F±= ∂µWµ±+ iξW e √ 2sW vG±, FZ = ∂µZµ+ ξZ e √ 2s2W vG0, FA= ∂µAµ. (4.5)
Les calculs intermédiaires vont alors dépendre des paramètres de fixation ξW, ξZ et ξA. Si on prend l’exemple du propagateur du boson Z, on obtient l’expression suivante,
ΓZZ(p) = −i p2− M2 Z+ iǫ gµν + (ξZ − 1)p2 pµpν − ξZM2 Z , (4.6)
qui dépend bien de ξZ. Cependant le résultat final ne doit plus en dépendre puisque ce ne sont pas des paramètres physiques. Il est d’ailleurs possible de choisir une valeur particulière pour ces paramètres dès le début des calculs afin de les simplifier. Le choix ξA = ξZ = ξW = 1, cor-respondant à la jauge de Feynman, permet ainsi d’annuler les derniers termes des propagateurs des bosons de jauge correspondants. Faire un tel choix ne permet en revanche pas de tester l’invariance de jauge des résultats, qui est un bon test pour savoir si l’implémentation d’un modèle dans un code est correcte. Afin de remédier à cela, on utilise dans SloopS une fixation de jauge non linéaire, ce qui permet de tester à nouveau l’invariance de jauge tout en se plaçant dans la jauge linéaire de Feynman. Les fonctions F+, FZ et FA du Lagrangien de fixation de jauge (4.4) deviennent alors :
F+ =(∂µ− ie˜αAµ− ig2cWβZ˜ µ)Wµ++ iξW
g2 2( √ 2v + ˜δ1h01+ ˜δ2h02+ ˜δ3h03 + i(˜κG0+ ˜ρ1A01+ ˜ρ2A02))G+, FZ =∂µZµ+ ξZ g2 2cW (√ 2v + ˜ǫ1h0 1+ ˜ǫ2h0 2+ ˜ǫ3h0 3)G0, FA =∂µAµ. (4.7)
Avec ces nouveaux termes de fixation de jauge, on ne modifie plus les propagateurs, mais on ajoute des nouveaux termes d’interaction. En jouant sur la valeur des paramètres (˜α, ˜β, ˜δi, ˜κ, ˜ρj, ˜ǫk), on peut ainsi tester l’invariance de jauge.
4.7 Le NMSSM dans SloopS
Dans SloopS, il existe un fichier d’input donnant tous les paramètres fondamentaux en fonction desquels toute la physique d’un modèle est écrite. Pour le NMSSM réel et sans violation de CP étudié ici, c’est-à-dire avec des matrices de masse diagonales dans l’espace des saveurs pour les sfermions, les quarks et les leptons, il s’agit :
EE = 0.31223D0 ! Couplage électromagnetique SW = 0.481D0 ! Sinus de l’angle de Weinberg GG = 1.238D0 ! Couplage fort
MZ = 91.1884D0 ! Masse du boson Z
wZ = 2.4944D0 ! Largeur de désintégration du Z wW = 2.08895D0 ! Largeur de désintégration du W
• des masses des fermions :
Me = 0.000511D0 ! Masse de l’électron Mm = 0.1057D0 ! Masse du muon Mu = 0.046D0 ! Masse du quark u Md = 0.046D0 ! Masse du quark d Mc = 1.42D0 ! Masse du quark c Ms = 0.2D0 ! Masse du quark s Ml = 1.777D0 ! Masse du tau Mt = 175D0 ! Masse du top Mb = 4.62D0 ! Masse du bottom
wt = 1.7524D0 ! Largeur de désintégration du top
• des paramètres du secteur Higgs :
tb = 4.5D0 ! tb=vu/vd
hL = 0.2D0 ! couplage lambda du superpotentiel hK = 0.05D0 ! couplage kappa du superpotentiel mue = 250D0 ! mue=lambda*s
4.7. LE NMSSM DANS SLOOPS hLs = 1250D0 ! Alambda
hKs = 0D0 ! Akappa
MG1 = 230D0 ! Masse soft du jaugino U(1) MG2 = 600D0 ! Masse soft du jaugino SU(2) MG3 = 1000D0 ! Masse soft du jaugino SU(3)
Ml1 = 1000D0 ! Masse sleptons gauches, première génération Ml2 = 1000D0 ! Masse sleptons gauches, deuxième génération Ml3 = 1000D0 ! Masse sleptons gauches, troisième génération Mr1 = 1000D0 ! Masse slepton chargé droit, première génération Mr2 = 1000D0 ! Masse slepton chargé droit, deuxième génération Mr3 = 149.5D0 ! Masse slepton chargé droit, troisième génération Al = 1000D0 ! Couplage trilinéaire du stau
Ae = 0D0 ! Couplage trilinéaire du sélectron Am = 0D0 ! Couplage trilinéaire du smuon
Mq1 = 1000D0 ! Masse squarks gauches, première génération Mq2 = 1000D0 ! Masse squarks gauches, deuxième génération Mq3 = 1500D0 ! Masse squarks gauches, troisième génération Mu1 = 1000D0 ! Masse squark u droit
Mu2 = 1000D0 ! Masse squark c droit Mu3 = 500D0 ! Masse squark t droit Md1 = 1000D0 ! Masse squark d droit Md2 = 1000D0 ! Masse squark s droit Md3 = 1000D0 ! Masse squark b droit
At = 2200D0 ! Couplage trilinéaire du stop Ab = 1000D0 ! Couplage trilinéaire du sbottom Au = 0D0 ! Couplage trilinéaire du s-up
