Name: Vladyslav Shtabovenko (email_not_shown)
Date: 08/13/15-07:36:31 PM Z


Dear Fabrizio,

both issues do not appear anymore in the most recent FeynCalc version

INT[X_] := OneLoop[k, X, Dimension -> D, OneLoopSimplify -> False]
AMPLITUDE = (GSD[k] + GSD[p]) FAD[{k + p, mi}] FAD[{k, M}]
INT[AMPLITUDE] // PaVeReduce // Simplify //FCE

-> (I \[Pi]^2 GS[
  p] ((M^2 - mi^2) B0[0, M^2, mi^2] +
   B0[SP[p, p], M^2, mi^2] (-M^2 + mi^2 + SP[p, p])))/(2 SP[p, p])

INT[X_] :=
  OneLoop[k, X, Dimension -> D, OneLoopSimplify -> False,
   ReduceGamma -> True];
PL = (1 - GA[5])/2;
\[CapitalDelta]g[k_, p_, \[Mu]_, \[Nu]_,
  m_, \[Xi]_] := -I Contract[(MTD[\[Mu], \[Nu]] - (1 - \[Xi]) (FVD[
           k, \[Mu]] - FVD[p, \[Mu]]).(FVD[k, \[Nu]] -
          FVD[p, \[Nu]]).FAD[{k - p, Sqrt[\[Xi]] m}]).FAD[{k - p,
      m}]]
AMPLITUDE =
 Contract[GAD[\[Alpha]].PL.(GSD[k] + GSD[p] +
     mi).GAD[\[Beta]].PL.FAD[{k + p, mi}].\[CapitalDelta]g[k,
    0, \[Alpha], \[Beta], M, 1]]
INT[AMPLITUDE] // PaVeReduce // Simplify // FCE

-> -(1/(2 SP[p,
   p]))\[Pi]^2 (-GS[p].GA[5] + GS[p]) ((M^2 - mi^2) B0[0, M^2, mi^2] -
     SP[p, p] + B0[SP[p, p], M^2, mi^2] (-M^2 + mi^2 + SP[p, p]))

Cheers,
Vladyslav

> Even simpler:
>
> INT[X_] := OneLoop[k, X, Dimension -> D, OneLoopSimplify -> False]
>
> AMPLITUDE = (GSD[k] + GSD[p]) FAD[{k + p, mi}] FAD[{k, M}]
>
> INT[AMPLITUDE] // PaVeReduce // Simplify
>
> gives a similar result, with kslash+pslash....
>
> (\[Pi] (\[Gamma]\[CenterDot]k+\[Gamma]\[CenterDot]p) ((M^2-mi^2) Subscript[B, 0](0,M^2,mi^2)-(M^2-mi^2+p^2) Subscript[B, 0](p^2,M^2,mi^2)))/(2 p^2)
>
> Again, kslash does not appear if using Dimension->4. What is the real difference there? Finite parts in dimensional regularization? Or am I missing something?
>
> Thanks, as usual, for your kind replies!



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