•Inspecting all contributions

end4old /. _RenormalizationState -> Sequence[]

1/((f _ ϕ^(ó  ))^2 ((m _ π^(ó  ))^2 - p _ 3^2) (p _ 1^2 - (m _ K^(ó  ))^2)) (8 (c _ 2^( ) (2 N _ 11^( ) (m _ π^(ó  ))^4 + 4 N _ 10^( ) (m _ K^(ó  ))^2 (m _ π^(ó  ))^2 + 4 N _ 11^( ) (m _ K^(ó  ))^2 (m _ π^(ó  ))^2 + 16 L _ 6^( ) p _ 1^2 (m _ π^(ó  ))^2 + 8 L _ 8^( ) p _ 1^2 (m _ π^(ó  ))^2 + N _ 8^( ) p _ 1^2 (m _ π^(ó  ))^2 - 2 N _ 11^( ) p _ 1^2 (m _ π^(ó  ))^2 - 16 L _ 6^( ) p _ 2^2 (m _ π^(ó  ))^2 - 8 L _ 8^( ) p _ 2^2 (m _ π^(ó  ))^2 - N _ 8^( ) p _ 2^2 (m _ π^(ó  ))^2 + 16 L _ 6^( ) p _ 3^2 (m _ π^(ó  ))^2 + 8 L _ 8^( ) p _ 3^2 (m _ π^(ó  ))^2 + N _ 8^( ) p _ 3^2 (m _ π^(ó  ))^2 - 2 N _ 11^( ) p _ 3^2 (m _ π^(ó  ))^2 + 32 L _ 6^( ) p _ 1^2 (m _ K^(ó  ))^2 + 8 L _ 8^( ) p _ 1^2 (m _ K^(ó  ))^2 + 2 N _ 5^( ) p _ 1^2 (m _ K^(ó  ))^2 + 2 N _ 8^( ) p _ 1^2 (m _ K^(ó  ))^2 - 4 N _ 10^( ) p _ 1^2 (m _ K^(ó  ))^2 - 4 N _ 11^( ) p _ 1^2 (m _ K^(ó  ))^2 - 32 L _ 6^( ) p _ 2^2 (m _ K^(ó  ))^2 - 8 L _ 8^( ) p _ 2^2 (m _ K^(ó  ))^2 - 2 N _ 5^( ) p _ 2^2 (m _ K^(ó  ))^2 - 2 N _ 8^( ) p _ 2^2 (m _ K^(ó  ))^2 + 32 L _ 6^( ) p _ 3^2 (m _ K^(ó  ))^2 + 8 L _ 8^( ) p _ 3^2 (m _ K^(ó  ))^2 + 2 N _ 5^( ) p _ 3^2 (m _ K^(ó  ))^2 + 2 N _ 8^( ) p _ 3^2 (m _ K^(ó  ))^2 - 4 N _ 10^( ) p _ 3^2 (m _ K^(ó  ))^2 - 4 N _ 11^( ) p _ 3^2 (m _ K^(ó  ))^2 - 4 N _ 12^( ) p _ 1^2 p _ 3^2 + 4 N _ 36^( ) (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (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)))) (!, _ 0^( ))^2)

end4 /. _RenormalizationState -> Sequence[]

1/(f _ ϕ^(ó  ))^2 (4 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) - (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)))/((p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (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)) (!, _ 0^( ))^2)

final2all = end2all /. _LeutwylerLambda -> 0 /. toEtaRules /. _RenormalizationState -> Sequence[] // Simplify

