Values for squared matrix element differ

Asked by Marcel on 2019-08-07

HI,

if i consider the a process like e+ e- > t t~ and only return a numerical value for the squared matrix element at a given phase space point, the value differs from the one i calculated by hand for this specific phase space point (1.443822e-02 GeV^0 by MadGraph, my result is 0.0146509 GeV^0, so a difference in the fifth digit).A process like e+ e- -> u u~ works perfectly fine (setting in my result mt ->0) or u u~ -> t t~ works again perfectly (momentum structure the same as in e+ e- -> t t~, just different prefactors). I will state my squared amplitude for e+ e- -> t t~ in the following:

MtreeQED[p1_,p2_,p3_,p4_,qs_,e_,mt_] :=
      128/9/(qs.qs)/(qs.qs)*p1.p2*e^4*mt^2 + 128/9/(qs.qs)/(qs.qs)*p1.p3*p2.p4*e^4 + 128/9/(qs.qs)/(qs.qs)*p1.p4*p2.p3*e^4;

qs = p1 + p2, the coupling e and the mass mt has been chosen in the same way as in Madgraph. This Amplitude needs to be multiplied by an additional factor of 3/4 for the color sum and the spin averaging factor for the two inc. leptons. What is wrong here?

Question information

Language:
English Edit question
Status:
Solved
For:
MadGraph5_aMC@NLO Edit question
Assignee:
No assignee Edit question
Solved by:
Olivier Mattelaer
Solved:
2019-08-09
Last query:
2019-08-09
Last reply:
2019-08-07

Hi I’m in Holliday for the moment. So can’t have a fee look for the moment. Bit Where is the term related to the z mass and z width?

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________________________________
From: <email address hidden> <email address hidden> on behalf of Marcel <email address hidden>
Sent: Wednesday, August 7, 2019 7:13:14 AM
To: Olivier Mattelaer <email address hidden>
Subject: [Question #682658]: Values for squared matrix element differ

New question #682658 on MadGraph5_aMC@NLO:
https://answers.launchpad.net/mg5amcnlo/+question/682658

HI,

if i consider the a process like e+ e- > t t~ and only return a numerical value for the squared matrix element at a given phase space point, the value differs from the one i calculated by hand for this specific phase space point (1.443822e-02 GeV^0 by MadGraph, my result is 0.0146509 GeV^0, so a difference in the fifth digit).A process like e+ e- -> u u~ works perfectly fine (setting in my result mt ->0) or u u~ -> t t~ works again perfectly (momentum structure the same as in e+ e- -> t t~, just different prefactors). I will state my squared amplitude for e+ e- -> t t~ in the following:

MtreeQED[p1_,p2_,p3_,p4_,qs_,e_,mt_] :=
      128/9/(qs.qs)/(qs.qs)*p1.p2*e^4*mt^2 + 128/9/(qs.qs)/(qs.qs)*p1.p3*p2.p4*e^4 + 128/9/(qs.qs)/(qs.qs)*p1.p4*p2.p3*e^4;

qs = p1 + p2, the coupling e and the mass mt has been chosen in the same way as in Madgraph. This Amplitude needs to be multiplied by an additional factor of 3/4 for the color sum and the spin averaging factor for the two inc. leptons. What is wrong here?

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Marcel (realmald) said : #3

Hi,

I am considering only a photon exchange for now, so the actual process is e+ e- > t t~ / Z.

Hi,

I have cross-checked MG5aMC with the HELAS program (and with old version of MG5aMC up to 1.0.0).

Here is the output of the MG5aMC code:

  Couplings of sm
  ---------------------------------

         GC_2 = 0.00000E+00 0.20530E+00
         GC_3 = -0.00000E+00 -0.30795E+00
   1000.0000000000000 500.00000000000000

  Phase space point:

 -----------------------------------------------------------------------------
 n E px py pz m
 1 0.5000000E+03 0.0000000E+00 0.0000000E+00 0.5000000E+03 0.0000000E+00
 2 0.5000000E+03 0.0000000E+00 0.0000000E+00 -0.5000000E+03 0.0000000E+00
 3 0.5000000E+03 0.1040730E+03 0.4173556E+03 -0.1872274E+03 0.1730000E+03
 4 0.5000000E+03 -0.1040730E+03 -0.4173556E+03 0.1872274E+03 0.1730000E+03
 -----------------------------------------------------------------------------
 Matrix element = 1.5108734465672517E-002 GeV^ 0
 -----------------------------------------------------------------------------

and for the HELAS package:

 FFV couplings:
 --------------

 gal(L) = 0.3079538 0.0000000 gal(R) = 0.3079538 0.0000000
 gau(L) = -0.2053025 0.0000000 gau(R) = -0.2053025 0.0000000
 gad(L) = 0.1026513 0.0000000 gad(R) = 0.1026513 0.0000000

  Phase space point:

 -----------------------------------------------------------------------------
 n E px py pz m
 1 0.5000000E+03 0.0000000E+00 0.0000000E+00 0.5000000E+03 0.0000000E+00
 2 0.5000000E+03 0.0000000E+00 0.0000000E+00 -0.5000000E+03 0.0000000E+00
 3 0.5000000E+03 0.1040730E+03 0.4173556E+03 -0.1872274E+03 0.1730000E+03
 4 0.5000000E+03 -0.1040730E+03 -0.4173556E+03 0.1872274E+03 0.1730000E+03
 -----------------------------------------------------------------------------
 Matrix element = 1.5108739026559992E-002 GeV^ 0
 -----------------------------------------------------------------------------

Can you check your formula with this phase-space point? What is the value of the coupling/mass in your case?

Cheers,

Olivier

PS: In MG5aMC, the coupling are define as (of course, you can have difference by factor i/-1 depending of your definition)
        GC_2 = (2*mdl_ee*mdl_complexi)/3. = 0.205302511496j
        GC_3 = -(mdl_ee*mdl_complexi) = (-0-0.307953767244j)

Marcel (realmald) said : #5

Hi,

for your given phase space point i obtain the following result: 0.0155873

During my calculation i already got rid of the complex i and i have chosen my coupling constant like you did:

e = 0.307953767244 (your mdl_ee)
mt = 173.0

The factor 2/3 for the quark/antiquark/photon vertex is also considered.

I guess that the issue is with the term 128/9/(qs.qs)/(qs.qs)*p1.p2*e^4*mt^2
that might have a wrong factor 2 (or the sign wrong). I would need to do the computation with a pen and paper (which means I need to be in my office -> end of next week).

Did you check your formulla with another package like calchep or FeynArts?

Cheers,

Olivier

Marcel (realmald) said : #8

Thanks Olivier Mattelaer, that solved my question.

Did you find the issue? If yes what was it?

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________________________________
From: <email address hidden> <email address hidden> on behalf of Marcel <email address hidden>
Sent: Friday, August 9, 2019 9:57:33 PM
To: Olivier Mattelaer <email address hidden>
Subject: Re: [Question #682658]: Values for squared matrix element differ

Question #682658 on MadGraph5_aMC@NLO changed:
https://answers.launchpad.net/mg5amcnlo/+question/682658

    Status: Open => Solved

Marcel confirmed that the question is solved:
Thanks Olivier Mattelaer, that solved my question.

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Marcel (realmald) said : #10

There was an error in one of my replacement rules in Mathematica. While i was replacing the momenta in the expression above i multiplied one of the momenta with a wrong factor, therefore i got nearly the same result. Now it fits perfectly for both e+ e- > t t~ / Z and e+ e- > t t~ g/Z.

Thank you for your time.