•Loading the amplitudes

end2all = CheckF[dum, "KSS2end2all"] ;

end2 = Plus @@ end2all /. _Log -> 0 // Simplify

1/(27 (f _ ϕ^(ó  ))^3) (!, _ 0^( ) (-1/(p _ 2^2 - (m _ K^(ó  ))^2) (((m _ π^(ó  r ))^2 - (m _ K^(ó  r ))^2) (c _ 5^( ) (-36 (f _ ϕ^(ó  ))^2 - 288 L _ 5^(r ) (m _ π^(ó  r ))^2 + 576 L _ 6^(r ) (m _ π^(ó  r ))^2 + 576 L _ 8^(r ) (m _ π^(ó  r ))^2 + 59 λ (m _ π^(ó  r ))^2 + 144 L _ 5^(r ) (m _ K^(ó  r ))^2 + 1152 L _ 6^(r ) (m _ K^(ó  r ))^2 + 576 L _ 8^(r ) (m _ K^(ó  r ))^2 + 304 λ (m _ K^(ó  r ))^2 - 27 λ (m _ η^(ó  r ))^2 + 144 L _ 4^(r ) ((m _ π^(ó  r ))^2 + 2 (m _ K^(ó  r ))^2)) - 12 c _ 2^( ) (6 N _ 11^(r ) (m _ π^(ó  r ))^2 + 12 N _ 10^(r ) (m _ K^(ó  r ))^2 + 12 N _ 11^(r ) (m _ K^(ó  r ))^2 + 5 λ (m _ K^(ó  r ))^2 - 6 N _ 21^(r ) p _ 2^2 - 5 λ p _ 2^2)) (6 δ _ (0 i)^(3) - 3 δ _ (3 i)^(3) - 3^(1/2) δ _ (8 i)^(3))) - 27 c _ 5^( ) (4 (f _ ϕ^(ó  ))^2 - λ (m _ π^(ó  ))^2 - 16 L _ 5^(r ) (m _ K^(ó  ))^2 - 8 λ (m _ K^(ó  ))^2 + λ (m _ η^(ó  ))^2 - 16 L _ 4^(r ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2)) (δ _ (3 i)^(3) - 3^(1/2) δ _ (8 i)^(3))))

res1 = CheckF[dum, "KSS2res1"] ;

res1old = CheckF[dum, "KSS2res1old"] ;

end4 = Plus @@ res1 // Simplify

-(2 c _ 2^( ) (N _ 22^( ) (p _ 1^2 - p _ 2^2 - p _ 3^2) + 2 N _ 21^( ) (p _ 1^2 + p _ 2^2 - p _ 3^2)) !, _ 0^( ) (σ _ (2 2)^i - σ _ (3 3)^i))/(f _ ϕ^(ó  ))^3

end4old = Plus @@ res1old // Simplify

1/(3 (f _ ϕ^(ó  ))^3) (8 !, _ 0^( ) (1/(p _ 2^2 - (m _ K^(ó  ))^2) (2 c _ 5^( ) ((m _ K^(ó  ))^2 - (m _ π^(ó  ))^2) (18 L _ 4^( ) (p _ 1^2 + p _ 2^2 - p _ 3^2) δ _ (0 i)^(3) + L _ 5^( ) (p _ 1^2 + p _ 2^2 - p _ 3^2) (6 δ _ (0 i)^(3) - 3 δ _ (3 i)^(3) - 3^(1/2) δ _ (8 i)^(3)) + 4 (2 L _ 8^( ) (-6 δ _ (0 i)^(3) + 3 δ _ (3 i)^(3) + 3^(1/2) δ _ (8 i)^(3)) (m _ K^(ó  ))^2 + L _ 6^( ) ((-6 δ _ (0 i)^(3) + 3 δ _ (3 i)^(3) + 3^(1/2) δ _ (8 i)^(3)) (m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2 (-15 δ _ (0 i)^(3) + 3 δ _ (3 i)^(3) + 3^(1/2) δ _ (8 i)^(3)))))) + 3 c _ 2^( ) (N _ 11^( ) ((m _ π^(ó  ))^2 (6 δ _ (0 i)^(3) + σ _ (2 2)^i - σ _ (3 3)^i) - 2 (m _ K^(ó  ))^2 (3 δ _ (0 i)^(3) - σ _ (2 2)^i + σ _ (3 3)^i)) + 2 N _ 10^( ) ((m _ π^(ó  ))^2 (2 δ _ (0 i)^(3) + σ _ (2 2)^i + σ _ (3 3)^i) - 2 (m _ K^(ó  ))^2 (δ _ (0 i)^(3) + σ _ (3 3)^i)))))