Ad = 0D0 ! Couplage trilinéaire du s-down As = 0D0 ! Couplage trilinéaire du s-strange Ac = 0D0 ! Couplage trilinéaire du s-charm
• des paramètres de fixation de jauge non linéaire, mis à zéro par défaut : nla = 0D0 nlb = 0D0 nld1 = 0D0 nld2 = 0D0 nld3 = 0D0 nlk = 0D0 nlr1 = 0D0 nlr2 = 0D0 nle1 = 0D0 nle2 = 0D0 nle3 = 0D0
considéré. Tous les termes de masse et les couplages apparaissant ci-dessus doivent être renormalisés si on souhaite calculer des sections efficaces ou des largeurs de désintégration à l’ordre d’une boucle.
Chapitre 5
Désintégration du boson de Higgs en un
photon et un boson Z dans le NMSSM
Contents
3.1 Introduction . . . 53 3.2 Les divergences ultraviolettes . . . 54 3.2.1 Théorie φ4 . . . 55 3.2.2 Critère de renormalisabilité . . . 58 3.2.3 Régularisation des intégrales divergentes . . . 60 3.2.4 Les limites du développement perturbatif . . . 62 3.3 Les divergences infrarouges . . . 63
Dans ce chapitre, on présente les résultats de mes travaux concernant l’étude, grâce à SloopS, de la désintégration du boson de Higgs en γZ dans le NMSSM. Ce processus n’existe pas à l’ordre des arbres mais est généré à une boucle, pouvant être parcourue par toutes les particules chargées présentes dans la Nature. Ce mode de désintégration est ainsi un très bon laboratoire pour détecter de la nouvelle physique. Les premiers résultats pour ce canal sont sortis lors du dernier run du LHC mais les statistiques sont encore trop faibles pour en tirer des conclusions. Le nouveau run du LHC devrait en revanche permettre de faire des analyses plus précises.
BOSON Z DANS LE NMSSM
Boosting Higgs decays into gamma and a Z in the NMSSM
Geneviève Bélanger1, Vincent Bizouard1 and Guillaume Chalons2 1
LAPTh, Université de Savoie, CNRS, 9 Chemin de Bellevue, B.P. 110, F-74941 Annecy-le-Vieux, France
2
LPSC, Université Grenoble-Alpes, CNRS/IN2P3, Grenoble INP, 53 rue des Martyrs,F-38026 Grenoble, France
Abstract
In this work we present the computation of the Higgs decay into a photon and a Z boson at one-loop level in the framework of the Next-to-Minimal Supersymmetric Standard Model (NMSSM). The numerical evaluation of this decay width was performed within the framework of the SloopS code, originally developed for the Minimal Supersymmetric Standard Model (MSSM) but which was recently extended to deal with the NMSSM. Thanks to the high level of automation of SloopS all contributions from the various sector of the NMSSM are consistently taken into account, in particular the non-diagonal chargino and sfermion contributions. We then explored the NMSSM parameter space, using HiggsBounds and HiggsSignals, to investigate to which extent the signal can be enhanced.
5.1 Introduction
The discovery of a 125 GeV Higgs boson at the LHC on July 2012 [4, 5], is a milestone in the road leading to the elucidation the ElectroWeak Symmetry Breaking (EWSB) riddle. Since then, its couplings to electroweak gauge bosons, third generation fermions and the loop-induced couplings to photons and gluons have been measured with an already impressive accuracy by the ATLAS and CMS collaborations [38, 39] during the 7 and 8 TeV runs. This great achievement was made possible since for a 125 GeV Higgs boson many different production and decay channels are detectable at the LHC. A spin and parity analysis of the Higgs boson in the decays H → γγ, H → ZZ∗ and H → W W∗ favors the JP = 0+ hypothesis [40, 41].
The couplings of the Higgs to photons Hγγ and gluons Hgg are induced at the quantum level, even in the Standard Model (SM), and thus are interesting probes of New Physics (NP) since both the SM and NP contributions enter at the same level. On the one hand, the updated CMS analysis [42] gives a signal strength for the diphoton which is now compatible with the SM, compared to the previous one. On the other hand, the updated ATLAS analysis [43] still observes a slight excess of events in this channel but recent measurements of the H → γγ differential cross sections do not show significant disagreements with expectations from a SM Higgs [44].
