•The infinities

Coefficient[Renormalize[end4old /. CouplingConstant[c_[4], n_] -> CouplingConstant[c[4], n, RenormalizationState[0]]] /. D -> Sequence[], LeutwylerLambda[]] /. _RenormalizationState -> Sequence[] /. gellmannOkubo /. CouplingConstant[ChPTW3[2], 2] -> 0 // Expand

-(104 c _ 2^( ) (!, _ 0^( ))^2 (m _ π^(ó  ))^4)/(9 (f _ ϕ^(ó  ))^2 ((m _ π^(ó  ))^2 - p _ 3^2) (p _ 1^2 - (m _ K^(ó  ))^2)) - (136 c _ 2^( ) (m _ K^(ó  ))^2 (!, _ 0^( ))^2 (m _ π^(ó  ))^2)/(9 (f _ ϕ^(ó  ))^2 ((m _ π^(ó  ))^2 - p _ 3^2) (p _ 1^2 - (m _ K^(ó  ))^2)) + (112 c _ 2^( ) p _ 1^2 (!, _ 0^( ))^2 (m _ π^(ó  ))^2)/(3 (f _ ϕ^(ó  ))^2 ((m _ π^(ó  ))^2 - p _ 3^2) (p _ 1^2 - (m _ K^(ó  ))^2)) - (112 c _ 2^( ) p _ 2^2 (!, _ 0^( ))^2 (m _ π^(ó  ))^2)/(9 (f _ ϕ^(ó  ))^2 ((m _ π^(ó  ))^2 - p _ 3^2) (p _ 1^2 - (m _ K^(ó  ))^2)) + (24 c _ 2^( ) p _ 3^2 (!, _ 0^( ))^2 (m _ π^(ó  ))^2)/((f _ ϕ^(ó  ))^2 ((m _ π^(ó  ))^2 - p _ 3^2) (p _ 1^2 - (m _ K^(ó  ))^2)) + (44 c _ 2^( ) p _ 1^2 (m _ K^(ó  ))^2 (!, _ 0^( ))^2)/((f _ ϕ^(ó  ))^2 ((m _ π^(ó  ))^2 - p _ 3^2) (p _ 1^2 - (m _ K^(ó  ))^2)) - (380 c _ 2^( ) p _ 2^2 (m _ K^(ó  ))^2 (!, _ 0^( ))^2)/(9 (f _ ϕ^(ó  ))^2 ((m _ π^(ó  ))^2 - p _ 3^2) (p _ 1^2 - (m _ K^(ó  ))^2)) + (172 c _ 2^( ) p _ 3^2 (m _ K^(ó  ))^2 (!, _ 0^( ))^2)/(3 (f _ ϕ^(ó  ))^2 ((m _ π^(ó  ))^2 - p _ 3^2) (p _ 1^2 - (m _ K^(ó  ))^2))

Coefficient[Renormalize[end4 /. CouplingConstant[c_[4], n_] -> CouplingConstant[c[4], n, RenormalizationState[0]]] /. D -> Sequence[], LeutwylerLambda[]] /. _RenormalizationState -> Sequence[] /. gellmannOkubo /. CouplingConstant[ChPTW3[2], 2] -> 0 // Expand

(20 c _ 2^( ) p _ 2^2 (!, _ 0^( ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2)) - (10 c _ 2^( ) p _ 1^2 (m _ K^(ó  ))^2 (!, _ 0^( ))^2)/((f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) - (10 c _ 2^( ) p _ 2^2 (m _ K^(ó  ))^2 (!, _ 0^( ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) + (10 c _ 2^( ) p _ 3^2 (m _ K^(ó  ))^2 (!, _ 0^( ))^2)/((f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) + (20 c _ 2^( ) p _ 2^2 (!, _ 0^( ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 1^2 - (m _ K^(ó  ))^2)) + (6 c _ 2^( ) p _ 2^4 (!, _ 0^( ))^2)/((f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) + (10 c _ 2^( ) p _ 1^2 (m _ π^(ó  ))^2 (!, _ 0^( ))^2)/((f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) + (10 c _ 2^( ) p _ 2^2 (m _ π^(ó  ))^2 (!, _ 0^( ))^2)/((f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) - (10 c _ 2^( ) p _ 3^2 (m _ π^(ó  ))^2 (!, _ 0^( ))^2)/((f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) - (6 c _ 2^( ) p _ 1^2 p _ 2^2 (!, _ 0^( ))^2)/((f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) - (6 c _ 2^( ) p _ 2^2 p _ 3^2 (!, _ 0^( ))^2)/((f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2))

