KSPiChecks.nb

•The third diagram

$tmp1 = -16 amplFC[[3]] /. {_DecayConstant -> 1, _SumOver -> 1, _QuarkCondensate -> 1, _FeynAmpDenominator -> 1, _PropagatorDenominator -> 1, Pi -> 1, SUNDelta[SUNIndex[i1], SUNIndex[I1]] -> 1} // Simplify$

${4/3 i c _ 5^( ), 4/3 i c _ 5^( ), 4/3 i c _ 5^( ), 4/3 i c _ 5^( ), 4/3 i c _ 5^( ), 4 i c _ 5^( ), 4/3 i c _ 5^( ), 4/3 i c _ 5^( )}$

$Table[M$CouplingMatrices[[-1, 2, 1, 1]] /. Wrap -> Identity /. {I3 -> ii, I2 -> ii, I1 -> i3, I4 -> I1} /. ((a : (SUNDelta | SU3Delta | SUNF | SU3F | SUND | SU3D))[b__]) :> a[Sequence @@ (SUNIndex /@ {b})] /. {I1 -> 6, i3 -> 3} // SUNReduce // SUNReduce // SUNReduce, {ii, 8}] // Simplify$

${4/3 i c _ 5^( ), 4/3 i c _ 5^( ), 4/3 i c _ 5^( ), 4/3 i c _ 5^( ), 4/3 i c _ 5^( ), 4 i c _ 5^( ), 4/3 i c _ 5^( ), 4/3 i c _ 5^( )}$

$Table[tmp2 /. ((a : (SUNDelta | SU3Delta | SUNF | SU3F | SUND | SU3D))[b__]) :> a[Sequence @@ (SUNIndex /@ {b})] /. {I1 -> 6, i3 -> 3} // SUNReduce // SUNReduce // SUNReduce, {I2, 8}] // Simplify$

${4/3 i c _ 5^( ), 4/3 i c _ 5^( ), 4/3 i c _ 5^( ), 4/3 i c _ 5^( ), 4/3 i c _ 5^( ), 4 i c _ 5^( ), 4/3 i c _ 5^( ), 4/3 i c _ 5^( )}$

${-4/3 π^2 A _ 0 ( (m _ π^(ó ))^2 ) c _ 5^( ), -4/3 π^2 A _ 0 ( (m _ π^(ó ))^2 ) c _ 5^( ), -4/3 π^2 A _ 0 ( (m _ π^(ó ))^2 ) c _ 5^( ), -4/3 π^2 A _ 0 ( (m _ K^(ó ))^2 ) c _ 5^( ), -4/3 π^2 A _ 0 ( (m _ K^(ó ))^2 ) c _ 5^( ), -4 π^2 A _ 0 ( (m _ K^(ó ))^2 ) c _ 5^( ), -4/3 π^2 A _ 0 ( (m _ K^(ó ))^2 ) c _ 5^( ), -4/3 π^2 A _ 0 ( (m _ η^(ó ))^2 ) c _ 5^( )}$

(c _ 5^( ) ((log((m _ η^(ó ))^2/μ^2) - 9 log((m _ π^(ó ))^2/μ^2)) (m _ π^(ó ))^2 - 2 (9 log((m _ K^(ó ))^2/μ^2) + 2 log((m _ η^(ó ))^2/μ^2)) (m _ K^(ó ))^2) (!, _ 0^( ))^2)/(36 π^2 (f _ ϕ^(ó ))^2 (p _ 1^2 - (m _ K^(ó ))^2))

Converted by Mathematica (July 10, 2003)