•Setting the squared source momentum to 0
Converted by
Mathematica
(July 10, 2003)
![looptreesKLM = Simplify[(finloops + DiscardOrders[(fpionfac - 1 + fkaonfac - 1 + sqrtZPi0inv + sqrtZK0inv - 1) finTrees, PerturbationOrder -> 4] + finCTs + finCTsold + finCTsstrongRaw) /. _RenormalizationState -> Sequence[] /. JBarToKL /. cancelLogs /. gellmannOkubo] /. {Log[l_] :> Log[l /. toEtaRules], K[l__] :> K[Sequence @@ ({l} /. toEtaRules)]}](../HTMLFiles/index_143.gif)
![1/(288 π^2 (f _ ϕ^(ó ))^2 ((m _ π^(ó ))^2 - (m _ K^(ó ))^2)) ((c _ 2^( ) (-2304 π^2 N _ 8^( ) (m _ π^(ó ))^6 - 2304 π^2 N _ 21^( ) (m _ π^(ó ))^6 - 1152 π^2 N _ 22^( ) (m _ π^(ó ))^6 - 2304 π^2 N _ 23^( ) (m _ π^(ó ))^6 + 63 log((m _ π^(ó ))^2/μ^2) (m _ π^(ó ))^6 - 9 log((m _ η^(ó ))^2/μ^2) (m _ π^(ó ))^6 - 1152 π^2 (f _ ϕ^(ó ))^2 (m _ π^(ó ))^4 - 4608 π^2 N _ 5^( ) (m _ K^(ó ))^2 (m _ π^(ó ))^4 - 4608 π^2 N _ 8^( ) (m _ K^(ó ))^2 (m _ π^(ó ))^4 + 4608 π^2 N _ 11^( ) (m _ K^(ó ))^2 (m _ π^(ó ))^4 + 9216 π^2 N _ 12^( ) (m _ K^(ó ))^2 (m _ π^(ó ))^4 + 6912 π^2 N _ 21^( ) (m _ K^(ó ))^2 (m _ π^(ó ))^4 + 3456 π^2 N _ 22^( ) (m _ K^(ó ))^2 (m _ π^(ó ))^4 + 6912 π^2 N _ 23^( ) (m _ K^(ó ))^2 (m _ π^(ó ))^4 - 36 log((m _ π^(ó ))^2/μ^2) (m _ K^(ó ))^2 (m _ π^(ó ))^4 + 126 log((m _ K^(ó ))^2/μ^2) (m _ K^(ó ))^2 (m _ π^(ó ))^4 + 8 log((m _ η^(ó ))^2/μ^2) (m _ K^(ó ))^2 (m _ π^(ó ))^4 + 2304 π^2 N _ 8^( ) p _ 2^2 (m _ π^(ó ))^4 - 2304 π^2 N _ 20^( ) p _ 2^2 (m _ π^(ó ))^4 + 2304 π^2 N _ 21^( ) p _ 2^2 (m _ π^(ó ))^4 + 1152 π^2 N _ 22^( ) p _ 2^2 (m _ π^(ó ))^4 + 2304 π^2 N _ 23^( ) p _ 2^2 (m _ π^(ó ))^4 - 18 log((m _ π^(ó ))^2/μ^2) p _ 2^2 (m _ π^(ó ))^4 + 18 log((m _ η^(ó ))^2/μ^2) p _ 2^2 (m _ π^(ó ))^4 + 2304 π^2 N _ 8^( ) (m _ K^(ó ))^4 (m _ π^(ó ))^2 + 9216 π^2 N _ 10^( ) (m _ K^(ó ))^4 (m _ π^(ó ))^2 + 4608 π^2 N _ 11^( ) (m _ K^(ó ))^4 (m _ π^(ó ))^2 - 9216 π^2 N _ 12^( ) (m _ K^(ó ))^4 (m _ π^(ó ))^2 - 6912 π^2 N _ 21^( ) (m _ K^(ó ))^4 (m _ π^(ó ))^2 - 3456 π^2 N _ 22^( ) (m _ K^(ó ))^4 (m _ π^(ó ))^2 - 6912 π^2 N _ 23^( ) (m _ K^(ó ))^4 (m _ π^(ó ))^2 - 99 log((m _ π^(ó ))^2/μ^2) (m _ K^(ó ))^4 (m _ π^(ó ))^2 + 72 log((m _ K^(ó ))^2/μ^2) (m _ K^(ó ))^4 (m _ π^(ó ))^2 + 125 log((m _ η^(ó ))^2/μ^2) (m _ K^(ó ))^4 (m _ π^(ó ))^2 + 2304 π^2 N _ 20^( ) p _ 2^4 (m _ π^(ó ))^2 - 45 log((m _ π^(ó ))^2/μ^2) p _ 2^4 (m _ π^(ó ))^2 - 9 log((m _ η^(ó ))^2/μ^2) p _ 2^4 (m _ π^(ó ))^2 + 4608 π^2 N _ 5^( ) p _ 2^2 (m _ K^(ó ))^2 (m _ π^(ó ))^2 + 2304 π^2 N _ 8^( ) p _ 2^2 (m _ K^(ó ))^2 (m _ π^(ó ))^2 - 4608 π^2 N _ 21^( ) p _ 2^2 (m _ K^(ó ))^2 (m _ π^(ó ))^2 + 144 log((m _ π^(ó ))^2/μ^2) p _ 2^2 (m _ K^(ó ))^2 (m _ π^(ó ))^2 - 144 log((m _ K^(ó ))^2/μ^2) p _ 2^2 (m _ K^(ó ))^2 (m _ π^(ó ))^2 - 60 log((m _ η^(ó ))^2/μ^2) p _ 2^2 (m _ K^(ó ))^2 (m _ π^(ó ))^2 + 1152 π^2 (f _ ϕ^(ó ))^2 p _ 2^2 (m _ π^(ó ))^2 + 4608 π^2 N _ 5^( ) (m _ K^(ó ))^6 + 4608 π^2 N _ 8^( ) (m _ K^(ó ))^6 - 9216 π^2 N _ 10^( ) (m _ K^(ó ))^6 - 9216 π^2 N _ 11^( ) (m _ K^(ó ))^6 + 2304 π^2 N _ 21^( ) (m _ K^(ó ))^6 + 1152 π^2 N _ 22^( ) (m _ K^(ó ))^6 + 2304 π^2 N _ 23^( ) (m _ K^(ó ))^6 - 198 log((m _ K^(ó ))^2/μ^2) (m _ K^(ó ))^6 - 52 log((m _ η^(ó ))^2/μ^2) (m _ K^(ó ))^6 + 1152 π^2 (f _ ϕ^(ó ))^2 (m _ K^(ó ))^4 - 4608 π^2 N _ 5^( ) p _ 2^2 (m _ K^(ó ))^4 - 4608 π^2 N _ 8^( ) p _ 2^2 (m _ K^(ó ))^4 + 2304 π^2 N _ 20^( ) p _ 2^2 (m _ K^(ó ))^4 + 2304 π^2 N _ 21^( ) p _ 2^2 (m _ K^(ó ))^4 - 1152 π^2 N _ 22^( ) p _ 2^2 (m _ K^(ó ))^4 - 2304 π^2 N _ 23^( ) p _ 2^2 (m _ K^(ó ))^4 + 108 log((m _ K^(ó ))^2/μ^2) p _ 2^2 (m _ K^(ó ))^4 - 48 log((m _ η^(ó ))^2/μ^2) p _ 2^2 (m _ K^(ó ))^4 - 2304 π^2 N _ 20^( ) p _ 2^4 (m _ K^(ó ))^2 + 18 log((m _ K^(ó ))^2/μ^2) p _ 2^4 (m _ K^(ó ))^2 + 36 log((m _ η^(ó ))^2/μ^2) p _ 2^4 (m _ K^(ó ))^2 - 1152 π^2 (f _ ϕ^(ó ))^2 p _ 2^2 (m _ K^(ó ))^2 + 288 π^2 K[p _ 2^2, (m _ π^(ó ))^2, (m _ K^(ó ))^2] (5 p _ 2^6 - 7 ((m _ π^(ó ))^2 + (m _ K^(ó ))^2) p _ 2^4 - ((m _ π^(ó ))^4 - 10 (m _ K^(ó ))^2 (m _ π^(ó ))^2 + (m _ K^(ó ))^4) p _ 2^2 + 3 ((m _ π^(ó ))^2 - (m _ K^(ó ))^2)^2 ((m _ π^(ó ))^2 + (m _ K^(ó ))^2)) + 96 π^2 K[p _ 2^2, (m _ K^(ó ))^2, (m _ η^(ó ))^2] (9 p _ 2^6 - 3 ((m _ π^(ó ))^2 + 9 (m _ K^(ó ))^2) p _ 2^4 + (-5 (m _ π^(ó ))^4 + 18 (m _ K^(ó ))^2 (m _ π^(ó ))^2 + 11 (m _ K^(ó ))^4) p _ 2^2 - ((m _ π^(ó ))^2 - 7 (m _ K^(ó ))^2) ((m _ π^(ó ))^2 - (m _ K^(ó ))^2)^2)) - 6 c _ 5^( ) (m _ K^(ó ))^2 (-3072 π^2 L _ 4^( ) (m _ π^(ó ))^4 + 6144 π^2 L _ 6^( ) (m _ π^(ó ))^4 + 21 log((m _ π^(ó ))^2/μ^2) (m _ π^(ó ))^4 - 7 log((m _ η^(ó ))^2/μ^2) (m _ π^(ó ))^4 - 384 π^2 (f _ ϕ^(ó ))^2 (m _ π^(ó ))^2 - 3072 π^2 L _ 4^( ) (m _ K^(ó ))^2 (m _ π^(ó ))^2 - 3072 π^2 L _ 5^( ) (m _ K^(ó ))^2 (m _ π^(ó ))^2 + 6144 π^2 L _ 6^( ) (m _ K^(ó ))^2 (m _ π^(ó ))^2 + 6144 π^2 L _ 8^( ) (m _ K^(ó ))^2 (m _ π^(ó ))^2 - 33 log((m _ π^(ó ))^2/μ^2) (m _ K^(ó ))^2 (m _ π^(ó ))^2 + 30 log((m _ K^(ó ))^2/μ^2) (m _ K^(ó ))^2 (m _ π^(ó ))^2 + 31 log((m _ η^(ó ))^2/μ^2) (m _ K^(ó ))^2 (m _ π^(ó ))^2 + 15 log((m _ π^(ó ))^2/μ^2) p _ 2^2 (m _ π^(ó ))^2 + 3 log((m _ η^(ó ))^2/μ^2) p _ 2^2 (m _ π^(ó ))^2 + 6144 π^2 L _ 4^( ) (m _ K^(ó ))^4 + 3072 π^2 L _ 5^( ) (m _ K^(ó ))^4 - 12288 π^2 L _ 6^( ) (m _ K^(ó ))^4 - 6144 π^2 L _ 8^( ) (m _ K^(ó ))^4 - 30 log((m _ K^(ó ))^2/μ^2) (m _ K^(ó ))^4 - 12 log((m _ η^(ó ))^2/μ^2) (m _ K^(ó ))^4 + 384 π^2 (f _ ϕ^(ó ))^2 (m _ K^(ó ))^2 - 6 log((m _ K^(ó ))^2/μ^2) p _ 2^2 (m _ K^(ó ))^2 - 12 log((m _ η^(ó ))^2/μ^2) p _ 2^2 (m _ K^(ó ))^2 - 96 π^2 K[p _ 2^2, (m _ π^(ó ))^2, (m _ K^(ó ))^2] (5 p _ 2^4 - 2 ((m _ π^(ó ))^2 + (m _ K^(ó ))^2) p _ 2^2 - 3 ((m _ π^(ó ))^2 - (m _ K^(ó ))^2)^2) - 96 π^2 K[p _ 2^2, (m _ K^(ó ))^2, (m _ η^(ó ))^2] (3 p _ 2^4 - 2 ((m _ π^(ó ))^2 + (m _ K^(ó ))^2) p _ 2^2 - ((m _ π^(ó ))^2 - (m _ K^(ó ))^2)^2))) (!, _ 0^( ))^2)](../HTMLFiles/index_144.gif)
![looptreesS = Simplify /@ Collect[Limit[looptreesKLM /. Log -> log, ParticleMass[Pion] -> 0] /. log -> Log /. KLToJBar /. gellmannOkubo /. {Log[l_] :> Log[l /. toEtaRules], K[l__] :> K[Sequence @@ ({l} /. toEtaRules)], LeutwylerJBar[l__] :> LeutwylerJBar[Sequence @@ ({l} /. toEtaRules)]} /. cancelLogs /. Log -> log /. _RenormalizationState -> Sequence[] /. ParticleMass[Pion] -> 0 /. log -> Log // Expand, {_LeutwylerJBar, _Log}]](../HTMLFiles/index_145.gif)
![(128 L _ 4^( ) c _ 5^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 + (64 L _ 5^( ) c _ 5^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 - (256 L _ 6^( ) c _ 5^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 - (128 L _ 8^( ) c _ 5^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 - (16 c _ 2^( ) N _ 5^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 - (16 c _ 2^( ) N _ 8^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 + (32 c _ 2^( ) N _ 10^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 + (32 c _ 2^( ) N _ 11^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 - (8 c _ 2^( ) N _ 21^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 - (4 c _ 2^( ) N _ 22^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 - (8 c _ 2^( ) N _ 23^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 - 4 c _ 2^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^2 + 8 c _ 5^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^2 + (16 c _ 2^( ) N _ 5^( ) p _ 2^2 (!, _ 0^( ))^2 (m _ K^(ó ))^2)/(f _ ϕ^(ó ))^2 + (16 c _ 2^( ) N _ 8^( ) p _ 2^2 (!, _ 0^( ))^2 (m _ K^(ó ))^2)/(f _ ϕ^(ó ))^2 - (8 c _ 2^( ) N _ 20^( ) p _ 2^2 (!, _ 0^( ))^2 (m _ K^(ó ))^2)/(f _ ϕ^(ó ))^2 - (8 c _ 2^( ) N _ 21^( ) p _ 2^2 (!, _ 0^( ))^2 (m _ K^(ó ))^2)/(f _ ϕ^(ó ))^2 + (4 c _ 2^( ) N _ 22^( ) p _ 2^2 (!, _ 0^( ))^2 (m _ K^(ó ))^2)/(f _ ϕ^(ó ))^2 + (8 c _ 2^( ) N _ 23^( ) p _ 2^2 (!, _ 0^( ))^2 (m _ K^(ó ))^2)/(f _ ϕ^(ó ))^2 + (8 c _ 2^( ) N _ 20^( ) p _ 2^4 (!, _ 0^( ))^2)/(f _ ϕ^(ó ))^2 + 4 c _ 2^( ) p _ 2^2 (!, _ 0^( ))^2 + (Overscript[J, _] _ ((m _ K^(ó ))^2 (m _ η^(ó ))^2)(p _ 2^2) (-(m _ K^(ó ))^4 - 2 p _ 2^2 (m _ K^(ó ))^2 + 3 p _ 2^4) (6 c _ 5^( ) (m _ K^(ó ))^2 + c _ 2^( ) (3 p _ 2^2 - 7 (m _ K^(ó ))^2)) (!, _ 0^( ))^2)/(18 (f _ ϕ^(ó ))^2 p _ 2^2) + (Overscript[J, _] _ (0 (m _ K^(ó ))^2)(p _ 2^2) (-3 (m _ K^(ó ))^4 - 2 p _ 2^2 (m _ K^(ó ))^2 + 5 p _ 2^4) (2 c _ 5^( ) (m _ K^(ó ))^2 + c _ 2^( ) (p _ 2^2 - (m _ K^(ó ))^2)) (!, _ 0^( ))^2)/(2 (f _ ϕ^(ó ))^2 p _ 2^2) - (log((m _ η^(ó ))^2/μ^2) (18 c _ 5^( ) ((m _ K^(ó ))^2 + p _ 2^2) (m _ K^(ó ))^2 + c _ 2^( ) (-13 (m _ K^(ó ))^4 - 12 p _ 2^2 (m _ K^(ó ))^2 + 9 p _ 2^4)) (!, _ 0^( ))^2)/(72 π^2 (f _ ϕ^(ó ))^2) - (log((m _ K^(ó ))^2/μ^2) (2 c _ 5^( ) (5 (m _ K^(ó ))^2 + p _ 2^2) (m _ K^(ó ))^2 + c _ 2^( ) (-11 (m _ K^(ó ))^4 + 6 p _ 2^2 (m _ K^(ó ))^2 + p _ 2^4)) (!, _ 0^( ))^2)/(16 π^2 (f _ ϕ^(ó ))^2)](../HTMLFiles/index_146.gif)
![looptreesS = Simplify /@ Collect[(looptreesKLM /. KLToJBar /. gellmannOkubo /. {Log[l_] :> Log[l /. toEtaRules], K[l__] :> K[Sequence @@ ({l} /. toEtaRules)], LeutwylerJBar[l__] :> LeutwylerJBar[Sequence @@ ({l} /. toEtaRules)]} /. cancelLogs /. Log -> log /. _RenormalizationState -> Sequence[] /. ParticleMass[Pion] -> 0 // Expand) /. log -> Log, {_LeutwylerJBar, _Log}]](../HTMLFiles/index_147.gif)
