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's, logs and lowest order contributions on-mass-shell (soft pion limit)
Converted by
Mathematica
(July 10, 2003)
![Overscript[J, _]](../HTMLFiles/index_122.gif){kind=small}
's, logs and lowest order contributions on-mass-shell (soft pion limit)'s, logs and lowest order contributions on-mass-shell (soft pion limit)![polyren = Limit[(fpionfac - 1 + fkaonfac - 1 + sqrtZPi0inv - 1 + sqrtZK0inv - 1) finpoly /. _RenormalizationState -> Sequence[], ParticleMass[Pion] -> 0] // Simplify](../HTMLFiles/index_123.gif){kind=small}
![polyren /. CouplingConstant[_[4], ___] -> 0](../HTMLFiles/index_125.gif){kind=small}
![Limit[finpoly, ParticleMass[Pion] -> 0] // Simplify](../HTMLFiles/index_127.gif){kind=small}
![Limit[finJBarsKLM, ParticleMass[Pion] -> 0] /. fixzeros // Simplify](../HTMLFiles/index_129.gif){kind=small}
![1/(18 (f _ ϕ^(ó ))^2) ((6 c _ 5^( ) (6 (3 K[p _ 2^2, (m _ π^(ó ))^2, (m _ K^(ó ))^2] + K[p _ 2^2, (m _ K^(ó ))^2, (m _ η^(ó ))^2]) (m _ K^(ó ))^2 + Overscript[J, _] _ ((m _ K^(ó ))^2 (m _ η^(ó ))^2)(p _ 2^2) (3 p _ 2^2 - 2 (m _ K^(ó ))^2) + 3 Overscript[J, _] _ ((m _ π^(ó ))^2 (m _ K^(ó ))^2)(p _ 2^2) (5 p _ 2^2 - 2 (m _ K^(ó ))^2)) (m _ K^(ó ))^2 + c _ 2^( ) (-6 (9 K[p _ 2^2, (m _ π^(ó ))^2, (m _ K^(ó ))^2] + 7 K[p _ 2^2, (m _ K^(ó ))^2, (m _ η^(ó ))^2]) (m _ K^(ó ))^4 + 9 Overscript[J, _] _ ((m _ π^(ó ))^2 (m _ K^(ó ))^2)(p _ 2^2) (-(m _ K^(ó ))^4 - 7 p _ 2^2 (m _ K^(ó ))^2 + 5 p _ 2^4) + Overscript[J, _] _ ((m _ K^(ó ))^2 (m _ η^(ó ))^2)(p _ 2^2) (11 (m _ K^(ó ))^4 - 27 p _ 2^2 (m _ K^(ó ))^2 + 9 p _ 2^4))) (!, _ 0^( ))^2)](../HTMLFiles/index_130.gif)
![Simplify /@ Collect[Limit[finLogs + polyren /. CouplingConstant[_[4], ___] -> 0, ParticleMass[Pion] -> 0], _Log]](../HTMLFiles/index_131.gif){kind=small}
