Name: Vladyslav Shtabovenko Date: 03/21/16-12:03:55 PM Z

• Next message: Xing-Bo Yuan: “bug in patched FeynArts of FeynRuls 9.0.1?”
• Previous message: Mikkel Bjoern: “Re: Traces on Mac vs Windows?”
• In reply to: Mikkel Bjoern: “Re: Traces on Mac vs Windows?”

---

Hi,

sorry for the very late reply.

I don’t really think this is something
related to Mac vs Windows, provided that you and your colleague are
using exactly the same FeynCalc versions and the same codes.

In general, FORM does a much better job avoiding spurious terms that
vanish by the Schouten identity. So you could use FeynCalcFormLink for
that. It is very easy to install

Import[“https://raw.githubusercontent.com/FormLink/formlink/master/\
install.m”]
InstallFormLink[]

Import[“https://raw.githubusercontent.com/FormLink/feyncalcformlink/\
master/install.m”]
InstallFeynCalcFormLink[]

and then on a fresh kernel you can do

«FeynCalc`
«FeynCalcFormLink`

$LeviCivitaSign = -1;
kinematicsreduce = {SP[SubPlus[k]] -> 0, SP[SubMinus[k]] -> 0,
   SP[k12] -> 2 SP[p1, p2], SP[k34] -> 2 SP[p3, p4],
   SP[k12, a_] -> SP[p1, a] + SP[p2, a],
   SP[k34, a_] -> SP[p3, a] + SP[p4, a], SP[p1] -> 0, SP[p2] -> 0,
   SP[p3] -> 0, SP[p4] -> 0, SP[SubPlus[k]] -> 0,
   SP[SubMinus[k]] -> 0};

\[Nu]\[Nu]SMpart1 =
  1/2 DiracTrace[GS[p1].GA[\[Mu]].GS[p2].GA[\[Mu]p]]

•    1/2 DiracTrace[GS[p1].GA[\[Mu]].GS[p2].GA[\[Mu]p].GA[5]];

\[Nu]\[Nu]SMpart2 =
  1/2 DiracTrace[GS[p3].GA[\[Alpha]].GS[p4].GA[\[Alpha]p]]

•    1/2 DiracTrace[GS[p3].GA[\[Alpha]].GS[p4].GA[\[Alpha]p].GA[5]];

\[Nu]\[Nu]SMpart3Bsquared =
  1/8 (DiracTrace[
      GS[SubPlus[k]].GA[\[Mu]].(GS[k12]

• GS[k34]).GA[\[Alpha]].GS[
          SubMinus[k]].GA[\[Alpha]p].(GS[k12]
• GS[k34]).GA[\[Mu]p]] -
       DiracTrace[
        GS[SubPlus[k]].GA[\[Mu]].(GS[k12]
• GS[k34]).GA[\[Alpha]].GS[
          SubMinus[k]].GA[\[Alpha]p].(GS[k12]
• GS[k34]).GA[\[Mu]p].GA[
          5]]);

res = FeynCalcFormLink[\[Nu]\[Nu]SMpart1.\[Nu]\[Nu]SMpart2.\[Nu]\[Nu]\
SMpart3Bsquared]

(res /. kinematicsreduce) // Simplify // FCE

which gives you

64 SP[p1, SubPlus[
  k]] ((SP[k34, p1] + SP[k34, p2]) SP[p2, p3] -
   SP[p1, p2] SP[p2,
     p3] + (SP[p1, p2] + SP[p2, p2]) (SP[p1, p3] +
      SP[p2, p3]) - (SP[p1, p3] + SP[p2, p3]) (SP[p2, p3] +
      SP[p2, p4]) -
   SP[p2, p3] SP[p3,
     p4] - (SP[p1, p2] + SP[p2, p2]) (SP[p3, p3] +
      SP[p3, p4]) + (SP[p2, p3] + SP[p2, p4]) (SP[p3, p3] +
      SP[p3, p4])) SP[p4, SubMinus[k]]

Cheers,
Vladyslav

Am 23.02.2016 um 15:55 schrieb Mikkel Bjoern:
> I am trying to evaluate the following lines
>
> kinematicsreduce = {SP[SubPlus[k]] -> 0, SP[SubMinus[k]] -> 0,
> SP[k12] -> 2 SP[p1, p2], SP[k34] -> 2 SP[p3, p4],
> SP[k12, a_] -> SP[p1, a] + SP[p2, a],
> SP[k34, a_] -> SP[p3, a] + SP[p4, a], SP[p1] -> 0, SP[p2] -> 0,
> SP[p3] -> 0, SP[p4] -> 0, SP[SubPlus[k]] -> 0,
> SP[SubMinus[k]] -> 0};
>
> \[Nu]\[Nu]SMpart1 =
> 1/2 Tr[GS[p1].GA[\[Mu]].GS[p2].GA[\[Mu]p]] -
> 1/2 Tr[GS[p1].GA[\[Mu]].GS[p2].GA[\[Mu]p].GA[5]];
>
> \[Nu]\[Nu]SMpart2 =
> 1/2 Tr[GS[p3].GA[\[Alpha]].GS[p4].GA[\[Alpha]p]] -
> 1/2 Tr[GS[p3].GA[\[Alpha]].GS[p4].GA[\[Alpha]p].GA[5]];
>
> \[Nu]\[Nu]SMpart3Bsquared =
> 1/8 (Tr[GS[SubPlus[
> k]].GA[\[Mu]].(GS[k12] - GS[k34]).GA[\[Alpha]].GS[SubMinus[
> k]].GA[\[Alpha]p].(GS[k12] - GS[k34]).GA[\[Mu]p]] -
*> Tr[GS[SubPlus[k]].GA[\[Mu]].(GS[k12]

• GS[k34]).GA[\[Alpha]].GS[*
  *> SubMinus[k]].GA[\[Alpha]p].(GS[k12]
• GS[k34]).GA[\[Mu]p].GA[*
  > 5]]);
  >
  > \[Nu]\[Nu]result2 =
  > Simplify[FCE[
  > Contract[\[Nu]\[Nu]SMpart1.\[Nu]\[Nu]SMpart2.\[Nu]\[Nu]\
  > SMpart3Bsquared ]] //. kinematicsreduce]
  >
  >
  > I have tried applying // Schouten but the Epsilons remain.
  >
  > On my colleagues Mac the last line is rather pretty, only involving scalar products, on my PC there are a lot of Epsilon terms as well.
  >
  > Best regards,
  > Mikkel
  >

---

• Next message: Xing-Bo Yuan: “bug in patched FeynArts of FeynRuls 9.0.1?”
• Previous message: Mikkel Bjoern: “Re: Traces on Mac vs Windows?”
• In reply to: Mikkel Bjoern: “Re: Traces on Mac vs Windows?”

---