4-fermion interaction with a point-like propagator

Asked by Krystsina on 2020-10-06

Dear CalcHep experts,

I was going to derive the 4-fermion vertices in Feynrules and to pass the generated model further to CalcHep. According to the most usable model, the contact interaction is described by four-fermions Lagrangian of the general form as follows: f¯ γμ f f¯ γμ f.

Eventually, after trying few more straightforward ways, the Lagrangian in the form Llqlq~(l γμ l¯)(q¯ γμ q)

from SMEFT package seemed to have succeeded. This is two-lepton two-quark interaction defined as "lq1" term in the SMEFT model.

However, the FeynRules producing outputs to CalcHep ended up with warnings:

    For CalcHep, the command WriteCHOutput[Llqlq] runs with the following warnings: "4 fermion vertices are not allowed in CH. They must be implemented via an auxilliary field. You can add this vertex by hand."
   (Similar as for MagGraph, the command WriteUFO[Llqlq] causes a similar warning: "Multi-Fermion operators are not yet fully supported!")

In several manuals written by you and your colleagues, four-fermion vertices are recommended to be split into 3-particle vertices by introducing an auxiliary field. Though those manuals could be outdated.

My question is: Is there a way to implement 4-fermion interaction with point-like propagator in CalcHep? Can it be done with FeynRules and/or LanHep?

Thanks a lot for any your help. Kristina

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Alexander Belyaev
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Best Alexander Belyaev (alexander.belyaev) said :
#1

Dear Krystina,
this can be done straightforwardly with LanHEP.

For example,
recently we have implemented DM contact interactions.

Analogous lagranian in LanHEP language is:

lterm gD5/Lam**2*(anti('~fdm')*gamma^mu*'~fdm')*(anti(q)*gamma^mu * q)
  where q=u; q=d ; q=s; q=c.

The complete model is at HEPMDB
http://hepmdb.soton.ac.uk/index.php?mod=user&act=showmodel&id=186

LanHEP will generate all auxiliaary filed for this contact interactions.

The LanHEP file for full model can be found under the "Download Source File" at HEPMDB

Regards,
Alexander

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Alexander Belyaev (alexander.belyaev) said :
#2

Dear Krystina,
did this solve your problem?
Alexander

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Krystsina (cunato) said :
#3

Dear Alexander,

Thank you very much for your prompt answer. I very appreciate your help.

I believe this will definitely help to resolve this issue.

I have got familiar with LanHEP, and now trying to implement contact and gauge-mediated interactions for excited leptons. There are still few errors but they are caused by my ignorance of the tools (both LanHEP and CalcHEP).

I will let you know within week and mark your answer as a solution.

Thanks.
Best regards,
Krystsina

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Krystsina (cunato) said :
#4

Thanks Alexander Belyaev, that solved my question.