![(128 L _ 4^( ) c _ 5^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 + (64 L _ 5^( ) c _ 5^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 - (256 L _ 6^( ) c _ 5^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 - (128 L _ 8^( ) c _ 5^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 - (16 c _ 2^( ) N _ 5^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 - (16 c _ 2^( ) N _ 8^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 + (32 c _ 2^( ) N _ 10^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 + (32 c _ 2^( ) N _ 11^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 - (8 c _ 2^( ) N _ 21^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 - (4 c _ 2^( ) N _ 22^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 - (8 c _ 2^( ) N _ 23^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^4)/(f _ ϕ^(ó ))^2 - 4 c _ 2^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^2 + 8 c _ 5^( ) (!, _ 0^( ))^2 (m _ K^(ó ))^2 + (16 c _ 2^( ) N _ 5^( ) p _ 2^2 (!, _ 0^( ))^2 (m _ K^(ó ))^2)/(f _ ϕ^(ó ))^2 + (16 c _ 2^( ) N _ 8^( ) p _ 2^2 (!, _ 0^( ))^2 (m _ K^(ó ))^2)/(f _ ϕ^(ó ))^2 - (8 c _ 2^( ) N _ 20^( ) p _ 2^2 (!, _ 0^( ))^2 (m _ K^(ó ))^2)/(f _ ϕ^(ó ))^2 - (8 c _ 2^( ) N _ 21^( ) p _ 2^2 (!, _ 0^( ))^2 (m _ K^(ó ))^2)/(f _ ϕ^(ó ))^2 + (4 c _ 2^( ) N _ 22^( ) p _ 2^2 (!, _ 0^( ))^2 (m _ K^(ó ))^2)/(f _ ϕ^(ó ))^2 + (8 c _ 2^( ) N _ 23^( ) p _ 2^2 (!, _ 0^( ))^2 (m _ K^(ó ))^2)/(f _ ϕ^(ó ))^2 + (8 c _ 2^( ) N _ 20^( ) p _ 2^4 (!, _ 0^( ))^2)/(f _ ϕ^(ó ))^2 + 4 c _ 2^( ) p _ 2^2 (!, _ 0^( ))^2 + (Overscript[J, _] _ ((m _ K^(ó ))^2 (m _ η^(ó ))^2)(p _ 2^2) (-(m _ K^(ó ))^4 - 2 p _ 2^2 (m _ K^(ó ))^2 + 3 p _ 2^4) (6 c _ 5^( ) (m _ K^(ó ))^2 + c _ 2^( ) (3 p _ 2^2 - 7 (m _ K^(ó ))^2)) (!, _ 0^( ))^2)/(18 (f _ ϕ^(ó ))^2 p _ 2^2) + (Overscript[J, _] _ (0 (m _ K^(ó ))^2)(p _ 2^2) (-3 (m _ K^(ó ))^4 - 2 p _ 2^2 (m _ K^(ó ))^2 + 5 p _ 2^4) (2 c _ 5^( ) (m _ K^(ó ))^2 + c _ 2^( ) (p _ 2^2 - (m _ K^(ó ))^2)) (!, _ 0^( ))^2)/(2 (f _ ϕ^(ó ))^2 p _ 2^2) - (log((m _ η^(ó ))^2/μ^2) (18 c _ 5^( ) ((m _ K^(ó ))^2 + p _ 2^2) (m _ K^(ó ))^2 + c _ 2^( ) (-13 (m _ K^(ó ))^4 - 12 p _ 2^2 (m _ K^(ó ))^2 + 9 p _ 2^4)) (!, _ 0^( ))^2)/(72 π^2 (f _ ϕ^(ó ))^2) - (log((m _ K^(ó ))^2/μ^2) (2 c _ 5^( ) (5 (m _ K^(ó ))^2 + p _ 2^2) (m _ K^(ó ))^2 + c _ 2^( ) (-11 (m _ K^(ó ))^4 + 6 p _ 2^2 (m _ K^(ó ))^2 + p _ 2^4)) (!, _ 0^( ))^2)/(16 π^2 (f _ ϕ^(ó ))^2)](../HTMLFiles/index_148.gif)
