•The kaon

zkaon = CheckF[dum, "ChPT3P60o2.Fac"]

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\Factors\\ChPT3P60o2.Fac

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1 - 1/(64 π^2 (f _ ϕ^(ó    ))^2) ((32 π^2 λ + log((m _ π^(ó    ))^2/μ^2)) (m _ π^(ó    ))^2 + 2 (32 π^2 (λ - 8 L _ 5^(  )) + 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 - 512 π^2 L _ 4^(  ) ((m _ π^(ó    ))^2 + 2 (m _ K^(ó    ))^2))

ff2 = -I * melsimplified /. _SU3Delta -> 1

2 f _ ϕ^(ó    ) !, _ 0^(  )

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

amploop = ampinfinities /. i1 -> 4 // SUNReduce // SUNReduce // Simplify

-((3 (32 π^2 λ + log((m _ π^(ó    ))^2/μ^2)) (m _ π^(ó    ))^2 + 6 (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^(  ))/(48 π^2 f _ ϕ^(ó    ))

ampct = -I * amp4 /. I2 -> I1 /. I1 -> 4 /. subpar /. udrules // SUNReduce // Simplify

(32 (L _ 8^(  ) (m _ K^(ó    ))^2 + L _ 6^(  ) ((m _ π^(ó    ))^2 + 2 (m _ K^(ó    ))^2)) !, _ 0^(  ))/f _ ϕ^(ó    )

ampwf = ff2 (1 + (2 - zkaon))/2 // Simplify

f _ ϕ^(ó    ) (1/(64 π^2 (f _ ϕ^(ó    ))^2) ((32 π^2 λ + log((m _ π^(ó    ))^2/μ^2)) (m _ π^(ó    ))^2 + 2 (32 π^2 (λ - 8 L _ 5^(  )) + 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 - 512 π^2 L _ 4^(  ) ((m _ π^(ó    ))^2 + 2 (m _ K^(ó    ))^2)) + 2) !, _ 0^(  )

ff4 = amploop + ampct + ampwf // ExpandAll // FullSimplify

1/(192 π^2 f _ ϕ^(ó    )) ((384 π^2 (f _ ϕ^(ó    ))^2 - 3 (32 π^2 (16 L _ 4^(  ) - 64 L _ 6^(  ) + 3 λ) + 3 log((m _ π^(ó    ))^2/μ^2)) (m _ π^(ó    ))^2 - 6 (32 π^2 (8 (2 L _ 4^(  ) + L _ 5^(  ) - 8 L _ 6^(  ) - 4 L _ 8^(  )) + 3 λ) + 3 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^(  ))

z = (ff4/ff2 /. gellmannOkubo // Renormalize // FullSimplify) /. toEtaRules

1/(1152 π^2 (f _ ϕ^(ó    ))^2) (1152 π^2 (f _ ϕ^(ó    ))^2 + (-4608 π^2 (L _ 4^(r  ) - 4 L _ 6^(r  )) - 27 log((m _ π^(ó    ))^2/μ^2) + log((m _ η^(ó    ))^2/μ^2)) (m _ π^(ó    ))^2 - 2 (2304 π^2 (2 L _ 4^(r  ) + L _ 5^(r  ) - 8 L _ 6^(r  ) - 4 L _ 8^(r  )) + 27 log((m _ K^(ó    ))^2/μ^2) + 2 log((m _ η^(ó    ))^2/μ^2)) (m _ K^(ó    ))^2)

CheckF[z, "ChPT3P00P60o2.Fac"] ;

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\Factors\\ChPT3P00P60o2.Fac

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Converted by Mathematica  (July 10, 2003)