•The infinities

lambdaloopend = fin1 // ScalarProductExpand // FullSimplify

-1/(54 (f _ ϕ^(ó  ))^4 (m _ K^(ó  ))^2 ((m _ K^(ó  ))^2 - s)) (i p _ 1^μ _ 1 µ _ μ _ 1(p _ 1) (3 c _ 2^( ) (80 (m _ π^(ó  ))^4 - 4 (17 (m _ K^(ó  ))^2 + 39 s) (m _ π^(ó  ))^2 + 48 (m _ K^(ó  ))^4 + 27 s^2 + 69 s (m _ K^(ó  ))^2) (m _ K^(ó  ))^2 + 4 c _ 5^( ) ((m _ π^(ó  ))^2 - (m _ K^(ó  ))^2) (10 (m _ π^(ó  ))^4 + 3 (s - 5 (m _ K^(ó  ))^2) (m _ π^(ó  ))^2 - 37 (m _ K^(ó  ))^4 + 15 s (m _ K^(ó  ))^2)))

lambdaCTend = CTlambdaCoeff // FullSimplify

1/(54 (f _ ϕ^(ó  ))^4 (m _ K^(ó  ))^2 ((m _ K^(ó  ))^2 - s)) (i p _ 1^μ _ 1 µ _ μ _ 1(p _ 1) (3 c _ 2^( ) (80 (m _ π^(ó  ))^4 - 4 (17 (m _ K^(ó  ))^2 + 39 s) (m _ π^(ó  ))^2 + 48 (m _ K^(ó  ))^4 + 27 s^2 + 69 s (m _ K^(ó  ))^2) (m _ K^(ó  ))^2 + 4 c _ 5^( ) ((m _ π^(ó  ))^2 - (m _ K^(ó  ))^2) (10 (m _ π^(ó  ))^4 + 3 (s - 5 (m _ K^(ó  ))^2) (m _ π^(ó  ))^2 - 37 (m _ K^(ó  ))^4 + 15 s (m _ K^(ó  ))^2)))

((lambdaloopend + lambdaCTend) /. _RenormalizationState :> Sequence[] // Expand)

0

Cancel[(MandelstamS - ParticleMass[Kaon, RenormalizationState[0]]^2) (lambdaCTend)] /. MandelstamS -> ParticleMass[Kaon, RenormalizationState[0]]^2 /. gellmannOkubo // FullSimplify

-(4 i p _ 1^μ _ 1 µ _ μ _ 1(p _ 1) ((m _ K^(ó  ))^2 - (m _ π^(ó  ))^2) (-5 c _ 5^( ) (m _ π^(ó  ))^4 + 6 (c _ 5^( ) - 5 c _ 2^( )) (m _ K^(ó  ))^2 (m _ π^(ó  ))^2 + (54 c _ 2^( ) + 11 c _ 5^( )) (m _ K^(ó  ))^4))/(27 (f _ ϕ^(ó  ))^4 (m _ K^(ó  ))^2)

Cancel[(MandelstamS - ParticleMass[Kaon, RenormalizationState[0]]^2) (lambdaloopend)] /. MandelstamS -> ParticleMass[Kaon, RenormalizationState[0]]^2 /. gellmannOkubo // FullSimplify

(4 i p _ 1^μ _ 1 µ _ μ _ 1(p _ 1) ((m _ K^(ó  ))^2 - (m _ π^(ó  ))^2) (-5 c _ 5^( ) (m _ π^(ó  ))^4 + 6 (c _ 5^( ) - 5 c _ 2^( )) (m _ K^(ó  ))^2 (m _ π^(ó  ))^2 + (54 c _ 2^( ) + 11 c _ 5^( )) (m _ K^(ó  ))^4))/(27 (f _ ϕ^(ó  ))^4 (m _ K^(ó  ))^2)

% + %% // Simplify

0

Converted by Mathematica  (July 10, 2003)