•Final  renormalized lowest order + counterterm expression

The total contribution from counterterms and leading order with multiplications:

CTcontrib = end4old + end4 + end2all /. CouplingConstant[c_[4], n_] -> CouplingConstant[c[4], n, RenormalizationState[0]] /. D -> Sequence[] /. RenormalizationState[1] -> RenormalizationState[0] // Simplify ;

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[1] -> RenormalizationState[0] /. gellmannOkubo // Simplify

1/(108 (f _ ϕ^(ó  ))^4 (p _ 2^2 - (m _ K^(ó  ))^2)) (i p _ 1^μ _ 1 µ _ μ _ 1(p _ 1) (c _ 2^( ) (p _ 2^2 - (m _ K^(ó  ))^2) (592 (m _ π^(ó  ))^4 - 16 (27 t - 73 (m _ K^(ó  ))^2) (m _ π^(ó  ))^2 - 383 (m _ K^(ó  ))^4 - 108 s^2 + 216 t^2 + 81 p _ 2^4 - 1053 s (m _ K^(ó  ))^2 - 216 t (m _ K^(ó  ))^2 + 216 s t - 3 p _ 2^2 (-152 (m _ π^(ó  ))^2 - 82 (m _ K^(ó  ))^2 + 45 s + 72 t)) - 4 c _ 5^( ) ((m _ π^(ó  ))^2 - (m _ K^(ó  ))^2) (142 (m _ π^(ó  ))^4 - 6 (18 (s + 3 t) - 37 (m _ K^(ó  ))^2) (m _ π^(ó  ))^2 + 29 (m _ K^(ó  ))^4 + 162 s^2 + 162 t^2 + 81 s (m _ K^(ó  ))^2 - 162 t (m _ K^(ó  ))^2 + 162 s t - 9 p _ 2^2 (-14 (m _ π^(ó  ))^2 - 13 (m _ K^(ó  ))^2 + 18 (s + t)))))

Converted by Mathematica  (July 10, 2003)