Name: Vladyslav Shtabovenko (email_not_shown)
Date: 04/12/16-12:12:27 PM Z


Am 12.04.2016 um 10:52 schrieb Xing-Bo Yuan:
> Hi, Vladyslav
> Thank you very much for the update.
> I have used the development version. Everything quite works well.
> However, I still have two questions:
> 1. After running your codes, I find most of the parameters in “SM_Unitary_Gauge” are modified as FCGV[EL], FCGV[SW], …. Is it to avoid conflicts with other definitions?

Yes, FCGV["parameter"] is a sort of placeholder for a FeynArts model
parameter that should prevent clashes with FeynCalc functions. For
example, SM.mod the top quark mass is defined as MT, which turns to be a
shortcut for the metric tensor in FeynCalc.

The idea is that the user can rename FCGV objects to whatever he/she
wants after the amplitude is generated. Furthermore, with the option
SMP->True one can get them renamed into SMP objects, which have some
typesetting attached to them:

This is pure cosmetics (i.e. SMP's currently have no properties attached
to them, except for the way how they are displayed), but it makes the
TraditionalForm output looks nicer and it avoid introducing dozens of
new objects (like me, mmu, mt etc.) for masses, coupling constants,
mixing angles etc. In future I might add something like SMPSimplify to
have things like alpha_s = e^2/(4Pi)
cos_W^2+sin_W^2 = 1 transformed, but at the moment there seems to be no
need for that.

Applied to your example:

FCFAConvert[CreateFeynAmp[inserttops3], ChangeDimension -> 4,
 LorentzIndexNames -> {lor}, IncomingMomenta -> {p1},
 OutgoingMomenta -> {k, k1, k2}, DropSumOver -> True, List -> False,
 SMP -> True]

> 2. I find the function LorentzIndexNames in FCFAConvert[] doesn’t work sometimes, in both 9.0.1 and development version, and for both default model and added model. For example, after running the following codes
> $LoadFeynArts = True;
> << FeynCalc`;
> $FAVerbose = 0;
> tops3 = CreateTopologies[0, 1 -> 3];
> inserttops3 =
> InsertFields[
> tops3, {F[2, {3}]} -> {F[1, {3}], -F[3, {1, o}], F[4, {1, o}]},
> InsertionLevel -> {Particles}, LastSelections -> {V[3]}];
> FCFAConvert[CreateFeynAmp[inserttops3], ChangeDimension -> 4,
> LorentzIndexNames -> {lor}, IncomingMomenta -> {p1},
> OutgoingMomenta -> {k, k1, k2}, DropSumOver -> True,
> List -> False] // Contract
> I find the option LorentzIndexNames doesn’t work if I set OutgoingMomenta -> {k, k1, k2} or {k0, k1, k2}, but not {k3,k1,k2}

The problem with your code is that there are in fact two Lorentz indices
in the amplitude, so you should supply a list with two elements to
LorentzIndex names to get the renaming properly

exp=FCFAConvert[CreateFeynAmp[inserttops3], ChangeDimension -> 4,
 LorentzIndexNames -> {\[Nu],\[Mu]}, IncomingMomenta -> {p1},
 OutgoingMomenta -> {k, k1, k2}, DropSumOver -> True, List -> False,
 SMP -> True]


LorentzIndexNames is actually another cosmetics option. FCFAConvert
works without, but then the Lorentz indices are labeled with Lor1, Lor2,
Lor3 etc. Since people like to have greek indices (as in papers and
books), I added LorentzIndexNames so that one can rename "Lor" indices,
to whatever one wants.

Hope this helps.


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