•Calculation and reduction of the amplitude

Calculation of the amplitude:

amplFC = CreateFCAmp[mesontreeinsert] /. {i1 -> 1, i3 -> 1} // DoSumOver // SUNReduce // Simplify

{-(5 i !, _ 0^( ))/(48 π^4 f _ π^(ó  ) (q _ 1^2 - (m _ π^(ó  ))^2))}

The loop integral is expressed in terms of a Passarino-Veltman symbol:

ampreduced = OneLoop[q1, #] & /@ amplFC

{(5 A _ 0 ( (m _ π^(ó  ))^2 ) !, _ 0^( ))/(48 π^2 f _ π^(ó  ))}

The divergence is singled out:

ampinfinities = VeltmanExpand[ampreduced[[1]], ExplicitLeutwylerJ0 -> True] // Simplify

-(5 (32 π^2 λ + log((m _ π^(ó  ))^2/μ^2)) (m _ π^(ó  ))^2 !, _ 0^( ))/(48 π^2 f _ π^(ó  ))

Converted by Mathematica  (July 10, 2003)