# Madgraph Matrix Element Integration

Dear MG5 team,

I am trying to integrate over the phase space the matrix element obtained numerically from Madgraph (from file matrix.f). Once I do that, I integrate over x1 and x2 considering the PDFs, and try to compare it with the result that Madgraph yields. However, I would like to know how does Madgraph perform such integration, if it considers a particular method, or if one should take some considerations (I could not find information about it).

The point would be performing such integration using the tool of the RAMBO generator for the momenta and applying it to compute the squared matrix element. Up to now, I performed the integration but parametrizing the momenta, and I got to the result Madgraph yields, but is there a way to do it using RAMBO? For example, I would like to integerate something that contains this:

CALL GET_MOMENTA(

CALL SMATRIX(P,MATELEM)

integral = integral + MATELEM

[and then multiply by some factors to obtain the partonic cross-section]

Thank you in advanced!

## Question information

- Language:
- English Edit question

- Status:
- Solved

- Assignee:
- Valentin Hirschi Edit question

- Solved by:
- Olivier Mattelaer

- Solved:
- 2018-07-05

- Last query:
- 2018-07-05

- Last reply:
- 2018-06-29

Hi,

The main idea for the phase-space integrator that we use inside madgraph are written in this paper:

hep-ph/0208156<http://

It is obviously a quite old paper and we have quite improve the optimization since then.

Some details on such optimization are include in the following paper:

arXiv:1106.0522<http://

If you prefer slide, I have presented at multiple occasion the "basic" of phase-space integration at various school. For example you can see: https:/

The point would be performing such integration using the tool of the RAMBO generator for the momenta and applying it to compute the squared matrix element.

For (very) simple integral, it should work but not for complicated processes.

We actually have a branch of madgraph that we use for testing idea on the PS integration and that one include an interface to RAMBO (but not in fortran)

I will assign Valentin to this thread if he wants to give you some information about that branch.

Cheers,

Olivier

On 29 Jun 2018, at 10:43, Laurent Vashmo <<email address hidden>

New question #670543 on MadGraph5_aMC@NLO:

https:/

Dear MG5 team,

I am trying to integrate over the phase space the matrix element obtained numerically from Madgraph (from file matrix.f). Once I do that, I integrate over x1 and x2 considering the PDFs, and try to compare it with the result that Madgraph yields. However, I would like to know how does Madgraph perform such integration, if it considers a particular method, or if one should take some considerations (I could not find information about it).

The point would be performing such integration using the tool of the RAMBO generator for the momenta and applying it to compute the squared matrix element. Up to now, I performed the integration but parametrizing the momenta, and I got to the result Madgraph yields, but is there a way to do it using RAMBO? For example, I would like to integerate something that contains this:

CALL GET_MOMENTA(

CALL SMATRIX(P,MATELEM)

integral = integral + MATELEM

[and then multiply by some factors to obtain the partonic cross-section]

Thank you in advanced!

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Laurent Vashmo (laurentvashmo) said : | #2 |

Hi Olivier,

thank you for your answer. I have read the papers you said, though I am not quite sure if they solve my problem.

My main doubt relies in the answer to: "The point would be performing such integration using the tool of the RAMBO generator for the momenta and applying it to compute the squared matrix element.".

I am able to compute the squared matrix element for a given random set of momenta generated by RAMBO, but I do not succeed in performing the integral of the matrix element over the phase space... I am not sure how should that be implemented.

However, thank you for the information provided.

Cheers,

L.

Laurent Vashmo (laurentvashmo) said : | #3 |

Thanks Olivier Mattelaer, that solved my question.

Laurent Vashmo (laurentvashmo) said : | #4 |

HI again,

I think I solved my problem. I just performed some MC integration by using the result of RAMBO, and it yielded the desired result. Thank you for your answer!