2 - i g^(μ _ 3 τ2) p _ 3^τ1) (p _ 1^τ2 δ _ (I _ 1 I _ 2) + 3 i p _ 1^τ2 f _ (3 I _ 1 I _ 2)))/(3 (f _ π^(ó  ))^2) - (i e^( ) l _ 6^( ) p _ 1^τ1 (i g^(μ _ 3 τ1) p _ 3^τ2 - i g^(μ _ 3 τ2) p _ 3^τ1) (p _ 2^τ2 δ _ (I _ 1 I _ 2) - 3 i p _ 2^τ2 f _ (3 I _ 1 I _ 2)))/(3 (f _ π^(ó  ))^2))

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

(k _ 1^( ) (20/9 p _ 1^μ _ 3 f _ (3 I _ 1 I _ 2)^(2) - 20/9 p _ 2^μ _ 3 f _ (3 I _ 1 I _ 2)^(2)) + k _ 2^( ) (20/9 p _ 1^μ _ 3 f _ (3 I _ 1 I _ 2)^(2) - 20/9 p _ 2^μ _ 3 f _ (3 I _ 1 I _ 2)^(2))) (e^( ))^3 + (l _ 6^( ) (2 p _ 1^μ _ 3 p _ 2 · p _ 3 f _ (3 I _ 1 I _ 2)^(2) - 2 p _ 2^μ _ 3 p _ 1 · p _ 3 f _ (3 I _ 1 I _ 2)^(2)) e^( ))/(f _ π^(ó  ))^2

mfacoll = MomentaCollect[melsimplified // Expand, ParticlesNumber -> 2, PerturbationOrder -> 4, ScalarProductForm -> Pair] ;

gencoup = GenericCoupling[mfacoll] ; 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}

classcoup = ClassesCoupling[mfacoll] // Together

( (2) ) 2 l f 6 3 I I 1 2 --------------- ó  2 (f ) π (2) 2 l f 6 3 I I 1 2 -------------- ó  2 (f ) π 20 (2) (2) -- (k f + k f ) 9 1 3 I I 2 3 I I 1 2 1 2 20 (2) (2) --- (k f + k f ) 9 1 3 I I 2 3 I I 1 2 1 2

$VeryVerbose = 2 ;

CheckF[gencoup, XName[VertexFields -> {PseudoScalar[2][0], PseudoScalar[2][0], Vector[1][0]}, PerturbationOrder -> 4, PhiModel -> ChPTVirtualPhotons2, XFileName -> Automatic] <> ".Gen"] ;

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\CouplingVectors\\ChPTVirtualPhotons2P20P20V10o4.Gen

File does not exist, evaluating

Saving

CheckF[classcoup, XName[VertexFields -> {PseudoScalar[2][0], PseudoScalar[2][0], Vector[1][0]}, PerturbationOrder -> 4, PhiModel -> ChPTVirtualPhotons2, XFileName -> Automatic] <> ".Mod"] ;

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\CouplingVectors\\ChPTVirtualPhotons2P20P20V10o4.Mod

File does not exist, evaluating

Saving

$VeryVerbose = 0 ;

Converted by Mathematica  (July 10, 2003)