•Loading the amplitudes

end2all = CheckF[dum, "KSPiend2all"] ;

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

1/(3 (f _ ϕ^(ó  ))^2) (2 (-(4 c _ 5^( ) (4 (6 L _ 5^(r ) (m _ π^(ó  ))^2 + 2 λ (m _ π^(ó  ))^2 + λ (m _ K^(ó  ))^2 + 6 L _ 4^(r ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2)) - 3 (f _ ϕ^(ó  ))^2))/(p _ 3^2 - (m _ π^(ó  ))^2) - (6 c _ 5^( ) (-2 (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)))/(p _ 1^2 - (m _ K^(ó  ))^2) - 1/((p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) (2 c _ 5^( ) (-6 (f _ ϕ^(ó  ))^2 + 48 L _ 5^(r ) (m _ π^(ó  r ))^2 + 96 L _ 6^(r ) (m _ π^(ó  r ))^2 + 19 λ (m _ π^(ó  r ))^2 + 192 L _ 6^(r ) (m _ K^(ó  r ))^2 + 96 L _ 8^(r ) (m _ K^(ó  r ))^2 + 32 λ (m _ K^(ó  r ))^2 - 3 λ (m _ η^(ó  r ))^2 + 48 L _ 4^(r ) ((m _ π^(ó  r ))^2 + 2 (m _ K^(ó  r ))^2)) (m _ K^(ó  r ))^2 + c _ 2^( ) (p _ 1^2 - p _ 2^2 + p _ 3^2) (6 (f _ ϕ^(ó  ))^2 - 48 L _ 5^(r ) (m _ π^(ó  r ))^2 - 19 λ (m _ π^(ó  r ))^2 - 48 L _ 5^(r ) (m _ K^(ó  r ))^2 - 32 λ (m _ K^(ó  r ))^2 + 3 λ (m _ η^(ó  r ))^2 - 96 L _ 4^(r ) ((m _ π^(ó  r ))^2 + 2 (m _ K^(ó  r ))^2)))) (!, _ 0^( ))^2)

res1 = CheckF[dum, "KSPires1"] ;

res1old = CheckF[dum, "KSPires1old"] ;

end4 = Plus @@ res1 // Simplify ;

end4old = Plus @@ res1old // Simplify ;

