# Values for squared matrix element differ

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[

128/

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

- 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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Subject: [Question #682658]: Values for squared matrix element differ

New question #682658 on MadGraph5_aMC@NLO:

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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[

128/

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.

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 = 1.5108734465672

------

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 = 1.5108739026559

------

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_

GC_3 = -(mdl_ee*

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

I guess that the issue is with the term 128/9/(

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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Subject: Re: [Question #682658]: Values for squared matrix element differ

Question #682658 on MadGraph5_aMC@NLO changed:

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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.