Wrong result with an effective operator

I think, the answer produced by CalcHEP is correct.

We use   public available  package for symbolic calculation Reduce to
check symbolic results obtained by CalcHEP.

Before "Symbolic calculations" you have an option to produce "REDUCE
program". It writes  a code  for calculation of diagrams written in
Reduce format.

In your case name on created file with Reduce code is
"results/p1_1.red".   You can open this file to check code generated by
CalcHEP for Reduce.

Then you can make symbolic calculation and  write down result in Reduce
format  "results/symb1.red".  We aslo have routine utile/check.red
which   calculates  diagram  using Reduce and compare result with  the
answer stored in symb1.red.  To activate it,  you have to launch Reduce
from  'work' directory and type Reduce command

in"../utile/check.red";

You will see result:  "1_1 OK"  which means successful comparison. Use
"bye;" to leave Reduce.

Alternative way is to load  in  Reduce p1_1.red directly

in"results/p1_1.red";

and check variable

numerator_;

   It gives you symbolic expression for numerator of diagram. It should
depend of scalar product p1.p2. To resolve this dependence type

       let p1.p2=MZ^2/2;

       numerator_;

It gives your final result which equivalent to one obtained in CalcHEP.

If you do not agree, tell me, please, what is wrong in "p1_1.red".

You can find  Reduce sources here:
https://sourceforge.net/projects/reduce-algebra/

Take into account that after installation executable "reduce" is stored
in /usr/lib/reduce/cslbuild/csl/

Best

     Alexander Pukhov

On 09.07.2019 1:27, Fabiola Elena Fortuna Montecillo wrote:
> New question #681866 on CalcHEP:
> https://answers.launchpad.net/calchep/+question/681866
>
> Hi!
> I've been struggling with the result of the Z decay into two dark fermions. The operator I'm using is (in LanHep notation):
>
> PLeff*B^mu^nu*anti(df)*(gamma^mu*deriv^nu-gamma^nu*deriv^mu)*(1-g5)/2*df where
> B^mu^nu=deriv^mu*B1^nu-deriv^nu*B1^mu.
>
> where PLeff is just a constant coupling defined as parameter, df is the dark fermion which I added as spinor, and B1 is the usual mixing of the Z boson and the photon.
>
> Using LanHep I generated the files for CalcHep and did the calculation of the decay (Z -> Df df), then I compared it with the result I had previously computed and they didn't match, I obtained an amplitude proportional to
>
> (m_Z^4 - 4*m_df^4)
>
> while CalcHep gives one proportional to
>
> (m_Z^4 + 4*m_df^4 - 2*m_Z^2*m_df^2).
>
> Besides, I checked the Feynman rule in the lgrng.mdl file, and I believe it's correct:
>
> Df |df |A | |-2*CW/2 |PLeff*m3.p2*G(p3)*(1-G5)-PLeff*p2.p3*G(m3)*(1-G5)
>
> and finally I performed the calculation both in the Feynman and in the unitary gauges.
>
> Basically I don't know where the problem comes from and I ran out of ideas.
>
> Than you.
>
>

Hi, doctor Pukhov

Thank you very much for your previous answer.

I did what you suggested and checked the reduce code generated "p1_1.red", as well as the final result in "symb1".

I think I know now what the problem is, if I'm understanding the correctly, the process followed by REDUCE is to calculate the self-energy of the Z boson and extract the result to Z -> \ba{f} f from it, and I think that process is exactly the problem, and it is due to the projector that appears in the operator.

I also verified that if I remove the projector from de operator, then the results match, the one I obtain in mathematica and the one I get from CalcHep (or REDUCE). My advisor told me that it is common that the presence of the gamma_5 causes sometimes this kind of troubles.

Do you think there is any way to fix this?

Regards,

Faby

Dear Faby,

when you say "I have calculated Z -> Df df" what do you mean -- the width or matrix element squared?
CalcHEP gives you matrix element squared. Did you compare it with your previous calculation when you have calculated also matrix element squared or what?
I would like to clarify this first.

Regards,
Alexander

Dear Dr. Pukhov,

Yes, I've been comparing expressions at the level of matrix element squared only.

Best wishes,
Faby

OK,

thank you,

could you send us

<email address hidden>

<email address hidden>

your lanhep file, please?

Thank you

Alexander

On 21/07/2019 00:13, Fabiola Elena Fortuna Montecillo wrote:
> Question #681866 on CalcHEP changed:
> https://answers.launchpad.net/calchep/+question/681866
>
> Status: Answered => Open
>
> Fabiola Elena Fortuna Montecillo is still having a problem:
> Dear Dr. Pukhov,
>
> Yes, I've been comparing expressions at the level of matrix element
> squared only.
>
> Best wishes,
> Faby
>
--
______________________________________________________________________
Prof. Alexander S Belyaev (<email address hidden>)
https://www.hep.phys.soton.ac.uk/content/alexander-belyaev

School of Physics & Astronomy, University of Southampton
Office 5047, SO17 1BJ, TEL: +44 23805 98509, FAX: +44 23805 93910
.....................................................................
Particle Physics Department, Rutherford Appleton Laboratory
Didcot, OX11 0QX, TEL: +44 12354 45562, FAX: +44 12354 46733
.....................................................................
CERN, CH-1211 Geneva 23, Switzerland
Office 40/1-B20, Mailbox: E27910, TEL: +41 2276 71642
______________________________________________________________________

Thanks Alexander Belyaev, that solved my question.