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

1/(3 (f _ ϕ^(ó  ))^2) (2 (-(4 c _ 5^( ) (4 (6 L _ 5^( ) (m _ π^(ó  ))^2 + 2 λ (m _ π^(ó  ))^2 + λ (m _ K^(ó  ))^2 + 6 L _ 4^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2)) - 3 (f _ ϕ^(ó  ))^2))/(p _ 3^2 - (m _ π^(ó  ))^2) + 1/(((m _ π^(ó  ))^2 - p _ 3^2) (p _ 1^2 - (m _ K^(ó  ))^2)) (12 (c _ 2^( ) (2 N _ 11^( ) (m _ π^(ó  ))^4 + 4 N _ 10^( ) (m _ K^(ó  ))^2 (m _ π^(ó  ))^2 + 4 N _ 11^( ) (m _ K^(ó  ))^2 (m _ π^(ó  ))^2 + 16 L _ 6^( ) p _ 1^2 (m _ π^(ó  ))^2 + 8 L _ 8^( ) p _ 1^2 (m _ π^(ó  ))^2 + N _ 8^( ) p _ 1^2 (m _ π^(ó  ))^2 - 2 N _ 11^( ) p _ 1^2 (m _ π^(ó  ))^2 - 16 L _ 6^( ) p _ 2^2 (m _ π^(ó  ))^2 - 8 L _ 8^( ) p _ 2^2 (m _ π^(ó  ))^2 - N _ 8^( ) p _ 2^2 (m _ π^(ó  ))^2 + 16 L _ 6^( ) p _ 3^2 (m _ π^(ó  ))^2 + 8 L _ 8^( ) p _ 3^2 (m _ π^(ó  ))^2 + N _ 8^( ) p _ 3^2 (m _ π^(ó  ))^2 - 2 N _ 11^( ) p _ 3^2 (m _ π^(ó  ))^2 + 32 L _ 6^( ) p _ 1^2 (m _ K^(ó  ))^2 + 8 L _ 8^( ) p _ 1^2 (m _ K^(ó  ))^2 + 2 N _ 5^( ) p _ 1^2 (m _ K^(ó  ))^2 + 2 N _ 8^( ) p _ 1^2 (m _ K^(ó  ))^2 - 4 N _ 10^( ) p _ 1^2 (m _ K^(ó  ))^2 - 4 N _ 11^( ) p _ 1^2 (m _ K^(ó  ))^2 - 32 L _ 6^( ) p _ 2^2 (m _ K^(ó  ))^2 - 8 L _ 8^( ) p _ 2^2 (m _ K^(ó  ))^2 - 2 N _ 5^( ) p _ 2^2 (m _ K^(ó  ))^2 - 2 N _ 8^( ) p _ 2^2 (m _ K^(ó  ))^2 + 32 L _ 6^( ) p _ 3^2 (m _ K^(ó  ))^2 + 8 L _ 8^( ) p _ 3^2 (m _ K^(ó  ))^2 + 2 N _ 5^( ) p _ 3^2 (m _ K^(ó  ))^2 + 2 N _ 8^( ) p _ 3^2 (m _ K^(ó  ))^2 - 4 N _ 10^( ) p _ 3^2 (m _ K^(ó  ))^2 - 4 N _ 11^( ) p _ 3^2 (m _ K^(ó  ))^2 - 4 N _ 12^( ) p _ 1^2 p _ 3^2 + 4 N _ 36^( ) (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) - 16 c _ 5^( ) (L _ 6^( ) (-(m _ π^(ó  ))^2 + (m _ K^(ó  ))^2 + p _ 1^2 + p _ 3^2) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2) + L _ 8^( ) (p _ 1^2 (m _ π^(ó  ))^2 + (m _ K^(ó  ))^2 (-(m _ π^(ó  ))^2 + (m _ K^(ó  ))^2 + p _ 3^2))))) + 6 c _ 2^( ) ((2 (N _ 22^( ) p _ 2^2 + N _ 23^( ) (p _ 1^2 + p _ 2^2 - p _ 3^2)))/(p _ 1^2 - (m _ K^(ó  ))^2) - 1/((p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) (2 N _ 20^( ) p _ 2^2 (p _ 1^2 - p _ 2^2 + p _ 3^2) - 2 N _ 21^( ) (p _ 1^2 + p _ 2^2 - p _ 3^2) ((m _ π^(ó  ))^2 - (m _ K^(ó  ))^2) - (N _ 22^( ) + 2 N _ 23^( )) (p _ 1^2 ((m _ π^(ó  ))^2 - (m _ K^(ó  ))^2) + p _ 3^2 ((m _ K^(ó  ))^2 - (m _ π^(ó  ))^2) + p _ 2^2 ((m _ π^(ó  ))^2 + (m _ K^(ó  ))^2))) + (2 (N _ 22^( ) p _ 2^2 + N _ 23^( ) (-p _ 1^2 + p _ 2^2 + p _ 3^2)))/(p _ 3^2 - (m _ π^(ó  ))^2)) - (6 c _ 5^( ) (-2 (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)))/(p _ 1^2 - (m _ K^(ó  ))^2) - 1/((p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) (2 c _ 5^( ) (-6 (f _ ϕ^(ó  ))^2 + 48 L _ 5^( ) (m _ π^(ó  ))^2 + 96 L _ 6^( ) (m _ π^(ó  ))^2 + 19 λ (m _ π^(ó  ))^2 + 192 L _ 6^( ) (m _ K^(ó  ))^2 + 96 L _ 8^( ) (m _ K^(ó  ))^2 + 32 λ (m _ K^(ó  ))^2 - 3 λ (m _ η^(ó  ))^2 + 48 L _ 4^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2)) (m _ K^(ó  ))^2 + c _ 2^( ) (p _ 1^2 - p _ 2^2 + p _ 3^2) (6 (f _ ϕ^(ó  ))^2 - 48 L _ 5^( ) (m _ π^(ó  ))^2 - 19 λ (m _ π^(ó  ))^2 - 48 L _ 5^( ) (m _ K^(ó  ))^2 - 32 λ (m _ K^(ó  ))^2 + 3 λ (m _ η^(ó  ))^2 - 96 L _ 4^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2)))) (!, _ 0^( ))^2)

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  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) (2 (4 c _ 5^( ) (2 p _ 1^2 ((m _ π^(ó  ))^2 + 5 (m _ K^(ó  ))^2) + (-(m _ π^(ó  ))^2 + (m _ K^(ó  ))^2 + p _ 3^2) (5 (m _ π^(ó  ))^2 + 7 (m _ K^(ó  ))^2)) + c _ 2^( ) (52 (m _ π^(ó  ))^4 + 68 (m _ K^(ó  ))^2 (m _ π^(ó  ))^2 - 93 p _ 3^2 (m _ π^(ó  ))^2 + 27 p _ 2^4 - 129 p _ 3^2 (m _ K^(ó  ))^2 + 3 p _ 1^2 (-21 (m _ π^(ó  ))^2 - 53 (m _ K^(ó  ))^2 + p _ 2^2) + p _ 2^2 (11 (m _ π^(ó  ))^2 + 61 (m _ K^(ó  ))^2 + 3 p _ 3^2))) (!, _ 0^( ))^2)

res4 = CheckF[dum, "KSPiAmps.2.m"] ;

ampinfinities = ((WriteString["stdout", "."] ; VeltmanExpand[Collect[# /. D -> Sequence[], {_A0, _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[]

