•The eta

zeta = CheckF[dum, "ChPT3P110o2.Fac"]

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\Factors\\ChPT3P110o2.Fac

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((32 π^2 (24 L _ 4^(  ) + 16 L _ 5^(  ) - 3 λ) - 3 log((m _ K^(ó    ))^2/μ^2)) (m _ K^(ó    ))^2 + 16 π^2 (3 (f _ ϕ^(ó    ))^2 + 8 (3 L _ 4^(  ) - L _ 5^(  )) (m _ π^(ó    ))^2))/(48 π^2 (f _ ϕ^(ó    ))^2)

ff2 = amp2 /. p2 -> -p1

-i f _ ϕ^(ó    ) p _ 1^μ _ 1

amploop = ampinfinities /. ρ1 -> μ1 /. i1 -> 8 // SUNReduce // Simplify

(i (32 π^2 λ + log((m _ K^(ó    ))^2/μ^2)) p _ 1^μ _ 1 (m _ K^(ó    ))^2)/(8 π^2 f _ ϕ^(ó    ))

ampwf4 = amp4 /. p2 -> -p1 /. I1 -> 8 // SUNReduce // Simplify

-(8 i p _ 1^μ _ 1 (3 L _ 4^(  ) ((m _ π^(ó    ))^2 + 2 (m _ K^(ó    ))^2) - L _ 5^(  ) ((m _ π^(ó    ))^2 - 4 (m _ K^(ó    ))^2)))/(3 f _ ϕ^(ó    ))

amppf4 = ff2 (1 + (2 - zeta))/2 // Simplify

-1/2 i f _ ϕ^(ó    ) p _ 1^μ _ 1 (3 - ((32 π^2 (24 L _ 4^(  ) + 16 L _ 5^(  ) - 3 λ) - 3 log((m _ K^(ó    ))^2/μ^2)) (m _ K^(ó    ))^2 + 16 π^2 (3 (f _ ϕ^(ó    ))^2 + 8 (3 L _ 4^(  ) - L _ 5^(  )) (m _ π^(ó    ))^2))/(48 π^2 (f _ ϕ^(ó    ))^2))

ff4 = (amploop + ampwf4 + amppf4 /. gellmannOkubo // ExpandAll // Simplify) /. etalogs

-(i p _ 1^μ _ 1 (96 π^2 (f _ ϕ^(ó    ))^2 - 128 π^2 L _ 5^(  ) (m _ π^(ó    ))^2 + 512 π^2 L _ 5^(  ) (m _ K^(ó    ))^2 - 288 π^2 λ (m _ K^(ó    ))^2 - 9 log((m _ K^(ó    ))^2/μ^2) (m _ K^(ó    ))^2 + 384 π^2 L _ 4^(  ) ((m _ π^(ó    ))^2 + 2 (m _ K^(ó    ))^2)))/(96 π^2 f _ ϕ^(ó    ))

ff0 = Renormalize[ff4] // Simplify

-(i p _ 1^μ _ 1 (96 π^2 (f _ ϕ^(ó    ))^2 - 128 π^2 L _ 5^(r  ) (m _ π^(ó    ))^2 + 512 π^2 L _ 5^(r  ) (m _ K^(ó    ))^2 - 9 log((m _ K^(ó    ))^2/μ^2) (m _ K^(ó    ))^2 + 384 π^2 L _ 4^(r  ) ((m _ π^(ó    ))^2 + 2 (m _ K^(ó    ))^2)))/(96 π^2 f _ ϕ^(ó    ))

c = Collect[Coefficient[-ff0/I/DecayConstant[PhiMeson, RenormalizationState[0]], Pair[LorentzIndex[μ1], Momentum[p1]]], _DecayConstant]

(-128 π^2 L _ 5^(r  ) (m _ π^(ó    ))^2 + 512 π^2 L _ 5^(r  ) (m _ K^(ó    ))^2 - 9 log((m _ K^(ó    ))^2/μ^2) (m _ K^(ó    ))^2 + 384 π^2 L _ 4^(r  ) ((m _ π^(ó    ))^2 + 2 (m _ K^(ó    ))^2))/(96 π^2 (f _ ϕ^(ó    ))^2) + 1

CheckF[c, "ChPT3A00P110o2.Fac"] ;

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\Factors\\ChPT3A00P110o2.Fac

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Converted by Mathematica  (July 10, 2003)