Pion Decay

Get Tracer gamma matrix package:

<< "dirac/Tracer.m"

VectorDimension[4]

Spur[1]

Matrix element for pion decay:

msq = 
      G[ll, pnue]**G[ll, pnue + pe]**(G[ll, U] - G[ll, G5])**
        G[ll, pe + me U]**G[ll, pnue + pe]**(G[ll, U] - G[ll, G5])

Get its trace:

msq1 = Simplify[msq /. ll -> 1]

Evaluate dot products:

list = {pe . pe -> (me^2), pnue . pnue -> 0}

msq2 = msq1 /. list

msq3 = 
      PowerExpand[
        Simplify[
          msq2 /. pe . pnue -> (Sqrt[(pcm^2) + (me^2)]) pcm + (pcm^2) /. 
            pcm -> (((mpi^2) - (me^2))/(2 mpi))]]