MadGraph5_aMC@NLO

Problem with vertice involving one scalar and three gluons

Asked by IvanSobolev

Dear MG5 team,

I have a problem with vertice involving one scalar (color singlet) and three gluons. The issue is the following. I want to calculate cross-section of a process g,g -> s,g (where g is a gluon and s is a scalar) using only diagram with three gluons and scalar (and omitting 3 others). I know that in practice it actually makes no sense (I'm just playing with MadGraph) since g-g-s and g-g-g-s vertices are connected by gauge invariance. For this I multiply g-g-s coupling by very small value (i.e. ~10^{-13}).

From dimensional analysis I'd expect this cross-section to behave in the following way: ~x^2*(1-x^2), where x is
x = MS/E ratio , MS is the scalar mass and E is center of mass energy. For example, it should vanish in the limit MS -> 0. What I get differs completely from my expectations. For instance, in the limit of small singlet masses this cross-section does not depend on MS at all.

The model I use is just a slight modification of "HiggsEffective":
https://cp3.irmp.ucl.ac.be/projects/madgraph/wiki/Models/HiggsEffective

Please find it attached to this post:
https://dl.dropboxusercontent.com/u/40782744/Scalar_gluons_UFO.zip

Where am I wrong?

Best,
Ivan

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Olivier Mattelaer
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Olivier Mattelaer (olivier-mattelaer) said : 		#1

Dear Ivan,

1) Selecting only one diagram also breaks lorentz invariance.
I have no idea how much usefull information can be obtained in such weird computation.
I have to strongly advised you against such type of computation.

2) When you say that from dimensional analysis you expect such type of cross-section. I doubt that you are correct.
You have the scale Lam in your model. It can play a role as well. In top of that I'm not sure which hyppothesis you use to get such
formula. But note that you can not use the fact that you preserve unitary behavior for such kind of computation.

3) For instance, in the limit of small singlet masses this cross-section does not depend on MS at all.
When looking at the matrix-element, I'm not surprised since the matrix-element does not depend in anyway of the scalar mass.
So the dependence is only in the phase-space and having lower mass means to have higher phase-space available.

Cheers,

Olivier

Revision history for this message
IvanSobolev (sobolev-ivan) said : 		#2

Dear Olivier,

Thanks a lot for your answer!

>2) When you say that from dimensional analysis you expect such type of cross-section. I doubt that you are correct.
You have the scale Lam in your model. It can play a role as well. In top of that I'm not sure which hyppothesis you use to get such
formula. But note that you can not use the fact that you preserve unitary behavior for such kind of computation.

>3) For instance, in the limit of small singlet masses this cross-section does not depend on MS at all.
When looking at the matrix-element, I'm not surprised since the matrix-element does not depend in anyway of the scalar mass.
So the dependence is only in the phase-space and having lower mass means to have higher phase-space available.

The squared matrix element is proportional to G^2/Lam^2*MS2^2 (I checked this with CalcHEP), the phase space is ~1-(MS/E)^2 and 1/E^2 comes from the standard formula of cross-section. I just retained the part which depends on mass and center of mass energy. Sorry for inconvenience.

>1) Selecting only one diagram also breaks lorentz invariance.
I have no idea how much usefull information can be obtained in such weird computation.
I have to strongly advised you against such type of computation.

I'm a newbie in MadGraph and just I'm playing with it. But I implemented the same vertice into CalcHEP and obtained the expected answer.

Best,
Ivan

Revision history for this message
Best Olivier Mattelaer (olivier-mattelaer) said : 		#3

Hi,

> The squared matrix element is proportional to G^2/Lam^2*MS2^2 (I checked
> this with CalcHEP),

I do not see it easily how the matrix-element depend of MS.
I guess it is possible that the lorentz structure provides such dependence but this is not trivial
and I would not take the time to do the computation.
You can obviously check that on evaluating the matrix-element on a single PS point.
(you have the standalone output for that)

> I'm a newbie in MadGraph and just I'm playing with it. But I implemented
> the same vertice into CalcHEP and obtained the expected answer.

I do not know if the diagram selection break lorentz invariance in CalcHEP as it does in MadGraph.

Cheers,

Olivier

> On Aug 30, 2016, at 15:08, IvanSobolev <email address hidden> wrote:
>
> Question #372550 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/372550
>
> Status: Answered => Open
>
> IvanSobolev is still having a problem:
> Dear Olivier,
>
> Thanks a lot for your answer!
>
>> 2) When you say that from dimensional analysis you expect such type of cross-section. I doubt that you are correct.
> You have the scale Lam in your model. It can play a role as well. In top of that I'm not sure which hyppothesis you use to get such
> formula. But note that you can not use the fact that you preserve unitary behavior for such kind of computation.
>
>> 3) For instance, in the limit of small singlet masses this cross-section does not depend on MS at all.
> When looking at the matrix-element, I'm not surprised since the matrix-element does not depend in anyway of the scalar mass.
> So the dependence is only in the phase-space and having lower mass means to have higher phase-space available.
>
> The squared matrix element is proportional to G^2/Lam^2*MS2^2 (I checked
> this with CalcHEP), the phase space is ~1-(MS/E)^2 and 1/E^2 comes from
> the standard formula of cross-section. I just retained the part which
> depends on mass and center of mass energy. Sorry for inconvenience.
>
>> 1) Selecting only one diagram also breaks lorentz invariance.
> I have no idea how much usefull information can be obtained in such weird computation.
> I have to strongly advised you against such type of computation.
>
> I'm a newbie in MadGraph and just I'm playing with it. But I implemented
> the same vertice into CalcHEP and obtained the expected answer.
>
> Best,
> Ivan
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Revision history for this message
IvanSobolev (sobolev-ivan) said : 		#4

Thanks Olivier Mattelaer, that solved my question.

Revision history for this message
IvanSobolev (sobolev-ivan) said : 		#5

Dear Olivier,

Thanks a lot for your answer!

All the best,
Ivan