•Conterterm contributions on-mass-shell

Counterterm contribution (N _ (5 - 13)):

finCTsold = Cancel[(Pair[Momentum[p3], Momentum[p3]] - ParticleMass[Pion]^2) (Pair[Momentum[p1], Momentum[p1]] - ParticleMass[Kaon]^2) * (end4old /. _RenormalizationState -> Sequence[])] /. onshellrules /. CouplingConstant[ChPT3[4], ___] -> 0 // Simplify

(8 c _ 2^( ) (2 (N _ 5^( ) (-(m _ π^(ó  ))^2 - (m _ K^(ó  ))^2 + p _ 2^2) + N _ 11^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2) + 2 (N _ 12^( ) (m _ π^(ó  ))^2 + N _ 10^( ) (m _ K^(ó  ))^2)) (m _ K^(ó  ))^2 + N _ 8^( ) (-(m _ π^(ó  ))^2 - (m _ K^(ó  ))^2 + p _ 2^2) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2)) (!, _ 0^( ))^2)/(f _ ϕ^(ó  ))^2

Counterterm contribution (L _ i):

finCTsstrong = Collect[(Cancel[(Pair[Momentum[p3], Momentum[p3]] - ParticleMass[Pion]^2) (Pair[Momentum[p1], Momentum[p1]] - ParticleMass[Kaon]^2) * (end4old /. _RenormalizationState -> Sequence[])] - finCTsold /. onshellrules // Simplify) + Simplify[(finTrees /. _Log -> 0) - (finTrees /. _Log -> 0 /. CouplingConstant[_[4], ___] -> 0) /. gellmannOkubo], {_CouplingConstant}] // Simplify

-1/(f _ ϕ^(ó  ))^2 (32 (2 L _ 4^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2) (c _ 5^( ) (m _ K^(ó  ))^2 + c _ 2^( ) (-(m _ π^(ó  ))^2 - (m _ K^(ó  ))^2 + p _ 2^2)) + L _ 5^( ) (2 c _ 5^( ) (m _ π^(ó  ))^2 (m _ K^(ó  ))^2 + c _ 2^( ) (-(m _ π^(ó  ))^2 - (m _ K^(ó  ))^2 + p _ 2^2) ((m _ π^(ó  ))^2 + (m _ K^(ó  ))^2)) - 2 (2 L _ 6^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2) (c _ 5^( ) (m _ K^(ó  ))^2 + c _ 2^( ) (-(m _ π^(ó  ))^2 - (m _ K^(ó  ))^2 + p _ 2^2)) + L _ 8^( ) (2 c _ 5^( ) (m _ π^(ó  ))^2 (m _ K^(ó  ))^2 + c _ 2^( ) (-(m _ π^(ó  ))^2 - (m _ K^(ó  ))^2 + p _ 2^2) ((m _ π^(ó  ))^2 + (m _ K^(ó  ))^2)))) (!, _ 0^( ))^2)

finCTsstrongRaw = Cancel[(Pair[Momentum[p3], Momentum[p3]] - ParticleMass[Pion]^2) (Pair[Momentum[p1], Momentum[p1]] - ParticleMass[Kaon]^2) * (end4old /. _RenormalizationState -> Sequence[])] - finCTsold /. onshellrules // Simplify

-(64 (c _ 2^( ) ((m _ π^(ó  ))^2 + (m _ K^(ó  ))^2 - p _ 2^2) - 2 c _ 5^( ) (m _ K^(ó  ))^2) (L _ 8^( ) ((m _ π^(ó  ))^2 + (m _ K^(ó  ))^2) + 2 L _ 6^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2)) (!, _ 0^( ))^2)/(f _ ϕ^(ó  ))^2

Simplify[(finTrees /. _Log -> 0) - (finTrees /. _Log -> 0 /. CouplingConstant[_[4], ___] -> 0) /. gellmannOkubo]

-1/(f _ ϕ^(ó  ))^2 (32 (4 c _ 5^( ) (L _ 8^( ) (m _ K^(ó  ))^2 + L _ 6^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2)) (m _ K^(ó  ))^2 + 2 L _ 4^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2) (c _ 5^( ) (m _ K^(ó  ))^2 + c _ 2^( ) (-(m _ π^(ó  ))^2 - (m _ K^(ó  ))^2 + p _ 2^2)) + L _ 5^( ) (2 c _ 5^( ) (m _ π^(ó  ))^2 (m _ K^(ó  ))^2 + c _ 2^( ) (-(m _ π^(ó  ))^2 - (m _ K^(ó  ))^2 + p _ 2^2) ((m _ π^(ó  ))^2 + (m _ K^(ó  ))^2))) (!, _ 0^( ))^2)

Counterterm contribution (N _ (20 - 23)):

finCTs = Cancel[(Pair[Momentum[p3], Momentum[p3]] - ParticleMass[Pion]^2) (Pair[Momentum[p1], Momentum[p1]] - ParticleMass[Kaon]^2) * (end4 /. _RenormalizationState -> Sequence[])] /. onshellrules // Simplify

(4 c _ 2^( ) (2 N _ 20^( ) p _ 2^2 (-(m _ π^(ó  ))^2 - (m _ K^(ó  ))^2 + p _ 2^2) + 2 N _ 21^( ) ((m _ π^(ó  ))^2 - (m _ K^(ó  ))^2) (-(m _ π^(ó  ))^2 + (m _ K^(ó  ))^2 + p _ 2^2) + (N _ 22^( ) + 2 N _ 23^( )) (p _ 2^2 ((m _ π^(ó  ))^2 + (m _ K^(ó  ))^2) - ((m _ π^(ó  ))^2 - (m _ K^(ó  ))^2)^2)) (!, _ 0^( ))^2)/(f _ ϕ^(ó  ))^2

Converted by Mathematica  (July 10, 2003)