•Final counterterm expression

end4 = Plus @@ res1 // Simplify ;

end4old = Plus @@ res1old // Simplify ;

The total contribution from counterterms and leading order with multiplications:

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) + 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)) + 1/(((m _ π^(ó  ))^2 - p _ 3^2) (p _ 1^2 - (m _ K^(ó  ))^2)) (12 (c _ 2^( ) (-4 N _ 12^( ) p _ 1^2 p _ 3^2 + N _ 8^( ) (p _ 1^2 - p _ 2^2 + p _ 3^2) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2) + 2 (N _ 11^( ) (m _ π^(ó  ))^4 + 2 N _ 10^( ) (m _ K^(ó  ))^2 (m _ π^(ó  ))^2 + 2 N _ 11^( ) (m _ K^(ó  ))^2 (m _ π^(ó  ))^2 - N _ 11^( ) p _ 1^2 (m _ π^(ó  ))^2 - N _ 11^( ) p _ 3^2 (m _ π^(ó  ))^2 + N _ 5^( ) p _ 1^2 (m _ K^(ó  ))^2 - 2 N _ 10^( ) p _ 1^2 (m _ K^(ó  ))^2 - 2 N _ 11^( ) p _ 1^2 (m _ K^(ó  ))^2 - N _ 5^( ) p _ 2^2 (m _ K^(ó  ))^2 + N _ 5^( ) p _ 3^2 (m _ K^(ó  ))^2 - 2 N _ 10^( ) p _ 3^2 (m _ K^(ó  ))^2 - 2 N _ 11^( ) p _ 3^2 (m _ K^(ó  ))^2 + 4 L _ 8^( ) (p _ 1^2 - p _ 2^2 + p _ 3^2) ((m _ π^(ó  ))^2 + (m _ K^(ó  ))^2) + 8 L _ 6^( ) (p _ 1^2 - p _ 2^2 + p _ 3^2) ((m _ π^(ó  ))^2 + 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 _ 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)

The corresponding infinities to be cancelled by the loops:

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 + 8 (m _ K^(ó  ))^2 (m _ π^(ó  ))^2 - 93 p _ 3^2 (m _ π^(ó  ))^2 + 27 p _ 2^4 - 69 p _ 3^2 (m _ K^(ó  ))^2 + 3 p _ 1^2 (-(m _ π^(ó  ))^2 - 53 (m _ K^(ó  ))^2 + p _ 2^2 - 20 p _ 3^2) + p _ 2^2 (11 (m _ π^(ó  ))^2 + 61 (m _ K^(ó  ))^2 + 3 p _ 3^2))) (!, _ 0^( ))^2)

Converted by Mathematica  (July 10, 2003)