CTcontrib = end4old + end4 + end2 /. CouplingConstant[c_[4], n_] -> CouplingConstant[c[4], n, RenormalizationState[0]] /. D -> Sequence[] /. _RenormalizationState -> Sequence[] // Simplify

1/(27 (f _ ϕ^(ó  ))^3) (!, _ 0^( ) (1/(p _ 2^2 - (m _ K^(ó  ))^2) (((m _ K^(ó  ))^2 - (m _ π^(ó  ))^2) (c _ 5^( ) (-36 (f _ ϕ^(ó  ))^2 - 288 L _ 5^( ) (m _ π^(ó  ))^2 + 576 L _ 6^( ) (m _ π^(ó  ))^2 + 576 L _ 8^( ) (m _ π^(ó  ))^2 + 59 λ (m _ π^(ó  ))^2 + 144 L _ 5^( ) (m _ K^(ó  ))^2 + 1152 L _ 6^( ) (m _ K^(ó  ))^2 + 576 L _ 8^( ) (m _ K^(ó  ))^2 + 304 λ (m _ K^(ó  ))^2 - 27 λ (m _ η^(ó  ))^2 + 144 L _ 4^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2)) - 12 c _ 2^( ) (6 N _ 11^( ) (m _ π^(ó  ))^2 + 12 N _ 10^( ) (m _ K^(ó  ))^2 + 12 N _ 11^( ) (m _ K^(ó  ))^2 + 5 λ (m _ K^(ó  ))^2 - 6 N _ 21^( ) p _ 2^2 - 5 λ p _ 2^2)) (6 δ _ (0 i)^(3) - 3 δ _ (3 i)^(3) - 3^(1/2) δ _ (8 i)^(3))) - 27 c _ 5^( ) (4 (f _ ϕ^(ó  ))^2 - λ (m _ π^(ó  ))^2 - 16 L _ 5^( ) (m _ K^(ó  ))^2 - 8 λ (m _ K^(ó  ))^2 + λ (m _ η^(ó  ))^2 - 16 L _ 4^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2)) (δ _ (3 i)^(3) - 3^(1/2) δ _ (8 i)^(3)) - 54 c _ 2^( ) (N _ 22^( ) (p _ 1^2 - p _ 2^2 - p _ 3^2) + 2 N _ 21^( ) (p _ 1^2 + p _ 2^2 - p _ 3^2)) (σ _ (2 2)^i - σ _ (3 3)^i) + 72 (1/(p _ 2^2 - (m _ K^(ó  ))^2) (2 c _ 5^( ) ((m _ K^(ó  ))^2 - (m _ π^(ó  ))^2) (18 L _ 4^( ) (p _ 1^2 + p _ 2^2 - p _ 3^2) δ _ (0 i)^(3) + L _ 5^( ) (p _ 1^2 + p _ 2^2 - p _ 3^2) (6 δ _ (0 i)^(3) - 3 δ _ (3 i)^(3) - 3^(1/2) δ _ (8 i)^(3)) + 4 (2 L _ 8^( ) (-6 δ _ (0 i)^(3) + 3 δ _ (3 i)^(3) + 3^(1/2) δ _ (8 i)^(3)) (m _ K^(ó  ))^2 + L _ 6^( ) ((-6 δ _ (0 i)^(3) + 3 δ _ (3 i)^(3) + 3^(1/2) δ _ (8 i)^(3)) (m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2 (-15 δ _ (0 i)^(3) + 3 δ _ (3 i)^(3) + 3^(1/2) δ _ (8 i)^(3)))))) + 3 c _ 2^( ) (N _ 11^( ) ((m _ π^(ó  ))^2 (6 δ _ (0 i)^(3) + σ _ (2 2)^i - σ _ (3 3)^i) - 2 (m _ K^(ó  ))^2 (3 δ _ (0 i)^(3) - σ _ (2 2)^i + σ _ (3 3)^i)) + 2 N _ 10^( ) ((m _ π^(ó  ))^2 (2 δ _ (0 i)^(3) + σ _ (2 2)^i + σ _ (3 3)^i) - 2 (m _ K^(ó  ))^2 (δ _ (0 i)^(3) + σ _ (3 3)^i))))))