The search for another important loop-induced Higgs decay channel, H → γZ, is also performed by the ATLAS and CMS experiments [45,46]. Within the SM, the partial width for this channel ΓγZ is about two thirds of that for the diphoton decay and its measurement can also provide insights about the properties of the boson, such as its mass, spin and parity [47] thanks to a clean final state topology. No excess above SM predictions has been found in the 120-160 GeV mass range and first limits on the Higgs boson production cross section times the H → γZ branching fraction have been derived [45,46]. The collaborations set an upper limit on the ratio
5.1. INTRODUCTION ΓγZ/ΓSM
γZ < 10. A measurement of ΓγZ can also provide insights about the underlying dynamics of the Higgs sector since new heavy charged particles can alter the SM prediction, just as for the H → γγ channel, without affecting the gluon-gluon fusion Higgs production cross section [48]. Moreover, the measurement of H → γZ and its rate compared to H → γγ is crucial for broadening our understanding of the EWSB pattern [49–51]. Testing the SM nature of this Higgs state and inspecting possible deviations in its coupling to SM particles will represent a major undertaking of modern particle physics and a probable probe of models going beyond the Standard Model (BSM).
Despite the fact that no significant deviation from the SM has been observed, there are many theoretical arguments and observations from astroparticle physics and cosmology supporting the fact that it cannot be the final answer for a complete description of Nature. If New Physics must enter the game, what the experimental results told us so far is that any BSM should exhibit decoupling properties. Among BSM, supersymmetry (SUSY), is probably the best motivated and most studied framework. Its minimal incarnation, the MSSM, although possessing such a decoupling regime, relies heavily on the features of the stop sector to reproduce a 125 GeV Higgs, see [52–55]. The introduction of an additional gauge-singlet superfield ˆS to the MSSM content, whose simplest version is dubbed as the Next-to-Minimal Supersymmetric Standard Model (NMSSM) [16,56], relaxes the upper bound on the Higgs mass and alters the dependence with respect to the stop sector. The singlet term provides an extra tree-level contribution to the Higgs mass matrix such that the MSSM limit can be exceeded, already at tree level [57–59]. The neutral CP-even Higgs sector is then enlarged with three states h0
i, where i ranges from 1 to 3 and ordered in increasing mass. In this context the lightest CP-even Higgs state might well be dominantly singlet with reduced couplings to the SM and thus could remain essentially invisible at colliders: the SM-like Higgs state would then be the second lightest and a small mixing effect with the singlet would in turn shift its mass towards slightly higher values. The NMSSM possesses another virtue, in addition to the ones of the MSSM: the so-called µ problem of the MSSM [60] can be circumvented as this term is dynamically generated once the singlet field gets a vacuum expectation value (vev) [16, 56]. All in all, the NMSSM appears now as more appealing than the MSSM and has received considerable attention [61–82].
In the present work, we investigate the γZ decay channel of the SM-like Higgs boson h of the NMSSM and its correlation with H → γγ. We compute these two decay widths with the help of the automatic code SloopS [33, 34], initially designed to tackle one-loop calculations in the MSSM [83–86]. This code has been recently further developed to deal with the NMSSM extended field content and applied to Dark Matter [87–89] and Higgs phenomenology [90]. Thanks to this implementation, all the relevant particles running in the loops are properly taken into account, in particular the non-diagonal contributions due to the non-diagonal couplings of the Z boson to charginos and sfermions. Our results are consistent with those presented in [91]. As compared to [91], we perform a more thorough exploration on the parameter space of the NMSSM, in particular considering also the small λ region, and we compute the expected signal strengths for both the vector boson fusion production mode (VBF) and the gluon fusion mode (gg). In addition we impose the most recent collider constraints on the Higgs sector using HiggsBounds [92] and HiggsSignals [93] to require that one of the Higgses fits the properties of the particle observed at LHC, thus illustrating that the most severe deviations from the SM expectations for H → γZ are already constrained. We further explicitly distinguish the case
BOSON Z DANS LE NMSSM
where the 125 GeV Higgs is the lightest or second lightest CP-even Higgs in the NMSSM. This work is organised as follows. In the first part we quickly review the CP-even Higgs sector of the NMSSM relevant for our work, in the second part we discuss the calculation of the H → γγ(Z) partial widths and review the effects of SM and SUSY particles inside the loops. In the next section we present the implementation and the numerical evaluation of the partial width within SloopS and then we carry out a numerical investigation to explore to which extent the signal can be enhanced in the NMSSM after applying various experimental constraints. In the last section we draw our conclusions.