Name: Vladyslav Shtabovenko 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) SubscriptB, 0-(M^2-mi^2+p^2)
SubscriptB, 0))/(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!