MadGraph5_aMC@NLO

using s,t,u variables in couplings

Asked by Guillaume Drieu

        Hello,
   Is it possible to write effective couplings that depend on the kinematical variables (s,t,u)? I am trying to include some loop from factor as effective couplings.
As an exemple the ggh effective vertex of the standard model depends on the momentum of h, and in the case of process like gg -> h -> hh, the internal h is not on-shell.

Thanks,
Guillaume

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Olivier Mattelaer
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Best Olivier Mattelaer (olivier-mattelaer) said : 		#1

Looks like the answer of Antoine Laureys is not display on the web page.
So let me add it. Sorry for those who will receive it twice:

Dear Guillaume,

We are currently working on MadGraph to have the possibility to include
form factors, but it isn't ready yet.
However, if you are interested in gg>hh, we have a MadGraphv4 code
available which includes the s-channel contribution gg>h>hh and also the
contribution from the box loops gg>hh with the exact dependence on the top
quark mass.

For this process, you should use MadGraph v4 which you can download here :
http://madgraph.hep.uiuc.edu/index.html

Then you can download the tarball
http://cp3.irmp.ucl.ac.be/~alaureys/gg_hh/heft2.tar.gz

Once untarred, you need to put the "heft2" directory in the "model"
directory of MadGraphv4 you downloaded.
In this tarball you will also find the run_card and proc_card to generate
the full process. Then you can use MGv4 as usual.

If you have any question or problem, I will be glad to help you.

Cheers,

Antoine

A few more comments :

1) in the proc_card you will see there are 2 processes with and without
particle b0. Don't care about it and leave it as it is, it is only an
artefact and it doesn't correspond to any physical particle.

2) only the top loop is implemented, not the bottom.

3) in the run_card, you need to leave the parameter "fixed_couplings" to
FALSE such that the formfactors are evaluated at each phase space point.

4) It is not possible to ask in the proc_card to decay the higgs. However
you can use the DecayPackage on the MadGraph website to decay the Higgs
aftewards.

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Guillaume Drieu (drieu) said : 		#2

        Thank you very much indeed. This does work pretty well I must say. Do you think this model can be translated to MG5 with a minimal amount of work (given that I am completely ignorant of MG internal architecture, however)? But I think I can do already many thing with the present version.
Thanks a lot, and I hope to hear soon about those form factor in MG!

Guillaume

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Antoine Laureys (antoine-laureys) said : 		#3

I'm note sure what you mean by this, but this would certainly take some time, but we can tell you when formfactors will be implemented in MG5.

On the other hand what you can do is (in mg5)

1. copy heft model (in models/heft/) to 'twohiggsprod' for exemple
2. modify the lorentz.py, vertices.py and couplings.py if needed to add the vertices you need for gg>hh and you choose a normalization such that you just need to multiply the matrix element with the formfactor squared.
3. generate your process: import model 'twohiggsprod', generate g g > h h, output gg_hh
4. go to gg_hh/SubProcesses/P0_gg_hh/ and open to matrix.f
5. there the subroutine SMATRIX returns the matrix element squared. So you can just link your formfactors there and multiply "ANS" with your result, formfactor squared for the s-channel + formfactor squared for the box.

note: if you have more than one diagram, say 2 ( A=A1+A2), then madgraph integrates first |A1|^2/(|A1|^2+|A2|^2)*(|A1+A2|^2), then |A2|^2/(|A1|^2+|A2|^2)*(|A1+A2|^2) and sums both contribution. Which is the same as integrating |A1+A2|^2. What SMATRIX actually returns is one of these ratios and not just |A1+A2|^2. In the end this doesn't matter if you just multiply ANS with your formfactors, but it can be usefull to know.

If you want to try this, maybe it is good to first try with gg -> h. the vertex already exists. you only need to modify the parameter GH which is an expansion of the formfactor when mtop>>mhiggs. so it has the form alpha_s/3/pi/vev*(1+corrections). set the corrections to zero in models/twohiggsprod/parameters.py before generating your process.

Cheers,

Antoine

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Guillaume Drieu (drieu) said : 		#4

        Thank you very much Antoine for the full how-to. I will certainly try those modifications myself, since it seems not as complicated as I thought.
       I appreciate very much the attention, so thank you again!

Cheers,
Guillaume