{(c _ 5^( ) (64 π^2 (f _ ϕ^(ó  ))^2 + log((m _ π^(ó  ))^2/μ^2) (m _ π^(ó  ))^2 - 512 π^2 L _ 5^( ) (m _ K^(ó  ))^2 + 2 log((m _ K^(ó  ))^2/μ^2) (m _ K^(ó  ))^2 + log((m _ η^(ó  ))^2/μ^2) (m _ η^(ó  ))^2 - 512 π^2 L _ 4^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2)) (!, _ 0^( ))^2)/(8 π^2 (f _ ϕ^(ó  ))^2 (p _ 1^2 - (m _ K^(ó  ))^2)), (c _ 5^( ) (48 π^2 (f _ ϕ^(ó  ))^2 - 384 π^2 L _ 5^( ) (m _ π^(ó  ))^2 + 2 log((m _ π^(ó  ))^2/μ^2) (m _ π^(ó  ))^2 + log((m _ K^(ó  ))^2/μ^2) (m _ K^(ó  ))^2 - 384 π^2 L _ 4^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2)) (!, _ 0^( ))^2)/(6 π^2 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2)), -((2 c _ 5^( ) (-576 π^2 (f _ ϕ^(ó  ))^2 + 4608 π^2 L _ 5^( ) (m _ π^(ó  ))^2 + 9216 π^2 L _ 6^( ) (m _ π^(ó  ))^2 - 33 log((m _ π^(ó  ))^2/μ^2) (m _ π^(ó  ))^2 - 4 log((m _ η^(ó  ))^2/μ^2) (m _ π^(ó  ))^2 + 18432 π^2 L _ 6^( ) (m _ K^(ó  ))^2 + 9216 π^2 L _ 8^( ) (m _ K^(ó  ))^2 - 30 log((m _ K^(ó  ))^2/μ^2) (m _ K^(ó  ))^2 + 16 log((m _ η^(ó  ))^2/μ^2) (m _ K^(ó  ))^2 - 9 log((m _ η^(ó  ))^2/μ^2) (m _ η^(ó  ))^2 + 4608 π^2 L _ 4^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2)) (m _ K^(ó  ))^2 + 3 c _ 2^( ) (p _ 1^2 - p _ 2^2 + p _ 3^2) (192 π^2 (f _ ϕ^(ó  ))^2 - 1536 π^2 L _ 5^( ) (m _ π^(ó  ))^2 + 11 log((m _ π^(ó  ))^2/μ^2) (m _ π^(ó  ))^2 - 1536 π^2 L _ 5^( ) (m _ K^(ó  ))^2 + 10 log((m _ K^(ó  ))^2/μ^2) (m _ K^(ó  ))^2 + 3 log((m _ η^(ó  ))^2/μ^2) (m _ η^(ó  ))^2 - 3072 π^2 L _ 4^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2))) (!, _ 0^( ))^2)/(144 π^2 (f _ ϕ^(ó  ))^2 (p _ 3^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2))}

Plus @@ final2all /. _RenormalizationState -> Sequence[] // Simplify

1/(144 π^2 (f _ ϕ^(ó  ))^2) (((24 c _ 5^( ) (48 π^2 (f _ ϕ^(ó  ))^2 - 384 π^2 L _ 5^( ) (m _ π^(ó  ))^2 + 2 log((m _ π^(ó  ))^2/μ^2) (m _ π^(ó  ))^2 + log((m _ K^(ó  ))^2/μ^2) (m _ K^(ó  ))^2 - 384 π^2 L _ 4^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2)))/(p _ 3^2 - (m _ π^(ó  ))^2) + (18 c _ 5^( ) (64 π^2 (f _ ϕ^(ó  ))^2 + log((m _ π^(ó  ))^2/μ^2) (m _ π^(ó  ))^2 - 512 π^2 L _ 5^( ) (m _ K^(ó  ))^2 + 2 log((m _ K^(ó  ))^2/μ^2) (m _ K^(ó  ))^2 + log((m _ η^(ó  ))^2/μ^2) (m _ η^(ó  ))^2 - 512 π^2 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^( ) (-576 π^2 (f _ ϕ^(ó  ))^2 + 4608 π^2 L _ 5^( ) (m _ π^(ó  ))^2 + 9216 π^2 L _ 6^( ) (m _ π^(ó  ))^2 - 33 log((m _ π^(ó  ))^2/μ^2) (m _ π^(ó  ))^2 - 4 log((m _ η^(ó  ))^2/μ^2) (m _ π^(ó  ))^2 + 18432 π^2 L _ 6^( ) (m _ K^(ó  ))^2 + 9216 π^2 L _ 8^( ) (m _ K^(ó  ))^2 - 30 log((m _ K^(ó  ))^2/μ^2) (m _ K^(ó  ))^2 + 16 log((m _ η^(ó  ))^2/μ^2) (m _ K^(ó  ))^2 - 9 log((m _ η^(ó  ))^2/μ^2) (m _ η^(ó  ))^2 + 4608 π^2 L _ 4^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2)) (m _ K^(ó  ))^2 + 3 c _ 2^( ) (p _ 1^2 - p _ 2^2 + p _ 3^2) (192 π^2 (f _ ϕ^(ó  ))^2 - 1536 π^2 L _ 5^( ) (m _ π^(ó  ))^2 + 11 log((m _ π^(ó  ))^2/μ^2) (m _ π^(ó  ))^2 - 1536 π^2 L _ 5^( ) (m _ K^(ó  ))^2 + 10 log((m _ K^(ó  ))^2/μ^2) (m _ K^(ó  ))^2 + 3 log((m _ η^(ó  ))^2/μ^2) (m _ η^(ó  ))^2 - 3072 π^2 L _ 4^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2)))) (!, _ 0^( ))^2)

