Different weights for different colour structures in LHE files?

Asked by oleh on 2018-04-25

Dear MadGraph experts,

I am trying to understand how MadGraph generates colour structures for Les-Houches files.

I consider a process g g > g g.
I found that in LHE file different combinations appear with different frequency.
I have written a simple python script that finds all different combinations and counts how often they appear.
Here is the output
combination = 504 501 503 502 503 501 504 502 with weight = 0.318418
combination = 503 501 504 502 503 502 504 501 with weight = 0.327642
combination = 502 501 504 502 503 501 504 503 with weight = 0.089904
combination = 503 501 501 502 503 504 504 502 with weight = 0.086785
combination = 502 501 503 502 503 504 504 501 with weight = 0.090514
combination = 504 501 501 502 503 502 504 503 with weight = 0.086737

So my questions are: 1) Why these combination are generated with different probability?
                                           Is there a certain hit-or-miss generation algorithm involved ?

                                     2) If it is possible, could you please give me some references
                                           with explanations on how MG generates these structures.

                                    3) Are colour structures and four-momenta generated independently?
                                         Or certain combinations of colours and four-momenta appear more often than the others?

Thank you!
With best regards,
Oleh

Question information

Language:
English Edit question
Status:
Solved
For:
MadGraph5_aMC@NLO Edit question
Assignee:
No assignee Edit question
Solved by:
Olivier Mattelaer
Solved:
2018-04-25
Last query:
2018-04-25
Last reply:
2018-04-25

> 2) If it is possible, could you please give me some references
> with explanations on how MG generates these structures.

for each phase-space point, we evaluate the amplitude contribution for each fermion flow independently
and square them against themself. Then we discard all the NLC contribution from those and then pick
one of the color by launching a random number (the contribution of each LC being weighted by the colored amplitude square associated).
Note that interference term are neglected here, they are NLC anyway.
then we write inside the event the associate structure.

> 1) Why these combination are generated with different probability?
> Is there a certain hit-or-miss generation algorithm involved ?

this is a random process. But not really hit or miss. Since we simply pick in a weighted way.

> 3) Are colour structures and four-momenta generated independently?
> Or certain combinations of colours and four-momenta appear more often than the others?

As you can see above this is not independent.

Cheers,

Olivier

> On 25 Apr 2018, at 11:08, oleh <email address hidden> wrote:
>
> New question #668241 on MadGraph5_aMC@NLO:
> https://answers.launchpad.net/mg5amcnlo/+question/668241
>
> Dear MadGraph experts,
>
> I am trying to understand how MadGraph generates colour structures for Les-Houches files.
>
> I consider a process g g > g g.
> I found that in LHE file different combinations appear with different frequency.
> I have written a simple python script that finds all different combinations and counts how often they appear.
> Here is the output
> combination = 504 501 503 502 503 501 504 502 with weight = 0.318418
> combination = 503 501 504 502 503 502 504 501 with weight = 0.327642
> combination = 502 501 504 502 503 501 504 503 with weight = 0.089904
> combination = 503 501 501 502 503 504 504 502 with weight = 0.086785
> combination = 502 501 503 502 503 504 504 501 with weight = 0.090514
> combination = 504 501 501 502 503 502 504 503 with weight = 0.086737
>
> So my questions are: 1) Why these combination are generated with different probability?
> Is there a certain hit-or-miss generation algorithm involved ?
>
> 2) If it is possible, could you please give me some references
> with explanations on how MG generates these structures.
>
> 3) Are colour structures and four-momenta generated independently?
> Or certain combinations of colours and four-momenta appear more often than the others?
>
> Thank you!
> With best regards,
> Oleh
>
>
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

oleh (fedkevych) said : #2

Dear Oliver,

many thanks for finding time to answer my question!

In spite of your answer I would like to ask you an additional question:

>>this is a random process. But not really hit or miss. Since we simply pick in a weighted way.
If it is possible could you please briefly explain how does MG turn weighted events into underweighted ones?

With best regards,
Oleh

Hi,

> If it is possible could you please briefly explain how does MG turn weighted events into underweighted ones?

That part is a standard hit and miss.
The part which is not a hit and miss is the pick of a particular color for a particular event.

For the color we have n valid choice each of the with associate weight w_i.

then we throw a random number and assign the color such that
\sum_{j=0}^iw_j < R*\sum w_j < \sum_{j=0}^{i+1} w_j

Cheers,

Olivier

> On 25 Apr 2018, at 16:02, oleh <email address hidden> wrote:
>
> Question #668241 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/668241
>
> Status: Answered => Open
>
> oleh is still having a problem:
> Dear Oliver,
>
> many thanks for finding time to answer my question!
>
> In spite of your answer I would like to ask you an additional question:
>
>>> this is a random process. But not really hit or miss. Since we simply pick in a weighted way.
> If it is possible could you please briefly explain how does MG turn weighted events into underweighted ones?
>
> With best regards,
> Oleh
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

oleh (fedkevych) said : #4

Dear Oliver,
thank you very much!

oleh (fedkevych) said : #5

Thanks Olivier Mattelaer, that solved my question.