# Transposed Spinors in Lagrangian

Dear colleagues,

I am greatly interested to use CalcHEP to calculate cross sections in the Nucleon Nucleon scattering. Is it possible to use CalcHEP, if the Lagrangian contains transposed spinors (\psi^T)? For example there are the following products in the terms of the Lagrangian:
$\psi^T C \gamma^\mu \psi$ or $\psi^T C \gamma^5 \psi$ and the corresponding hermitian conjugates (C is the matrix of charge conjugation).

I would be grateful if you could answer my question asap. If transposed spinors are possible with CalcHEP, it would be appreciated if you could give me instructions how to proceed.

Best wishes
Werner Deinet

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 Revision history for this message Alexander Pukhov (pukhov) said on 2014-02-05: #1

See details on manual p 106 - 109. In 2 word, just remove T and C. See formula 9.
But it seems vector current with 2 identical fermions is zero.
Please take into account that Lagrangian table in CalcHEP presents Feynman rules.
So, in case of identical fermions factor 2 and symmetry properties are expected. Use formula 10 for For example, vertor current with 2 identical fermions is zero. See formula 10.

 Revision history for this message Werner Deinet (wd-y) said on 2014-04-09: #2

Dear Mr. Pukhov,

thank you for yor answer from February 5, 2014 to my question #243366.
It helped us to make cross section-calculations in the s-channel with a
propagator denominator of a particle at the tree level. The results appear
reasonable to us.

For a better understanding of your sentence "In 2 words, just remove T and
C", I will describe how we did proceed:
We replaced $\psi^T C$ by $\bar{\psi}_c$ and $C\bar{psi}^T$ by $\psi_c$.
That means, that we have introduced the spinors of the antiparticles and
got results.

Following your sentence we would have to replace:
$\psi^T C$ by $\psi$ and $C\bar{psi}$ by $\psi$.
In this case we would have only the spinors of the particles. (I have seen
in the literature that people sometimes omit the tranposition sign with
spinors.)
We were not successful with this procedure using calcHEP. Did we overlook
anything or is only the first interpretation correct?

We have also started with tests using the Breit-Wigner propagator. First
we have chosen the decay width Gamma=constant, but we did not get an
agreement with calculations made with the trace technology.
Then we tried to calculate the width Gamma as a function of the momentum
in the cms. We did not get a result.

I would be greatful, if you could give us a suggestion on how to proceed.

With best wishes
Werner Deinet

> Your question #243366 on CalcHEP changed:
>
>
> Alexander Pukhov proposed the following answer:
>
> See details on manual p 106 - 109. In 2 word, just remove T and C. See
> formula 9.
> But it seems vector current with 2 identical fermions is zero.
> Please take into account that Lagrangian table in CalcHEP presents
> Feynman rules.
> So, in case of identical fermions factor 2 and symmetry properties are
> expected. Use formula 10 for For example, vertor current with 2
> identical fermions is zero. See formula 10.
>
> --
> know that it is solved:
>
> If you still need help, you can reply to this email or go to the
> following page to enter your feedback:
>
>
>

 Revision history for this message Launchpad Janitor (janitor) said on 2014-04-25: #3

This question was expired because it remained in the 'Open' state without activity for the last 15 days.

 Revision history for this message Alexander Pukhov (pukhov) said on 2014-04-25: #4

$\psi^T C \gamma^\mu \psi$ ==0

Indeed It reads as $\psi^T \gamma_0 C \gamma^\mu \psi$
In Majorana basis C=1, \gamma_0^T=-\gamma_0 \gamma_i^T=\gamma_i
So, you have 2 identical spinors and symmetrix matrix. It is zero. No way to present it in CalcHEP.

$\psi^T C \gamma^5 \psi$ - it should work. Such vertex is presented in MSSM and connect odd Higgs and 2 neutralino.

But dont forger to add factor 2 in CalcHEP Feynman rules because you have 2 identical fermions.

Best
Alexander Pukhov

 Revision history for this message Werner Deinet (wd-y) said on 2014-05-27: #5

Dear Mr. Pukhov,

thank you for your mail of April 26. I still have a problem with the calculation of the width GAMMA of a resonance by CalcHEP. If I understand chapter 5.5 (Breit-Wigner propagator) of the user's manual correct, GAMMA is calculated by CalcHEP for three different regimes, where the user has the possibility to choose a parameter R, to influence the result.

My question is:
Is it possible to work with a user defined, momentum dependent function for GAMMA in CalcHEP?

I would be grateful for an answer asap.
With best wishes
Werner Deinet

 Revision history for this message Alexander Pukhov (pukhov) said on 2014-05-28: #6

One can rewrite prepDen function from
c_source/num/sqme_aux.c
It seems in some versions we had a special gate for this job. Now I don't see it. The function was rewritten recently for more precise treatment of interference of closed resonances. I a little bit forget it. May be Alexander Belyaev remember.

I can restore this option or/and help you to realise your functions for running width, but today I have not time for this job busy.

Sasha

 Revision history for this message Alexander Belyaev (alexander.belyaev) said on 2014-05-28: #7

Dear Werner,
sorry for entering late into this discussion.

1) about Lagrangian -- yes it is possible to introduce Lagrangian at the Nucleon level --
just give us example of the Lagrangian you would like to implement and we will help you.
From discussion above I see only current, not the Lagrangian

2) About using momentum dependent width in the propagator --
the answer is yes -- user can introduce this dependence in sqme_aux.c
file which you can copy from c_source/num/sqme_aux.c as Sasha Pukhov said,
and then modify it and link via model libraries -- the last item in the model description

Sasha Belyaev