# Generate amplitude for processes with final state gluon, where the spin correlated contribution is given separately from the rest of the amplitude

Hello,

I have a question related to the standalone mode in MadGraph.

I want to generate the amplitude for a given phase space point, for diagrams involving at least one final state gluon.
Is there a way to get the numerical value of the amplitude split into the contribution which comes from the spin correlations of the final state gluon and the rest?

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Olivier Mattelaer
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2019-08-08
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2019-08-08
2019-08-07
 Olivier Mattelaer (olivier-mattelaer) said on 2019-08-06: #1

Could you define exatctly what you define by "rest" and "spin correlation" ?

Cheers,

Olivier

> On 6 Aug 2019, at 09:57, Jasmina <email address hidden> wrote:
>
> New question #682625 on MadGraph5_aMC@NLO:
>
> Hello,
>
> I have a question related to the standalone mode in MadGraph.
>
> I want to generate the amplitude for a given phase space point, for diagrams involving at least one final state gluon.
> Is there a way to get the numerical value of the amplitude split into the contribution which comes from the spin correlations of the final state gluon and the rest?
>
>
> --

 Jasmina (jasmin9) said on 2019-08-07: #2

Sorry for the lack of details.

If I have a process, say : u(p1) g(p2) > u(p3) g(p4), and I assume the z axis to be the longitudinal direction, I would like to get the amplitude given as a sum of two separate contributions. For this I need to decompose the 3-momenta of the gluons (inital and final state in this case) in the longitudinal "z" and the transverse part "x and y".

Then the first part of the result for the amplitude would include all the terms that have at least one scalar product of the transverse momenta of the gluons. So in other words terms that have at least one of the: dot(p1x,...),dot(p2x,...), dot(p1y,....),dot(p2y,....) , with dot(p1,p2) being the scalar product of the 4-momenta p1 and p2, and p1x being a four momentum with only one x component.
In this context, "spin correlated" was the wrong term, I apologize for the confusion.

Everything else that doesn't fit the category above (if there happens to be be any remainder) would be given as the a second term in the result.

Both terms together would then of course give me back the amplitude result I get now with the standalone procedure.

Do you think this is possible to do, by say changing the routine in matrix.f ?

Thanks a lot!

 Olivier Mattelaer (olivier-mattelaer) said on 2019-08-07: #3

Hi,

Our representation of the matrix-element at tree level does not allow for easy analytical manipulation of the amplitude.
So I would either suggest to use a code doing the computation analytically (like FeynArts or calchep) or that you need to use some numerical trick (basically evaluating the amplitude at various momenta and resolve a system of equation to extract the factor that you want).

Another (quite complex) method would be to write a plugin for MG5aMC where you use (maybe modify) the code use to evaluate the numerator of the loop in MadLoop. Such code returns the numerator as a function of the loop-momenta:
C_0 + C_\mu l^mu + C_{\mu\nu} l^\mu l^nu
If you can use such decomposition, then it should be possible to trick MG5aMC to output such decomposition for tree diagram (where you put l^\mu= p1^\mu). But this would be quite complex work (worth a paper actually).

Cheers,

Olivier

 Jasmina (jasmin9) said on 2019-08-08: #4

Thanks a lot for the detailed answer Olivier!
Have a nice day!

 Jasmina (jasmin9) said on 2019-08-08: #5

Thanks Olivier Mattelaer, that solved my question.