= Higgs pair production =

This page contains the codes for calculating cross sections or generate event for Higgs pair production at LHC through gluon fusion.

'''Authors :  Benoit Hespel and Eleni Vryonidou'''

== SM ==

[[Image(SMdiagrams.png)]]

We calculated the Higgs pair production at LO for a top quark circulating in the loops (exact form factors at LO for the triangle loop and the box from Michael Spira's code (hpair) as given in [http://arxiv.org/abs/hep-ph/9603205 arxiv:9603205] [hep-ph]). 

The corresponding code out of MG5 can be downloaded here: [attachment:SM.tar.gz SM]   

== BSM : tthh coupling ==

[[Image(tthh.png)]]

Here we have implemented a new coupling tthh which has been described in terms of a new parameter c2 (see arxiv:1205.5444v2 [hep-ph]). You can modify its value in the block bsminputs of the paramcard. So by setting c2 to 0 you will recover the above SM result. 

Again the full top mass dependence of the loop matrix elements is taken into account.

The corresponding code out of MG5 can be downloaded here: [attachment:tthh.tar.gz tthh] 

== BSM : Additional heavy scalar resonance ==

[[Image(heavyscalar.png)]]

In this case we have considered the possibility of having a heavy scalar H (called hh in the MG files) as an intermediate state (so that we have the additional process p p > H > h h that is taken into account). For this model in the param_card.dat the user has the freedom of modifying a wide range of parameters :
* the top yukawa coupling (via the parameter cy) 
* the SM-Higgs trilinear coupling (ctr)
* the H coupling to the top (cyH)
* the H coupling to 2 SM-Higgs (ctrH)
The parameters cy and ctr are just factors that multiply the SM couplings. The couplings for the heavy scalar are obtained similarly by multiplying the corresponding SM couplings with the parameters cyH and ctrH. By default they are all fixed to 1. 
Finally you can also modify :
* the H mass (MHH)
* the H decay width (WHH)


The corresponding code out of MG5 can be downloaded here: [attachment:HeavyScalar.tar.gz HeavyScalar] 


== Complete 2HDM ==

We calculated the H bosons pair production through gluon fusion at LO in the Two Higgs Doublet Model, allowing the following 7 final states: hh,hH,HH,hA,HA,AA,H+H- where h (H) stands for the light (heavy) scalar boson and A is the pseudoscalar neutral boson. This model contains the exact form factors at LO for the triangle loop and the box as given in [http://arxiv.org/abs/hep-ph/9603205 arxiv:9603205] [hep-ph] and [http://arxiv.org/abs/hep-ph/9707430 arxiv:9707430] [hep-ph] and includes both contribution of top quark and bottom quark in the loops. 

It is important to note that in this model we didn't restrict ourselves to the more constrained MSSM, which means for example that the masses of the 5 new bosons are left as free parameters, as well as all their extended Yukawa coupling to top and bottom quarks (expressed as rescaling factor with respect to their SM value) so that they can be changed at will in the parameter card for any phenomonological study. For convenience we attached here some benchmark param_cards that we used in our paper: [attachment:param_cards.tar.gz param_cards] 

The corresponding code out of MG5_aMC@NLO can be downloaded here for every final state: [attachment:h1h1.tar.gz hh], [attachment:h1h2.tar.gz hH], [attachment:h1h3.tar.gz hA], [attachment:h2h2.tar.gz HH], [attachment:h2h3.tar.gz HA], [attachment:h3h3.tar.gz AA], [attachment:hphm.tar.gz h+h-]