Coefficient[Renormalize[end2 /. CouplingConstant[c_[4], n_] -> CouplingConstant[c[4], n, RenormalizationState[0]]] /. D -> Sequence[], LeutwylerLambda[]] /. _RenormalizationState -> Sequence[] /. gellmannOkubo /. CouplingConstant[ChPTW3[2], 2] -> 0 // Expand

(56 c _ 2^( ) p _ 1^2 (m _ K^(ó  ))^2 (!, _ 0^( ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) - (56 c _ 2^( ) p _ 2^2 (m _ K^(ó  ))^2 (!, _ 0^( ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) + (56 c _ 2^( ) p _ 3^2 (m _ K^(ó  ))^2 (!, _ 0^( ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) + (40 c _ 2^( ) p _ 1^2 (m _ π^(ó  ))^2 (!, _ 0^( ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) - (40 c _ 2^( ) p _ 2^2 (m _ π^(ó  ))^2 (!, _ 0^( ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) + (40 c _ 2^( ) p _ 3^2 (m _ π^(ó  ))^2 (!, _ 0^( ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2))

ctl = CTlambdaCoeff /. CouplingConstant[ChPTW3[2], 2] -> 0 /. _RenormalizationState -> Sequence[] // Expand

(104 c _ 2^( ) (!, _ 0^( ))^2 (m _ π^(ó  ))^4)/(9 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) + (136 c _ 2^( ) (m _ K^(ó  ))^2 (!, _ 0^( ))^2 (m _ π^(ó  ))^2)/(9 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) - (14 c _ 2^( ) p _ 1^2 (!, _ 0^( ))^2 (m _ π^(ó  ))^2)/((f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) + (22 c _ 2^( ) p _ 2^2 (!, _ 0^( ))^2 (m _ π^(ó  ))^2)/(9 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) - (62 c _ 2^( ) p _ 3^2 (!, _ 0^( ))^2 (m _ π^(ó  ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) - (106 c _ 2^( ) p _ 1^2 (m _ K^(ó  ))^2 (!, _ 0^( ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) + (122 c _ 2^( ) p _ 2^2 (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)) - (86 c _ 2^( ) p _ 3^2 (m _ K^(ó  ))^2 (!, _ 0^( ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) + (6 c _ 2^( ) p _ 2^4 (!, _ 0^( ))^2)/((f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) + (2 c _ 2^( ) p _ 1^2 p _ 2^2 (!, _ 0^( ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) + (2 c _ 2^( ) p _ 2^2 p _ 3^2 (!, _ 0^( ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2))

loopl = LOOPlambdaCoeff /. CouplingConstant[ChPTW3[2], 2] -> 0 /. _RenormalizationState -> Sequence[] // Expand

-(104 c _ 2^( ) (!, _ 0^( ))^2 (m _ π^(ó  ))^4)/(9 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) - (136 c _ 2^( ) (m _ K^(ó  ))^2 (!, _ 0^( ))^2 (m _ π^(ó  ))^2)/(9 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) + (14 c _ 2^( ) p _ 1^2 (!, _ 0^( ))^2 (m _ π^(ó  ))^2)/((f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) - (22 c _ 2^( ) p _ 2^2 (!, _ 0^( ))^2 (m _ π^(ó  ))^2)/(9 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) + (62 c _ 2^( ) p _ 3^2 (!, _ 0^( ))^2 (m _ π^(ó  ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) + (106 c _ 2^( ) p _ 1^2 (m _ K^(ó  ))^2 (!, _ 0^( ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) - (122 c _ 2^( ) p _ 2^2 (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)) + (86 c _ 2^( ) p _ 3^2 (m _ K^(ó  ))^2 (!, _ 0^( ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) - (6 c _ 2^( ) p _ 2^4 (!, _ 0^( ))^2)/((f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) - (2 c _ 2^( ) p _ 1^2 p _ 2^2 (!, _ 0^( ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) - (2 c _ 2^( ) p _ 2^2 p _ 3^2 (!, _ 0^( ))^2)/(3 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2))

diff = ctl + loopl // Expand

0

Converted by Mathematica  (July 10, 2003)