•Preliminaries

At O(p^4) we don't need to distinguish renormalized and unrenormalized masses.

ren4Rule = {ParticleMass[p__, RenormalizationState[0]] :> ParticleMass[p, RenormalizationState[1]], CouplingConstant[QED[1], RenormalizationState[0]] -> CouplingConstant[QED[1], RenormalizationState[1]]}

{m _ p__^(ó  ) :> m _ p^(ó  r ), e^( ) -> e^(r )}

Mandelstam reduction:

manred[s_] := (MandelstamReduce[#, Cancel -> s, Masses -> ({ParticleMass[Pion, SUNIndex[d1], RenormalizationState[1]], ParticleMass[Pion, SUNIndex[d2], RenormalizationState[1]], ParticleMass[Pion, SUNIndex[d3], RenormalizationState[1]], ParticleMass[Pion, SUNIndex[d4], RenormalizationState[1]]} // IsoToChargedMasses)] &) ;

The parameter fixing parameter of QED in general Lorentz gauge. 1 is Feynman guage:

$Gauge = 1 ;

Some quick hacks are used to exclude non-one-particle-irreducible graphs. Choose whether or not to include one-particle irreducible graphs:

opi = False ;

Rule for dropping higher orders in e , applied to analytical expressions:

(* eDrop = CouplingConstant[QED[1], ___]^(_ ? ((# > 3) &)) :> 0 ; *)

eDrop = {} ;

Log reduction:

scaleRule = CouplingConstant[l_[4], i_, r___] :> RenormalizationCoefficients[l[4]][[i]]/(32 Pi^2) (CouplingConstant[l[4], i, r] + Log[ParticleMass[PionPlus]^2/ScaleMu^2]) /; RenormalizationCoefficients[l[4]][[i]] =!= 0 ;

logRule = Log[a_] :> 0 /; FreeQ[{a}, ScaleMu] ;

logRule1 = Log[a_ * b_] -> Log[a] + Log[b] ;

Converted by Mathematica  (July 10, 2003)