Are there full examples not using FeynArts?

[foice]

Hello there! I see a huge list of examples in Gallery, that is very useful. However it seems that all the examples I have opened are based on matrix element calculations from FeynArts.

Is there any full process calculation based on amplitudes written by hand?

Of course the Reference Guide provides the bits and pieces one has to patch together to write an amplitude, but it is not impossible to get stuck in pitfalls. So I thought a full example including the writing of the amplitude using FeynCalc technology might be very useful.

[vsht]

Not really. The reason being that writing amplitudes by hand (at least within FeynCalc)
is not so convenient.

What kind of processes do you actually have in mind? Text-book level stuff or
something related to the real-life research?

The only thing I could imagine where one would enter something by hand
could be scattering amplitudes in theories where everything is cut constructible.
Although even there people most likely use automation for this step.

For anything else FeynArts and Qgraf can actually cater for all your needs.

[foice]

Thanks for the reference, seems to go in the direction I meant!

Just to mention a pitfall I met in my recent attempts:

QuarkPropagator[ke - kV, Explicit -> True, Dimension -> 4]

If the Dimension option is not given you get an error. This is kind of easy to spot with FCGetDimensions[], once you realize the source of the issue (as with most debugging). There might be others I have not met yet of course. Your contact with beginners may contribute to the list.

FeynRules is great, I am aware of it, but it has its own quirks and overhead. In any case, at least in my practice, is not uncommon that going to FeynRules is just not worth for the same reason I said it is not worth involving FeynArts. You are there and you want to see what the amplitude is going to be in a bunch of different cases for which it is just not worth building a whole FA or FR or UFO model for each of them. Having some guidance on how to use the Spinor, the Gamma matrices, the propagators and so on can give people a kick-start. I think we are talking about few basic QED and EW processes that's all.

Of course FeynArts and other diagram generators cannot be replaced for a final computation, but I guess you see that I am talking about the level of complexity around that of textbook calculations, be the target a textbook calculation or something BSM as simple as that. Plus ... even a single diagram process can benefit of this!

[vsht]

Hmm, perhaps I'm somehow missing your point, but it seems to me that the aspects
you mention belong to the basic familiarity with FeynCalc.

It's true that QuarkPropagator and alike are d-dim by default. But normally one would immediately
notice that already from the typesetting (no bars on top of vertices and Dirac matrices).

Then you write that

Having some guidance on how to use the Spinor, the Gamma matrices, the propagators and so on can give people a kick-start.

But how is it related to the way the amplitude was obtained? I mean, if one is not comfortable
manipulating those objects, it won't really help to have the amplitude from FeynArts.

To me it seems that if you go through the tutorial (FeynCalc/Tutorials/Intro in the Documentation center)
and the available examples, you should already be familiar with most of the stuff.

Though the usage of QuarkPropagator, QuarkGluonVertex etc. is not covered there, I'm not sure that
those functions are really the most convenient way to enter amplitudes by hand. As I wrote, I don't usually
do that myself, so perhaps I'm lacking a good insight into bootstrapping such calculations.

[foice]

Exactly, basic familiarity about FeynCalc is largely demonstrated on what happens once the amplitude is somehow given to you from FeynArts. Instead I might decide to write it on my own or process it in ways that are following the template you also present in the documentation.

My limited experience is to play with things like

M = Contract[
  SpinorVBar[Momentum[kE], 0].GA[\[Mu]].QuarkPropagator[ke - kV, 
    Explicit -> True, Dimension -> 4].GA[\[Nu]].GA[7].SpinorU[
    Momentum[ke], 0]]
Mstar = ComplexConjugate[
   M] //. {LorentzIndex[\[Mu]] -> LorentzIndex[mu], 
   LorentzIndex[\[Nu]] -> LorentzIndex[nu]}
FermionSpinSum[
  Mstar M* PolarizationSum[\[Mu], mu, kW]*
   PolarizationSum[\[Nu], nu, kV]];
DiracSimplify[%]

which are coming from earlier versions Help and stratification on it. Since now there is a very comprehensive list of processes, all falling under the same template, what I was suggesting is to add a few more examples that go along another template, e.g. they amplitude can be computed from its FeynCalc building blocks. There are probably other interesting variations that can be thought of. I think having fully fleshed examples will help beginners and students who need or want to follow a different path than the current template.

[vsht]

Well, I suppose there are all kind of examples one could add, but as you can see we are quite short
on manpower and there are still a lot of things to add/improve that are more urgent.

You are of course free to post your examples here, then I could link to this thread when similar requests arise.

[vsht]

There are actually some interesting nuclear physics examples that I would like to
work out when I find time (#84). Those would probably fit into your request for codes not
using FeynArts.

As far as the tree-level QED is concerned, the lecture notes of Jorge Romao are
good enough and I see no point to duplicate that.