![Simplify /@ Collect[Limit[looptreesS /. LeutwylerJBar[s_, m12_, m22_, ___] :> (s (m12^2 - m22^2 + 2 m12 m22 Log[m22/m12]))/(32 (m12 - m22)^3 π^2) /; m12 =!= 0 /. gellmannOkubo /. Log[l_] :> Log[l /. toEtaRules] /. cancelLogs, ParticleMass[Pion] -> 0], _Log]](../HTMLFiles/index_149.gif)
![(log((m _ K^(ó ))^2/μ^2) (c _ 2^( ) (25 (m _ K^(ó ))^6 + 16 p _ 2^2 (m _ K^(ó ))^4 - 55 p _ 2^4 (m _ K^(ó ))^2 + 18 p _ 2^6) - 2 c _ 5^( ) (m _ K^(ó ))^2 (11 (m _ K^(ó ))^4 + 13 p _ 2^2 (m _ K^(ó ))^2 - 18 p _ 2^4)) (!, _ 0^( ))^2)/(16 π^2 (f _ ϕ^(ó ))^2 (m _ K^(ó ))^2) - (log((m _ η^(ó ))^2/μ^2) (c _ 2^( ) (50 (m _ K^(ó ))^6 + 87 p _ 2^2 (m _ K^(ó ))^4 - 234 p _ 2^4 (m _ K^(ó ))^2 + 81 p _ 2^6) - 18 c _ 5^( ) (m _ K^(ó ))^2 (2 (m _ K^(ó ))^4 + 5 p _ 2^2 (m _ K^(ó ))^2 - 9 p _ 2^4)) (!, _ 0^( ))^2)/(72 π^2 (f _ ϕ^(ó ))^2 (m _ K^(ó ))^2) + 1/(192 π^2 (f _ ϕ^(ó ))^2 p _ 2^2 (m _ K^(ó ))^2) ((6 c _ 5^( ) (-96 π^2 Overscript[J, _] _ (0 (m _ K^(ó ))^2)(p _ 2^2) (m _ K^(ó ))^6 + 2 (80 π^2 Overscript[J, _] _ (0 (m _ K^(ó ))^2)(p _ 2^2) - 7) p _ 2^4 (m _ K^(ó ))^2 + 21 p _ 2^6 + p _ 2^2 ((4096 π^2 L _ 4^( ) + 2048 π^2 L _ 5^( ) - 8192 π^2 L _ 6^( ) - 4096 π^2 L _ 8^( ) - 64 π^2 Overscript[J, _] _ (0 (m _ K^(ó ))^2)(p _ 2^2) - 7) (m _ K^(ó ))^4 + 256 π^2 (f _ ϕ^(ó ))^2 (m _ K^(ó ))^2)) (m _ K^(ó ))^2 + c _ 2^( ) (288 π^2 Overscript[J, _] _ (0 (m _ K^(ó ))^2)(p _ 2^2) (m _ K^(ó ))^8 + 3 (512 π^2 N _ 20^( ) + 160 π^2 Overscript[J, _] _ (0 (m _ K^(ó ))^2)(p _ 2^2) - 63) p _ 2^6 (m _ K^(ó ))^2 + 63 p _ 2^2^4 + p _ 2^4 ((3072 π^2 N _ 5^( ) + 3072 π^2 N _ 8^( ) - 1536 π^2 N _ 20^( ) - 1536 π^2 N _ 21^( ) + 768 π^2 N _ 22^( ) + 1536 π^2 N _ 23^( ) - 672 π^2 Overscript[J, _] _ (0 (m _ K^(ó ))^2)(p _ 2^2) + 77) (m _ K^(ó ))^4 + 768 π^2 (f _ ϕ^(ó ))^2 (m _ K^(ó ))^2) - p _ 2^2 ((3072 π^2 N _ 5^( ) + 3072 π^2 N _ 8^( ) - 6144 π^2 N _ 10^( ) - 6144 π^2 N _ 11^( ) + 1536 π^2 N _ 21^( ) + 768 π^2 N _ 22^( ) + 1536 π^2 N _ 23^( ) + 96 π^2 Overscript[J, _] _ (0 (m _ K^(ó ))^2)(p _ 2^2) - 49) (m _ K^(ó ))^6 + 768 π^2 (f _ ϕ^(ó ))^2 (m _ K^(ó ))^4))) (!, _ 0^( ))^2)](../HTMLFiles/index_150.gif)
![looptrees0 = (looptreesKLM /. Pair[Momentum[p2], Momentum[p2]] -> 0 /. KLToJBar /. gellmannOkubo /. {Log[l_] :> Log[l /. toEtaRules], K[l__] :> K[Sequence @@ ({l} /. toEtaRules)]} /. cancelLogs /. Log -> log /. _RenormalizationState -> Sequence[] /. ParticleMass[Pion] -> 0 // Simplify) /. log -> Log](../HTMLFiles/index_151.gif)
