Possible missing diagram in gg > hh for the heft model

Hi Wouter,

> 1) Why are the gluon mediated t- and u-channels not appearing in the default heft model, but are in the FeynRules one?

In fact those contributions are NOT physical. Indeed the HEFT implementation correspond to an Effective Field theory where the
parameter of expansion is mh/mt. Only the first term of the Lagrangian expansion is taken into account. Therefore a diagram with
two interaction is at the same level of expansion as term which are neglected. i.e. your expansion doesn't makes sense.

The model implemented in MG5 has the information that such coupling is allowed theoretically to appear only once, which is not the case of the model
that you load on FR website.

> 2) Why is there no four-point coupling present in g g > h h?

According to the wiki information: https://cp3.irmp.ucl.ac.be/projects/madgraph/wiki/Models/HiggsEffective
the Lagrangian implemented in FR is GGH, and therefore it doesn't contains g g h h interactions.

One of the reason is that the FR author (and myself) are not sure at all how good is the heft approximation in the case of pair production.
since in that case sqrt{s} = 2mh>mt.

Now I suppose that editing the FR file in order to change to the Lagramgian which include the four point interaction should be kind of easy.
(But I'm not an expert in FR)

Cheers,

Olivier

On Jul 3, 2013, at 10:06 AM, Wouter van den Wollenberg <email address hidden> wrote:

> New question #231808 on MadGraph5:
> https://answers.launchpad.net/madgraph5/+question/231808
>
> Hi everyone!
>
> I am trying to replicate in Madgraph 5 the cross section for gluon-gluon fusion into a Higgs pair. There is a program by Michael Spira called HPAIR which puts the 14 TeV value at around 36 fb (it depends a bit on the Higgs mass). This value is also mentioned in some papers (for example see http://inspirehep.net/record/470212). However the MG5 heft-full cross section is about 2.7 fb.
>
> Looking at the diagrams I also found that according to heft there is only one diagram contributing here, which is a Higgs mediated s-channel. However one would also expect a t- and u-channel with a mediating gluon and a gluon-gluon-Higgs-Higgs four-point coupling (which originates from a box top loop diagram).
>
> On the FeynRules page of the heft model (http://feynrules.irmp.ucl.ac.be/wiki/HiggsEffectiveTheory#), one can find a UFO implementation. Using that one in MG5 I do get the gluon t- and u-channels, but the gluon-gluon-Higgs-Higgs four-point coupling is still missing. It also gives a different cross section: 3.7 fb.
>
> According to HPAIR the cross section without the box coupling (i.e. the gluon-gluon-Higgs-Higgs four-point coupling) the cross section should be about 2-3 fb so it sounds somewhat reasonable (especially since HPAIR incorperates some NLO effects, so that might account for the small difference between it and MG5). But with the box coupling it should be about 36 fb.
>
> So my questions would be:
>
> 1) Why are the gluon mediated t- and u-channels not appearing in the default heft model, but are in the FeynRules one?
> 2) Why is there no four-point coupling present in g g > h h?
>
> Cheers,
>
> Wouter van den Wollenberg
>
> --
> You received this question notification because you are a member of
> MadTeam, which is an answer contact for MadGraph5.