finalloops = ((Simplify /@ #) & /@ Collect[Together[endloops /. _LeutwylerLambda -> 0 /. toEtaRules /. _RenormalizationState -> Sequence[]], {_DecayConstant, _Pair, _LeutwylerJBar, _Log, _CouplingConstant}]) ;

The Overscript[J, _] terms vanish for p _ 2^2->0.

limitjs = finalloops /. {p3 -> -p1, CouplingConstant[_[4], ___] -> 0} /. _RenormalizationState -> Sequence[] /. _Log -> 0 // Simplify

1/(36 (f _ ϕ^(ó  ))^2 p _ 2^2 (p _ 1^2 - (m _ π^(ó  ))^2) (p _ 1^2 - (m _ K^(ó  ))^2)) ((c _ 2^( ) (3 Overscript[J, _] _ ((m _ π^(ó  ))^2 (m _ K^(ó  ))^2)(p _ 2^2) (-(m _ π^(ó  ))^2 - (m _ K^(ó  ))^2 + p _ 2^2) (5 p _ 2^4 + 12 p _ 1^2 p _ 2^2 - 9 ((m _ π^(ó  ))^2 + 3 (m _ K^(ó  ))^2) p _ 2^2 + 36 p _ 1 · p _ 2 ((m _ K^(ó  ))^2 - (m _ π^(ó  ))^2)) + Overscript[J, _] _ ((m _ K^(ó  ))^2 (m _ η^(ó  ))^2)(p _ 2^2) (-(m _ K^(ó  ))^2 - (m _ η^(ó  ))^2 + p _ 2^2) (3 p _ 2^4 - 12 p _ 1^2 p _ 2^2 + (-8 (m _ π^(ó  ))^2 + 11 (m _ K^(ó  ))^2 - 15 (m _ η^(ó  ))^2) p _ 2^2 + 36 p _ 1 · p _ 2 ((m _ η^(ó  ))^2 - (m _ K^(ó  ))^2))) - 2 c _ 5^( ) (m _ K^(ó  ))^2 (Overscript[J, _] _ ((m _ K^(ó  ))^2 (m _ η^(ó  ))^2)(p _ 2^2) (-3 p _ 2^4 + 12 p _ 1^2 p _ 2^2 + (8 (m _ π^(ó  ))^2 - 11 (m _ K^(ó  ))^2 + 15 (m _ η^(ó  ))^2) p _ 2^2 + 36 p _ 1 · p _ 2 ((m _ K^(ó  ))^2 - (m _ η^(ó  ))^2)) - 3 Overscript[J, _] _ ((m _ π^(ó  ))^2 (m _ K^(ó  ))^2)(p _ 2^2) (5 p _ 2^4 + 12 p _ 1^2 p _ 2^2 - 9 ((m _ π^(ó  ))^2 + 3 (m _ K^(ó  ))^2) p _ 2^2 + 36 p _ 1 · p _ 2 ((m _ K^(ó  ))^2 - (m _ π^(ó  ))^2)))) (!, _ 0^( ))^2)

Converted by Mathematica  (July 10, 2003)