= Higgs pair production =

This page contains the codes for calculating cross sections or generate event for Higgs pair production at LHC through gluon fusion. Associated Higgs production with a Z boson can be found here: [wiki:ZHProduction ZHProduction]

'''Authors :  Benoit Hespel [https://cp3.irmp.ucl.ac.be/Members/bhespel email] and Eleni Vryonidou [https://cp3.irmp.ucl.ac.be/Members/evryonidou email] '''

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== 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]   

Please cite: R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, et al., Higgs pair production at the LHC with NLO and parton-shower effects, [http://xxx.lanl.gov/abs/1401.7340 arXiv:1401.7340] (published in Phys.Lett. B732 (2014) 142-149)

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== 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] 

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== 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] 


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== Complete 2HDM ==          

We calculate Higgs pair production through gluon fusion at LO and NLO in the Two Higgs Doublet Model, for 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. Details of the calculation can be found in this paper: arxiv:1407.0281

* Diagrams contributing to CP-even final states: hh, hH, HH, AA, H+H-

[[Image(cp_even.png)]]

* Diagrams contributing to CP-mixed final states: hA, HA

[[Image(cp_mix.png)]]

Here we provide the LO codes of MG5_aMC@NLO 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-]. The LO calculation codes are based on the form factors for the triangle and the box diagrams, as given in ​arxiv:9603205 [hep-ph] and ​arxiv:9707430 [hep-ph] and have been checked against the 2HDM implementation in the NLOCT package of arXiv:1406.3030.

For convenience we also attach the benchmark parameter cards used in arxiv:1407.0281: [attachment:param_cards.tar.gz param_cards]. Assistance can be provided to obtain parameter cards for other benchmarks.  

NLO codes can also be provided upon request. 

Please cite: B. Hespel, D. López-Val, E. Vryonidou, Higgs pair production through gluon fusion in the Two-Higgs-Doublet Model, [http://arxiv.org/abs/1407.0281 arXiv:1407.0281] (published in JHEP 1409 (2014) 124)