Implementing 4-fermion operators in LanHEP

Asked by Basabendu on 2020-12-16

Dear CalcHEP experts,

I am trying to implement 4-fermion vertices involving singlet Majorana/Dirac BSM field with SM fermion fields in LanHEP to use the model files further in CalcHEP and in MicrOmegas. Now, I am experiencing a couple of things for which I need some help to understand them:

(a) For implementing an operator with, say, vector current e.g., c_q*\bar{X}\gamma^mu X\bar{q}\gamma^mu q I am not mentioning the 'AuxPrt' separately, rather writing such an interaction directly in LanHEP is generating 'Aux' fields automatically. The model is also showing 'OK' in CalcHEP. However, is that the correct way to do it? I have found similar model implementation in HEPMDB where the authors have defined 'AuxPrt' separately and then written down the operators as lterms (

(b) In the expression for \sigma.v I am always getting a factor of 2 less from the model file when I'm comparing the results with analytical expressions. I am unable to find out the error. Does the LanHEP use some different normalization to relate the operator scale with the mass of the auxiliary field? maybe I am missing something here.

(c) For interactions which are not Hermitian conjugate, omitting the 'AddHermConj' command in LanHEP is not showing any error. Again, is that due to a wrong auxiliary field implementation?

I can send my model files if you wish to see them. Thank you for the help.

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

Dear Basabendu,

the model implemented in
via aux particles
and the way you have suggested are equivalent, since LanHEP will generate automatically
aux fields for the contact term you have mentioned -- c_q*\bar{X}\gamma^mu X\bar{q}\gamma^mu q
You can check this -- the analytical and numerical result for both approached should be the same.

b) When you calculate things by hand you need to take into account the fact that you have indeticl (Majorama particles), so you need to symmetrise result
When you write "I am always getting a factor of 2 less from the model file when I'm comparing the results with analytical expressions"
it is not clear what do you mean under "analytical expressions".
Are those "analytical expressions" from you or from CalcHEP?
What do you mean "factor of 2 less from the model file"?
Do you mean matrix element or Feynman rules?
For feynman rules you must have factor 1/2 for mass term for majorana particles for example.

c) This is actually a special feature of CalcHEP -- the implementation of Aux particles sometimes involve non-hermitian constructions and CalcHEP does not give an error in such a cases by design

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Basabendu (bb1988-1) said :

Thanks Alexander Belyaev, that solved my question.