{-(16 c _ 5^( ) (7 (m _ π^(ó  ))^2 + 8 (m _ K^(ó  ))^2) (!, _ 0^( ))^2)/(9 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2)), -(16 c _ 5^( ) (4 (m _ π^(ó  ))^2 + 11 (m _ K^(ó  ))^2) (!, _ 0^( ))^2)/(9 (f _ ϕ^(ó  ))^2 (p _ 1^2 - (m _ K^(ó  ))^2)), -(16 c _ 5^( ) (4 (m _ π^(ó  ))^2 + 11 (m _ K^(ó  ))^2) (!, _ 0^( ))^2)/(9 (f _ ϕ^(ó  ))^2 (p _ 1^2 - (m _ K^(ó  ))^2)), -(16 c _ 5^( ) (7 (m _ π^(ó  ))^2 + 8 (m _ K^(ó  ))^2) (!, _ 0^( ))^2)/(9 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2)), (8 (7 (m _ π^(ó  ))^2 + 8 (m _ K^(ó  ))^2) (c _ 2^( ) (p _ 1^2 - p _ 2^2 + p _ 3^2) - 2 c _ 5^( ) (m _ K^(ó  ))^2) (!, _ 0^( ))^2)/(9 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)), -(8 (2 c _ 5^( ) (m _ K^(ó  ))^2 + c _ 2^( ) (p _ 2^2 - 2 ((m _ π^(ó  ))^2 + (m _ K^(ó  ))^2))) (!, _ 0^( ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 1^2 - (m _ K^(ó  ))^2)), 1/(27 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) (4 (c _ 2^( ) (-16 (m _ π^(ó  ))^4 - 16 (m _ K^(ó  ))^2 (m _ π^(ó  ))^2 + 36 p _ 3^2 (m _ π^(ó  ))^2 + 86 (m _ K^(ó  ))^4 + 99 p _ 3^2 (m _ K^(ó  ))^2 + 9 p _ 1^2 (4 (m _ π^(ó  ))^2 + 11 (m _ K^(ó  ))^2) - 9 p _ 2^2 (4 (m _ π^(ó  ))^2 + 11 (m _ K^(ó  ))^2)) - 42 c _ 5^( ) (m _ K^(ó  ))^2 ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2)) (!, _ 0^( ))^2), (8 (4 (m _ π^(ó  ))^2 + 11 (m _ K^(ó  ))^2) (c _ 2^( ) (p _ 1^2 - p _ 2^2 + p _ 3^2) - 2 c _ 5^( ) (m _ K^(ó  ))^2) (!, _ 0^( ))^2)/(9 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)), -(8 (2 c _ 5^( ) (m _ K^(ó  ))^2 + c _ 2^( ) (p _ 2^2 - 2 ((m _ π^(ó  ))^2 + (m _ K^(ó  ))^2))) (!, _ 0^( ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2)), 1/(27 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) (2 (6 c _ 5^( ) (10 (m _ π^(ó  ))^2 + 14 (m _ K^(ó  ))^2 + 9 p _ 1^2 - 27 p _ 2^2 + 9 p _ 3^2) (m _ K^(ó  ))^2 + c _ 2^( ) (-52 (m _ π^(ó  ))^4 - 28 (m _ K^(ó  ))^2 (m _ π^(ó  ))^2 + 3 p _ 3^2 (m _ π^(ó  ))^2 - 100 (m _ K^(ó  ))^4 - 81 p _ 2^4 - 111 p _ 3^2 (m _ K^(ó  ))^2 + 3 p _ 1^2 (-29 (m _ π^(ó  ))^2 - 7 (m _ K^(ó  ))^2 + 9 p _ 2^2) + 9 p _ 2^2 (15 (m _ π^(ó  ))^2 + 23 (m _ K^(ó  ))^2 + 3 p _ 3^2))) (!, _ 0^( ))^2)}

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

-1/(9 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) (2 (c _ 2^( ) (52 (m _ π^(ó  ))^4 + 68 (m _ K^(ó  ))^2 (m _ π^(ó  ))^2 - 93 p _ 3^2 (m _ π^(ó  ))^2 + 27 p _ 2^4 - 129 p _ 3^2 (m _ K^(ó  ))^2 + 3 p _ 1^2 (-21 (m _ π^(ó  ))^2 - 53 (m _ K^(ó  ))^2 + p _ 2^2) + p _ 2^2 (11 (m _ π^(ó  ))^2 + 61 (m _ K^(ó  ))^2 + 3 p _ 3^2)) + 2 c _ 5^( ) (-32 (m _ π^(ó  ))^4 - 108 (m _ K^(ó  ))^2 (m _ π^(ó  ))^2 + 14 (m _ K^(ó  ))^4 + 27 p _ 2^2 (m _ K^(ó  ))^2 + p _ 1^2 (56 (m _ π^(ó  ))^2 + 67 (m _ K^(ó  ))^2) + p _ 3^2 (32 (m _ π^(ó  ))^2 + 91 (m _ K^(ó  ))^2))) (!, _ 0^( ))^2)

Converted by Mathematica  (July 10, 2003)