MadGraph5_aMC@NLO

Feeding external effective vertices as a function to MadGraph

Asked by Venus Keus

Hi there,

I have implemented a 3-Higgs doublet model (3HDM) with a CP-conserving the scalar sector in SARAH. The two extra doublets are odd under a Z2 symmetry which protects them from decaying to SM particles.

To produce the param_card.dat for MadGraph, I run the model through Spheno. The heavy CP-even scalar (H2) decays dominantly to the light CP-even scalar (H1) and an off-shell photon (which should further decay to, say, l lbar) at one loop. The tree-level decays of H2 are sub-dominant. For some reason, Spheno sees this as a two body decay of H2 -> H1 \gamma which is worrying, because this photon can not be on-shell, otherwise the decay violates spin.

In any case, MadGraph only accepts tree-level decays of H2, even though the Branching ratio of H2->H1 \gamma^* is almost 100%.
So, I would like to put in the H2-H1-\gamma^* effective vertex in MadGraph by hand.

My first question: Is it possible to feed an external vertex to MadGraph?

I would like to also keep the information of the angular momenta of the loop in the definition of the effective vertex, i.e. the effective vertex is not just a number but is a function.

So, my second question: Is it possible to put in an external effective vertex as a function of momenta in MadGraph?

My third question: Is it possible to define the photon in the effective vertex to be off-shell in MadGraph?

I appreciate any help/advice you can give me! Thanks a million!

Venus

Question information

Language:
English Edit question
Status:
Solved
For:
MadGraph5_aMC@NLO Edit question
Assignee:
No assignee Edit question
Solved by:
Olivier Mattelaer
Solved:
Last query:
Last reply:
Revision history for this message
Best Olivier Mattelaer (olivier-mattelaer) said : 		#1

Hi,

> Is it possible to feed an external vertex to MadGraph?

All vertex are "external" and define in the UFO model (which in your case is produced by SARAH).
So you can edit (in a consistent way obviously) the UFO model in a way that fit your need.

> Is it possible to put in an external effective vertex as a function of momenta in MadGraph?

In the UFO format, you can put arbitrary complex lorentz structure.
and one extension of the UFO format is particularly usefull in this context:
https://cp3.irmp.ucl.ac.be/projects/madgraph/wiki/FormFactors
In 2012, we use method one, to include in the UFO model the full function for the contracted vertex of the ggghh top loop.
Now in general, most people prefer to use method #2 which makes the code more readable (but only compatible with MG5aMC)

 > Is it possible to define the photon in the effective vertex to be off-shell in MadGraph?

The UFO model is benchmark agnostic and you do not have any indication if a particle is going to be onshell or offshell.
So within your UFO model you should support both since depending of the process requested a given vertex can receive both onshell or offshell photon. If the function is not continuous between the two cases, you have to use some "if" statement.

Now nothing prevent you to assume a benchmark and to put those restriction in the documentation of the model. However, the UFO convention do not have a nice way to check if some model hyppothesis are valid or not.

> In any case, MadGraph only accepts tree-level decays of H2, even though the Branching ratio of H2->H1 \gamma^* is almost 100%.

I'm not sure to understand(or agree with) that statement.

If I understand correctly this process is a loop-induced decay.
MG5aMC is able to compute loop-induced decay (see 1507.00020)

But for that you need a specific UFO model that includes additional pieces (for loop-induced only the R2 are in general needed).
As far as I know SARAH does not support the creation of such UFO model (you need to use FeynRules and NLOCT for that)

Now having loop-induced decay coded as an effective vertex can have advantages in order to use madspin, auto-width, ...
So I do not say that this is a bad strategy.

Cheers,

Olivier

Revision history for this message
Venus Keus (vkeus) said : 		#2

Thanks Olivier Mattelaer, that solved my question.