Massless graviton vertices of FFST and SSST type

Hi,

MG5aMC is fully model agnostic, the full information about the model is the one written in the UFO file.
(This is also true for the SM).

So if your cross-section/shape does not change when changing some coupling it can means multiple stuff:
1) You do not have any dependence of that coupling in the generated Feynman diagram.
--here one solution to check is to have one model without those interaction and one with those interactions and check that the number of Feynman Diagram generated are different)
2) You do have a dependence in that coupling but it is negligeable compare to the rest.
3) something different (a bug is always a possibility)

> These vertices are needed to cancel some IR divergences.

Are you doing NLO computation or LO?
From your statement i would assume that you need such term only for NLO computation but I can be wrong obviously since I do not have that much information/knowledge about what you trying to achieve.

Cheers,

Olivier

> On 22 Jul 2021, at 11:40, Jiaming Zheng <email address hidden> wrote:
>
> New question #698109 on MadGraph5_aMC@NLO:
> https://answers.launchpad.net/mg5amcnlo/+question/698109
>
> Hi,
>
> I am trying to use MG5 as a phase space integrator for gravitational processes. When I search for how massless graviton are implemented in MG5, I was mostly pointed to the reference arXiv:0805.2554 by Aquino, Hagiwara, Li, and Maltoni. This reference provides a list of vertices added to HELAS at that time.
>
> However, the subroutines for vertices of type FFST, SSST among others are not presented in that reference. These vertices are needed to cancel some IR divergences. I can generate a UFO file with this kind of vertices with FeynRules, and their coupling does affect the result from MG5. So I assume these kinds of vertices are already included in MG5. Is this right? Is there any further documentation about them? I want to know whether they are already tested or are still experimental features.
>
> thanks in advance,
> Jiaming Zheng
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Thanks for the prompt reply!

Probably my wording was confusing. Changing the coupling of the SSST vertex DOES change the outcome, and MG5 outputs the diagram with such a vertex. I just want to confirm that this vertex is not an experimental feature in HELAS, as it is not presented in any reference I found(and arXiv:0805.2554 states that this vertex was not included in HELAS back then).

The toy process I played with was S->S1+S1+S2+S2 at tree level, with S1-S1-S couple with a cubic interaction and S2 couples to everything else with massless graviton. Everything except the graviton is real singlet scalar. The IR divergence from the graviton propagator when S2 mass ->0 will cancel if I sum up all the diagrams.

The cancellation was checked analytically with the same rules from FeynRules. However, when I generate such a 1>4 process in MADGRAPH, the mass dependence of the width demonstrates a trend of quadratic divergence.

It is very likely to be my mistake somewhere in operating FeynRules and MADGRAPH. I just want to completely rule out the possibility that it was an issue of MADGRAPH/HELAS.

Hi Olivia,

     Thank you very much for the informative reply!

> My first advise is to check that all width are set to zero.

     Indeed, setting all the widths to 0 gives me the right behavior. Previously I set the width of the decaying phi to AUTO and it was determined by the two-body decay.

     Probably it is off-topic from the original question, but is setting all widths to 0 always necessary in a 1>N simulation and why is it different from setting it to AUTO?

thanks again,
Jiaming Zheng

Thanks Olivier Mattelaer, that solved my question.

The problem stem from the fact that the default handling for the width is done in the fix-width scheme where the width is used to put an imaginary part to the denominator.
The issue is that such effect is not a LO effect but a full order effect and therefore this is not fully consistent.
And this can lead to breaking of gauge invariance/...

This is quite often irrelevant effect at LO but can lead to breaking of unitary or miss-cancelation like you face here.
A typical solution --available within MG5aMC-- for that is to use the complex-mass-scheme but this scheme of computation fully forbids to have particle with a width in the initial/final state so this an unlikely solution to your problem.

Another work-around is to set all the width to zero (possible only if you do not have a onshell resonance obviously) since in that case you do not need the width as regulator and this is consistent at LO accuracy.

Cheers,

Olivier

Hi Olivier,

Thanks a lot for the explanation! It makes perfect sense to me that the width of the initial state in the propagator is causing all the non-cancellation.

Indeed, non of the immediate state goes on-shell in this problem so setting the width to 0 is consistent.

Thank you very much for clearing my confusion!

Best,
Jiaming