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 Though those manuals could be outdated.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 :

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

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


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Alexander Belyaev (alexander.belyaev) said :

Dear Krystina,
did this solve your problem?

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Krystsina (cunato) said :

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.

Best regards,

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Krystsina (cunato) said :

Thanks Alexander Belyaev, that solved my question.