CTlambdaCoeff = Coefficient[Renormalize[end4old + end4 + end2 /. CouplingConstant[c_[4], n_] -> CouplingConstant[c[4], n, RenormalizationState[0]]] /. D -> Sequence[], LeutwylerLambda[]] /. _RenormalizationState -> Sequence[] /. gellmannOkubo // Simplify

1/(9 (f _ ϕ^(ó  ))^3 (p _ 2^2 - (m _ K^(ó  ))^2)) (!, _ 0^( ) (-2 c _ 5^( ) (24 δ _ (0 i)^(3) (m _ π^(ó  ))^4 - 12 δ _ (3 i)^(3) (m _ π^(ó  ))^4 - 4 3^(1/2) δ _ (8 i)^(3) (m _ π^(ó  ))^4 - 96 (m _ K^(ó  ))^2 δ _ (0 i)^(3) (m _ π^(ó  ))^2 - 108 p _ 3^2 δ _ (0 i)^(3) (m _ π^(ó  ))^2 - 12 (m _ K^(ó  ))^2 δ _ (3 i)^(3) (m _ π^(ó  ))^2 + 27 p _ 3^2 δ _ (3 i)^(3) (m _ π^(ó  ))^2 - 12 3^(1/2) (m _ K^(ó  ))^2 δ _ (8 i)^(3) (m _ π^(ó  ))^2 + 9 3^(1/2) p _ 3^2 δ _ (8 i)^(3) (m _ π^(ó  ))^2 + 72 (m _ K^(ó  ))^4 δ _ (0 i)^(3) + 108 p _ 3^2 (m _ K^(ó  ))^2 δ _ (0 i)^(3) + 60 (m _ K^(ó  ))^4 δ _ (3 i)^(3) - 27 p _ 3^2 (m _ K^(ó  ))^2 δ _ (3 i)^(3) - 20 3^(1/2) (m _ K^(ó  ))^4 δ _ (8 i)^(3) - 9 3^(1/2) p _ 3^2 (m _ K^(ó  ))^2 δ _ (8 i)^(3) + 9 p _ 1^2 ((m _ π^(ó  ))^2 - (m _ K^(ó  ))^2) (12 δ _ (0 i)^(3) - 3 δ _ (3 i)^(3) - 3^(1/2) δ _ (8 i)^(3)) + 3 p _ 2^2 ((m _ π^(ó  ))^2 (36 δ _ (0 i)^(3) - 11 δ _ (3 i)^(3) - 3^(1/2) δ _ (8 i)^(3)) - (m _ K^(ó  ))^2 (36 δ _ (0 i)^(3) + δ _ (3 i)^(3) - 13 3^(1/2) δ _ (8 i)^(3)))) - c _ 2^( ) (p _ 2^2 - (m _ K^(ó  ))^2) (4 (60 δ _ (0 i)^(3) - 15 δ _ (3 i)^(3) - 5 3^(1/2) δ _ (8 i)^(3) - 11 σ _ (2 2)^i - 37 σ _ (3 3)^i) (m _ π^(ó  ))^2 + 15 (3 p _ 1^2 + p _ 2^2 - 3 p _ 3^2) (σ _ (2 2)^i - σ _ (3 3)^i) + 4 (m _ K^(ó  ))^2 (-60 δ _ (0 i)^(3) + 15 δ _ (3 i)^(3) + 5 3^(1/2) δ _ (8 i)^(3) + 26 σ _ (2 2)^i + 22 σ _ (3 3)^i))))

