•Conterterm contributions on-mass-shell (soft pion limit)

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

Limit[finCTsold, ParticleMass[Pion] -> 0] // FullSimplify

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

Counterterm contribution (L _ i):

Limit[finCTsstrong + polyren /. _Log -> 0, ParticleMass[Pion] -> 0] // FullSimplify

(64 (2 L _ 4^( ) + L _ 5^( ) - 2 (2 L _ 6^( ) + L _ 8^( ))) c _ 5^( ) (m _ K^(ó  ))^4 (!, _ 0^( ))^2)/(f _ ϕ^(ó  ))^2

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

Limit[finCTs, ParticleMass[Pion] -> 0] // FullSimplify

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

Converted by Mathematica  (July 10, 2003)