•Preliminaries

SetOptions[A0, A0ToB0 -> True] ; SetOptions[B0, BReduce -> False] ;

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

$Gauge = 1 ;

Rules for obtaining compacter expressions.

pimassrule = ParticleMass[Pion, i_ ? (! IntegerQ[#] &) | SUNIndex[i_ ? (! IntegerQ[#] &)], r___]^2 -> (SU2Delta[SUNIndex[i], SUNIndex[1]] + SU2Delta[SUNIndex[i], SUNIndex[2]]) ParticleMass[PionPlus, r]^2 + SU2Delta[SUNIndex[i], SUNIndex[3]] ParticleMass[PionZero, r]^2

ParticleMass(π, i_ ? (¬ IntegerQ[#1] &) | i_ ? (¬ IntegerQ[#1] &), r___)^2 -> (δ _ (1 i)^(2) + δ _ (2 i)^(2)) ParticleMass(π^+, r)^2 + ParticleMass(π^0, r)^2 δ _ (3 i)^(2)

delrules = {SU2Delta[SUNIndex[1], SUNIndex[i1]] + SU2Delta[SUNIndex[2], SUNIndex[i1]] -> (1 - SU2Delta[SUNIndex[3], SUNIndex[i1]]), a_ * SU2Delta[SUNIndex[1], SUNIndex[i1]] + a_ * SU2Delta[SUNIndex[2], SUNIndex[i1]] -> a * (1 - SU2Delta[SUNIndex[3], SUNIndex[i1]])}

{δ _ (1 i _ 1)^(2) + δ _ (2 i _ 1)^(2) -> 1 - δ _ (3 i _ 1)^(2), a_ δ _ (1 i _ 1)^(2) + a_ δ _ (2 i _ 1)^(2) -> a (1 - δ _ (3 i _ 1)^(2))}

cancelScales = Log[ParticleMass[PionPlus, RenormalizationState[0]]^2/ScaleMu^2] -> Log[ParticleMass[PionZero, RenormalizationState[0]]^2/ScaleMu^2] + Log[ParticleMass[PionPlus, RenormalizationState[0]]^2/ParticleMass[PionZero, RenormalizationState[0]]^2]

log((m _ π^+^(ó  ))^2/μ^2) -> log((m _ π^+^(ó  ))^2/(m _ π^0^(ó  ))^2) + log((m _ π^0^(ó  ))^2/μ^2)

Function for collecting the EM coupling constants.

collectk[x_] := (x /. Plus[a : (((_ ? (FreeQ[#, _CouplingConstant] &)) * CouplingConstant[ChPTVirtualPhotons2[4], _ ? ((# > 10) &), ___] | CouplingConstant[ChPTVirtualPhotons2[4], _ ? ((# > 10) &), ___]) ..), b___ ? (FreeQ[#, CouplingConstant[ChPTVirtualPhotons2[4], _ ? ((# > 10) &), ___]] &)] :> wrap[a] + b /. wrap[a_ * b_CouplingConstant, c___] :> a * ((#/a) & /@ wrap[a * b, c]) // FullSimplify) /. wrap -> Plus // FullSimplify ;

Converted by Mathematica  (July 10, 2003)