res4 = CheckF[dum, "KSS2res4"] ;

ampinfinities = ((WriteString["stdout", "."] ; VeltmanExpand[Collect[# /. D -> Sequence[], _B0], ExplicitLeutwylerJ0 -> True]) & /@ res4) ;

....

endloops = Collect[Plus @@ ampinfinities, {_QuarkCondensate, _DecayConstant, (Pair[__] - ParticleMass[__]^2)^(-2)}] /. Times[a___, (Pair[b__] - ParticleMass[c__]^2)^p_, d___] :> Times[Collect[Times[a, d], {_Pair, _ParticleMass, _CouplingConstant, _Log, _LeutwylerLambda}], (Pair[b] - ParticleMass[c]^2)^p] ;

looplambdas = (Simplify[Coefficient[#, LeutwylerLambda[]] /. gellmannOkubo /. MomentaRules // MomentumExpand // ExpandScalarProduct] & /@ ampinfinities) /. _RenormalizationState -> Sequence[]

{(8 c _ 5^( ) (4 (m _ π^(ó  ))^2 + 11 (m _ K^(ó  ))^2) !, _ 0^( ) (δ _ (3 i)^(3) - 3^(1/2) δ _ (8 i)^(3)))/(9 (f _ ϕ^(ó  ))^3), 1/(9 (f _ ϕ^(ó  ))^3) (!, _ 0^( ) (c _ 2^( ) (16 (15 δ _ (0 i)^(3) - δ _ (3 i)^(3) + 4 3^(1/2) δ _ (8 i)^(3)) (m _ π^(ó  ))^2 - 8 (m _ K^(ó  ))^2 (30 δ _ (0 i)^(3) + 13 δ _ (3 i)^(3) - 7 3^(1/2) δ _ (8 i)^(3)) + 15 (p _ 1^2 - p _ 2^2 + 3 p _ 3^2) (δ _ (3 i)^(3) - 3^(1/2) δ _ (8 i)^(3))) - 8 c _ 5^( ) ((m _ π^(ó  ))^2 - (m _ K^(ó  ))^2) (30 δ _ (0 i)^(3) - 3 δ _ (3 i)^(3) - 3^(1/2) δ _ (8 i)^(3)))), (4 c _ 5^( ) ((m _ K^(ó  ))^2 - (m _ π^(ó  ))^2) !, _ 0^( ) ((48 δ _ (0 i)^(3) - 21 δ _ (3 i)^(3) + 7 3^(1/2) δ _ (8 i)^(3)) (m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2 (66 δ _ (0 i)^(3) - 7 (3 δ _ (3 i)^(3) + 2 3^(1/2) δ _ (8 i)^(3)))))/(27 (f _ ϕ^(ó  ))^3 (p _ 2^2 - (m _ K^(ó  ))^2)), 1/(9 (f _ ϕ^(ó  ))^3 (p _ 2^2 - (m _ K^(ó  ))^2)) (2 c _ 5^( ) ((m _ π^(ó  ))^2 - (m _ K^(ó  ))^2) !, _ 0^( ) (12 δ _ (0 i)^(3) (m _ π^(ó  ))^2 - 4 δ _ (3 i)^(3) (m _ π^(ó  ))^2 + 8 3^(1/2) δ _ (8 i)^(3) (m _ π^(ó  ))^2 + 12 (m _ K^(ó  ))^2 δ _ (0 i)^(3) - 108 p _ 3^2 δ _ (0 i)^(3) - 20 (m _ K^(ó  ))^2 δ _ (3 i)^(3) + 27 p _ 3^2 δ _ (3 i)^(3) - 16 3^(1/2) (m _ K^(ó  ))^2 δ _ (8 i)^(3) + 9 3^(1/2) p _ 3^2 δ _ (8 i)^(3) + p _ 1^2 (36 δ _ (0 i)^(3) - 9 δ _ (3 i)^(3) - 3 3^(1/2) δ _ (8 i)^(3)) + p _ 2^2 (36 δ _ (0 i)^(3) - 9 δ _ (3 i)^(3) - 3 3^(1/2) δ _ (8 i)^(3))))}

