•The pion

zpion = CheckF[dum, "ChPT3P20o2.Fac"]

(2 (32 π^2 (6 (L _ 4^( ) + L _ 5^( )) - λ) - log((m _ π^(ó  ))^2/μ^2)) (m _ π^(ó  ))^2 + (32 π^2 (24 L _ 4^( ) - λ) - log((m _ K^(ó  ))^2/μ^2)) (m _ K^(ó  ))^2)/(48 π^2 (f _ ϕ^(ó  ))^2) + 1

ff2 = amplFC2 /. D -> Sequence[] /. i1 -> 1

(4 (f _ ϕ^(ó  ))^2 (!, _ 0^( ))^2)/((m _ π^(ó  ))^2 - p _ 3^2)

$ConstantIsoIndices = {i1, i3, I1, I2} ;

amploop = Plus @@ ampinfinities /. i1 -> 1 // SUNReduce // SUNReduce // Simplify

((5 (32 π^2 λ + log((m _ π^(ó  ))^2/μ^2)) (m _ π^(ó  ))^2 + 4 (32 π^2 λ + log((m _ K^(ó  ))^2/μ^2)) (m _ K^(ó  ))^2 + (32 π^2 λ + log((m _ η^(ó  ))^2/μ^2)) (m _ η^(ó  ))^2) (!, _ 0^( ))^2)/(12 π^2 (p _ 3^2 - (m _ π^(ó  ))^2))

Take[amplFC4, {1, 1}] /. i1 -> 1 // Simplify

{16 (H _ 2^( ) - 2 L _ 8^( )) (!, _ 0^( ))^2}

ampct = Plus @@ Take[amplFC4, {1, 3}] /. i1 -> 1 // Simplify

(16 (H _ 2^( ) ((m _ π^(ó  ))^2 - p _ 3^2) + 2 L _ 8^( ) (3 (m _ π^(ó  ))^2 + p _ 3^2) + 8 L _ 6^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2)) (!, _ 0^( ))^2)/((m _ π^(ó  ))^2 - p _ 3^2)

Z^(-1) ~~ 1 + ϵ. The first order tree amplitude is multiplied with Z ~~ 1 - ϵ = 1 - (Z^(-1) - 1) = 2 - Z^(-1):

ampwf = ff2 * (2 - zpion) // FullSimplify

-((48 π^2 (f _ ϕ^(ó  ))^2 + 2 (32 π^2 (λ - 6 (L _ 4^( ) + L _ 5^( ))) + log((m _ π^(ó  ))^2/μ^2)) (m _ π^(ó  ))^2 + (32 π^2 (λ - 24 L _ 4^( )) + log((m _ K^(ó  ))^2/μ^2)) (m _ K^(ó  ))^2) (!, _ 0^( ))^2)/(12 π^2 (p _ 3^2 - (m _ π^(ó  ))^2))

ff4 = amploop + ampct + ampwf /. D -> Sequence[] // FullSimplify

1/(12 π^2 (p _ 3^2 - (m _ π^(ó  ))^2)) ((-48 π^2 (f _ ϕ^(ó  ))^2 + (32 π^2 λ + log((m _ η^(ó  ))^2/μ^2)) (m _ η^(ó  ))^2 - 384 π^2 L _ 8^( ) (3 (m _ π^(ó  ))^2 + p _ 3^2) + 3 ((32 π^2 (4 (L _ 4^( ) + L _ 5^( ) - 4 L _ 6^( )) + λ) + log((m _ π^(ó  ))^2/μ^2)) (m _ π^(ó  ))^2 + (32 π^2 (8 L _ 4^( ) - 32 L _ 6^( ) + λ) + log((m _ K^(ó  ))^2/μ^2)) (m _ K^(ó  ))^2 + 64 π^2 H _ 2^( ) (p _ 3^2 - (m _ π^(ó  ))^2))) (!, _ 0^( ))^2)

z = (ff4/ff2 // Renormalize // Cancel // Simplify) /. Pair[Momentum[p3], Momentum[p3]] -> ParticleMass[Pion, RenormalizationState[0]]^2 /. gellmannOkubo /. a_Log :> (a /. toEtaRules) // FullSimplify

1/(144 π^2 (f _ ϕ^(ó  ))^2) (144 π^2 (f _ ϕ^(ó  ))^2 + (-1152 π^2 (L _ 4^(r ) + L _ 5^(r ) - 4 (L _ 6^(r ) + L _ 8^(r ))) - 9 log((m _ π^(ó  ))^2/μ^2) + log((m _ η^(ó  ))^2/μ^2)) (m _ π^(ó  ))^2 - (2304 π^2 (L _ 4^(r ) - 4 L _ 6^(r )) + 9 log((m _ K^(ó  ))^2/μ^2) + 4 log((m _ η^(ó  ))^2/μ^2)) (m _ K^(ó  ))^2)

$VeryVerbose = 2 ;

CheckF[z, "ChPT3P02o2.Fac"] ;

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\Factors\\ChPT3P02o2.Fac

File does not exist, evaluating

Saving

$VeryVerbose = 0 ;

Converted by Mathematica  (July 10, 2003)