Name: Vladyslav Shtabovenko Date: 11/04/15-07:18:54 PM Z
NDR just tells you that in D-dimensions g^5 anticommutes with all
other
Dirac matrices. However, this statement is not sufficient to define
traces with an odd number of g^5 matrices unambiguously. This is why
you
need an additional prescription that tells you how to compute such
traces with anticommuting g^5.
If you don’t specify such a prescription, FeynCalc refuses to compute
the trace in NDR, as it would give a non-sensical result.
However, FeynCalc works not only with NDR, but also the the “non-naive
scheme”.
So, you can either use the t’Hooft-Veltman-Maison-Breitenlohner
scheme,
where g^5 is not anticommuting,
<<http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1103900439>>
$Larin = False;
$West = True;
$BreitMaison = True;
DiracTrace[
DiracGamma[LorentzIndex[Lor1, D],
D].DiracGamma[Momentum[Lor2, D],
D].DiracGamma[LorentzIndex[Lor3, D],
D].DiracGamma[
Momentum[Lor4, D],
D].DiracGamma[LorentzIndex[Lor5, D],
D].DiracGamma[Momentum[Lor6, D],
D].DiracGamma[5],
DiracTraceEvaluate -> True]
or if you want to stick with the anitcommuting g^5, you can use the
Larin-Gorishny-Akyeampong-Delburgo prescription
(<<http://arxiv.org/pdf/hep-ph/9302240.pdf>>)
$Larin = True;
$West = False;
$BreitMaison = False;
DiracTrace[
DiracGamma[LorentzIndex[Lor1, D],
D].DiracGamma[Momentum[Lor2, D],
D].DiracGamma[LorentzIndex[Lor3, D],
D].DiracGamma[
Momentum[Lor4, D],
D].DiracGamma[LorentzIndex[Lor5, D],
D].DiracGamma[Momentum[Lor6, D],
D].DiracGamma[5],
DiracTraceEvaluate -> True]
Cheers,
Vladyslav
Am 04.11.2015 um 16:52 schrieb Sun Qingfeng:
> I noticed that in dimensional regulation, the NDR scheme is adopted
in FeynCalc 9.0. When I deal with the DiracTrace below:
> DiracTrace[
> DiracGamma[LorentzIndex[Lor1, D],
D].DiracGamma[Momentum[Lor2, D],
> D].DiracGamma[LorentzIndex[Lor3, D],
D].DiracGamma[
> Momentum[Lor4, D],
D].DiracGamma[LorentzIndex[Lor5, D],
> D].DiracGamma[Momentum[Lor6, D],
D].DiracGamma[5]]
> There will be warnings, So how can I deal with the DiracTrace above
in dimensional regulation with FC9.0?
>
> Thanks alot!
>
> Sun Qingfeng
>