LOOPlambdaCoeff = Plus @@ looplambdas /. gellmannOkubo // MomentumExpand // ExpandScalarProduct // Simplify

1/(27 (f _ ϕ^(ó  ))^3) (!, _ 0^( ) (24 c _ 5^( ) (4 (m _ π^(ó  ))^2 + 11 (m _ K^(ó  ))^2) (δ _ (3 i)^(3) - 3^(1/2) δ _ (8 i)^(3)) + 1/(p _ 2^2 - (m _ K^(ó  ))^2) (6 c _ 5^( ) ((m _ π^(ó  ))^2 - (m _ K^(ó  ))^2) (12 δ _ (0 i)^(3) (m _ π^(ó  ))^2 - 4 δ _ (3 i)^(3) (m _ π^(ó  ))^2 + 8 3^(1/2) δ _ (8 i)^(3) (m _ π^(ó  ))^2 + 12 (m _ K^(ó  ))^2 δ _ (0 i)^(3) - 108 p _ 3^2 δ _ (0 i)^(3) - 20 (m _ K^(ó  ))^2 δ _ (3 i)^(3) + 27 p _ 3^2 δ _ (3 i)^(3) - 16 3^(1/2) (m _ K^(ó  ))^2 δ _ (8 i)^(3) + 9 3^(1/2) p _ 3^2 δ _ (8 i)^(3) + p _ 1^2 (36 δ _ (0 i)^(3) - 9 δ _ (3 i)^(3) - 3 3^(1/2) δ _ (8 i)^(3)) + p _ 2^2 (36 δ _ (0 i)^(3) - 9 δ _ (3 i)^(3) - 3 3^(1/2) δ _ (8 i)^(3)))) + (4 c _ 5^( ) ((m _ K^(ó  ))^2 - (m _ π^(ó  ))^2) ((48 δ _ (0 i)^(3) - 21 δ _ (3 i)^(3) + 7 3^(1/2) δ _ (8 i)^(3)) (m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2 (66 δ _ (0 i)^(3) - 7 (3 δ _ (3 i)^(3) + 2 3^(1/2) δ _ (8 i)^(3)))))/(p _ 2^2 - (m _ K^(ó  ))^2) + 3 (c _ 2^( ) (16 (15 δ _ (0 i)^(3) - δ _ (3 i)^(3) + 4 3^(1/2) δ _ (8 i)^(3)) (m _ π^(ó  ))^2 - 8 (m _ K^(ó  ))^2 (30 δ _ (0 i)^(3) + 13 δ _ (3 i)^(3) - 7 3^(1/2) δ _ (8 i)^(3)) + 15 (p _ 1^2 - p _ 2^2 + 3 p _ 3^2) (δ _ (3 i)^(3) - 3^(1/2) δ _ (8 i)^(3))) - 8 c _ 5^( ) ((m _ π^(ó  ))^2 - (m _ K^(ó  ))^2) (30 δ _ (0 i)^(3) - 3 δ _ (3 i)^(3) - 3^(1/2) δ _ (8 i)^(3)))))

Converted by Mathematica  (July 10, 2003)