Understanding difference between models via wavefunctions

Asked by Aurelijus Rinkevicius on 2018-11-30

Hello,

The problem is that the model I am investigating is not well documented. The resonance there is supposed to be Z prime, but it somewhat looks different from the SM Z based on a wavefunction flow. I was unable to pin down a clear reference on HELAS that explains the different numbers in the wavefunctions calls, i.e., FFVX_Y_Z, what XYZ stand for. The difference between the two models boils down to a difference between using FFV2_3_3 (for SM Z) and using FFV2_5_3 (for Z'). The code snippet looks as the following:

ixxxxx(p[perm[0]], mME[0], hel[0], +1, w[0]);
oxxxxx(p[perm[1]], mME[1], hel[1], -1, w[1]);
oxxxxx(p[perm[2]], mME[2], hel[2], +1, w[2]);
ixxxxx(p[perm[3]], mME[3], hel[3], -1, w[3]);
oxxxxx(p[perm[4]], mME[4], hel[4], +1, w[4]);
ixxxxx(p[perm[5]], mME[5], hel[5], -1, w[5]);
FFV1P0_3(w[0], w[1], pars->GC_2, pars->ZERO, pars->ZERO, w[6]);
FFV2_3_3(w[3], w[2], pars->GC_9, pars->GC_10, pars->mdl_ZpM, pars->mdl_ZpW, w[7]);
FFV1_1(w[4], w[6], pars->GC_3, pars->mdl_MMU, pars->ZERO, w[8]);
FFV2_5_3(w[3], w[2], pars->GC_29, pars->GC_34, pars->mdl_MZ, pars->mdl_WZ, w[11]);

// Calculate all amplitudes
// Amplitude(s) for diagram number 0
FFV2_3_0(w[5], w[8], w[7], pars->GC_11, pars->GC_12, amp[0]);
FFV2_5_0(w[5], w[8], w[11], pars->GC_29, pars->GC_34, amp[4]);

If I match Z and Z' couplings, masses, and widths, amplitudes are still different: an unexpected result based on a model description. However, I clearly see that different calls are being used FFV2_3_3 vs. FFV2_5_3.

Could somebody explain what is going on?
Where can I read myself for future reference on a precise wavefunction building in MadGraph5_aMC@NLO?
(HELAS paper from '92 lacks content here)

Thank you so much!

Best,
Aurelijus

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2018-11-30
 Aurelijus Rinkevicius (odysei) said on 2018-11-30: #1

I made a typo: FFV2_5_3 (for SM Z) and using FFV2_3_3 (for Z').

 Olivier Mattelaer (olivier-mattelaer) said on 2018-11-30: #2

Hi,

The paper that you are interested to read are :
http://inspirehep.net/record/922833?ln=en
(section 3.1) which should explain the convention associated to those names.

You will see that FFVX_Y_3 is just the sum of the wavefunction created by
FFVX_3 and FFVY_3
(you will also see the meaning of the _3 in the paper)

What you will not find is the meaning of FFVX and FFVY since those are model dependent (i.e. two different model can have the same function existing but meaning something different).

Note that, It is possible that FFV2_3_3 and FFV2_5_3 are at the end of the equivalent if you consider the difference of the coupling used to called those functions.

Cheers,

Olivier