Name: Vladyslav Shtabovenko Date: 12/17/16-07:28:51 PM Z

Hi,

in FeynCalc 9.2 I introduced strict checking on the dimensions of the
input in TID. This is done to avoid issues like this one:

<1115.html>

where people don’t pay attention to their input expressions and then
complain about seemingly inconsistent results. So unless people have
activated the BMHV regularization scheme, TID will complain about
expressions that contain both 4-dim and D-dim objects, as such terms are
not allowed in the naive/conventional dimensional regularization, where
*everything* is taken to be D-dimensional and the limit D->4 is taken
only at the very end of the calculation.

In your case everything is almost correct, up to the spinors.
SpinorUBar, SpinorU etc. always depend on 4-dim momenta, so putting
something like Momentum[p1, D] there doesn’t really make sense. I guess,
I should better block this kind of input, so thanks for this example.

Anyhow, in FC 9.2 there are now also FCE input expressions for spinors
that depend on D-dim momenta, namely SpinorUBarD, SpinorUD etc., c.f.

<https://github.com/FeynCalc/feyncalc/blob/master/FeynCalc/Changelog.md#version-920-november-2016>

So, the correct expression reads:

TID[(SpinorUBarD[p3, mN].GAD[\[Mu]].SpinorUD[p1, mN]) (SpinorUBarD[p4,
       mN].GAD[\[Nu]].GAD[\[Omega]].GAD[\[Rho]].SpinorUD[p2,
      mN]) ((2 FVD[l, \[Mu]] + FVD[q, \[Mu]]) FVD[
      l, \[Nu]] (FVD[p4, \[Omega]] -
       FVD[l, \[Omega]]) (FVD[l, \[Rho]] +
       FVD[q, \[Rho]])) FeynAmpDenominator[
    PropagatorDenominator[Momentum[l, D], m\[Pi]],
    PropagatorDenominator[Momentum[l + q, D], m\[Pi]],
    PropagatorDenominator[Momentum[p4 - l, D], mN]], l,
  UsePaVeBasis -> True, PaVeAutoReduce -> False]

BTW, there is no need to use FeynAmpDenominator when writing down input
integrals, FAD is fully sufficient and makes things shorter and faster
to write:

TID[(SpinorUBarD[p3, mN].GAD[\[Mu]].SpinorUD[p1, mN]) (SpinorUBarD[p4,
       mN].GAD[\[Nu]].GAD[\[Omega]].GAD[\[Rho]].SpinorUD[p2,
      mN]) ((2 FVD[l, \[Mu]] + FVD[q, \[Mu]]) FVD[
      l, \[Nu]] (FVD[p4, \[Omega]] -
       FVD[l, \[Omega]]) (FVD[l, \[Rho]] + FVD[q, \[Rho]])) FAD[{l,
     m\[Pi]}, {l + q, m\[Pi]}, {-l + p4, mN}], l, UsePaVeBasis -> True,
   PaVeAutoReduce -> False]

Cheers,
Vladyslav

Am 17.12.2016 um 11:19 schrieb Xiu-Lei Ren:
> Dear Vladyslav,
>
> Recently, I use the TID to calcualte a triangle diagram,
> where the dirac spinors are explicitly involved.
>
> TID[ (SpinorUBar[Momentum[p3, D], mN].GAD[\[Mu]].SpinorU[
> Momentum[p1, D], mN]) (SpinorUBar[Momentum[p4, D],
> mN].GAD[\[Nu]].GAD[\[Omega]].GAD[\[Rho]].SpinorU[
*> Momentum[p2, D], mN]) ((2 FVD[l, \[Mu]]