aa r X i v : . [ h e p - ph ] J un LPT Orsay 13-50
Higgs pair production in the NMSSM at the LHC
Ulrich Ellwanger
Laboratoire de Physique Th´eorique, UMR 8627,CNRS and Universit´e de Paris–Sud, F-91405 Orsay, France
Abstract
In the NMSSM it is well possible to find an additional Higgs boson with a massbelow 125 GeV which remains invisible in standard Higgs boson search channels.We study the Higgs pair production cross sections times branching fractions in thisscenario, focusing on gluon fusion and the b ¯ b + τ + τ − and b ¯ b + γγ final states. Summingover the SM-like and the lighter Higgs states, the production cross sections timesbranching fractions are never below the ones for SM Higgs pair production. Sizableenhancements of the signal rates are also possible, notably if a lighter Higgs stateis produced. However, the rates involving at least one lighter Higgs boson are notalways sufficiently large to guarantee its discovery. Introduction
The couplings of the 125 GeV Higgs boson to electroweak gauge bosons, third generationfermions and the loop induced couplings to gluons and photons have been measured by theATLAS and CMS collaborations with an astonishing precision already after the 7-8 TeVruns [1, 2]. Clearly, these measurements impose constraints on models with extended Higgssectors.However, extended Higgs sectors can manifest themselves mainly through deviationsof Higgs self couplings from the values within the Standard Model (SM), which can nowbe determined once the Higgs mass is known. For this reason, measurements of Higgs selfcouplings (actually only the trilinear self coupling seems accessible in the foreseeable future)at the LHC at 14 TeV at high integrated luminosity and/or at future colliders are of utmostimportance.The trilinear Higgs self coupling contributes to Higgs pair production which allows,in principle, its measurement. Many corresponding studies have been performed in theSM and its supersymmetric (Susy) extensions, notably at hadron colliders and consideringgluon fusion [3–30], the production mode with the largest cross section.Among the Susy extensions of the SM, the Next-to-Minimal Supersymmetric StandardModel (NMSSM) [31] has received considerable attention [32–54], since a Higgs mass of125 GeV is more natural within its parameter space than in the MSSM. Due to the ad-ditional gauge singlet superfield S compared to the MSSM, the NMSSM contains threeneutral CP-even Higgs states H i , i = 1 , , H SM near 125 GeV is actually the second lightest state H , wheras the lightest state H is mostly singlet-like; then mixing effects contribute to the increase of the mass of H SM .A lighter mostly singlet-like state H can well be compatible with the constraints fromLEP [55] (simultaneously with a SM-like state near 125 GeV [45]), and might even explainthe mild ( ∼ σ ) excess in e + e − → Zb ¯ b near M b ¯ b ∼
100 GeV [55].The pair production of two states H SM in the NMSSM has been considered recentlyin [26, 30]. In [26] it was found that, in the presence of light stops present in the loop-induced amplitudes, the production rate can be considerably larger than in the SM. In [30]it was emphasized that loop corrections to the trilinear Higgs couplings and hence to thepair production of two states H SM can potentially be large. (The range of the trilinear Higgscouplings within some regions of the parameter space of the NMSSM have been studiedin [56].)In the present paper we concentrate on the case where the mostly SM-like state H SM near 125 GeV corresponds to H , and study the prospects of H + H , H + H and H + H pair production. Notably in the case of a small non-singlet component of H , H will hardlycouple to electroweak gauge bosons and fermions, and be practically invisible in standardHiggs search channels. However, the NMSSM-specific H H H and/or H H H couplingscan still be large. These would allow to detect H in H → H + H decays if M H < ∼ M H / M H > ∼ M H /
2, the case considered here, Higgs pair production might be the only wayto observe the H state.In principle H could also be produced in H decays [51, 57]. However, this strategywould also fail if H is too heavy. Subsequently we make the pessimistic assumption that1his is the case, and that H does not contribute to the Higgs pair production cross section.Likewise we assume that stops are too heavy to affect the Higgs pair production crosssection; otherwise stops are likely to be discovered before the observation of Higgs pairproduction processes. Also light pseudoscalars are assumed to be absent. If the assumptionsof a heavy H , heavy pseudoscalars and heavy stops turn out to be wrong, we would bepleased to redo the calculations with correspondingly known masses.At present the most promising search strategy for Higgs pair production at the LHC at14 TeV seems the application of subjet-based analysis techniques to boosted kinematicalregimes of the dihiggs system [19]. According to [19], the b ¯ b + τ + τ − final state seemsaccessible by this method. In the case of the NMSSM, the branching fractions into b ¯ b and τ + τ − can differ from the SM. Notably the lighter state H will hardly decay into electroweakgauge bosons W ± and Z , which implies a somewhat larger branching fraction into b ¯ b (and τ + τ − ) than the ∼
60% of a SM-like Higgs boson. The corresponding branching fractionsof H can well be reduced. For these reasons we will study the Higgs pair production crosssections multiplied by the corresponding branching fractions normalized to the SM.The b ¯ b + W + W − final state in boosted kinematical regimes has been analysed as wellusing jet substructure techniques [21]. However, due to the reduced branching fractionsof H into W + W − we will not consider this channel here. More recently, analyses of the b ¯ b + b ¯ b final state [27] have been proposed as promising in the case of Higgs pair productionvia heavy resonances.Another possible final state is b ¯ b + γγ [17]. In spite of the limited statistics, Higgs pairproduction may be observable in this channel if fake b -jets and photons are sufficiently undercontrol. Hence we extend our analysis to this final state, again multiplying the Higgs pairproduction cross sections by the corresponding branching fractions normalized to the SM.In the case of the state H near 125 GeV, the measured couplings [1,2] imply bounds onpossible deviations from the SM. Here we will apply bounds (at the 95% confidence level)on all couplings from a recent combination of the ATLAS, CMS and Tevatron results [58].These constrain not only the H branching fractions and couplings, but all NMSSM specificparameters.In the next Section we describe our calculations, in Section 4 our results. Conclusionsare devoted to Section 3. In any model for the Higgs sector, the effective potential describes the Higgs vacuum ex-pectation values (vevs), the (running) Higgs masses and Higgs self couplings. Radiativecorrections to the effective potential will affect all these quantities simultaneously. Giventhe knowledge of the values of the SU (2) × U (1) symmetry breaking vev and the SM-likeHiggs mass, it is crucial to compute the Higgs self couplings at the same level of precisionas the SM-like Higgs mass.For a given set of input parameters (see below), the radiative corrections to the Higgsmasses and couplings in the NMSSM can be sizable [30, 31]. For not too light Higgs2tates circulating in the loops (as considered here), the dominant radiative correctionsto the effective potential originate from stop/top quark loops. Since we scan over the inputparameters of the general Z -invariant NMSSM (and, to some extent, radiative correctionsto couplings can be absorbed by modifications of the input parameters such that the SM-likeHiggs mass remains unchanged) we confine ourselves to the dominant radiative correctionsfrom stop/top quark loops to masses and Higgs self couplings in the leading logarithmicapproximation. To this end we employ a correspondingly modified version of the codeNMSSMTools [59–61].The field content of the Higgs sector of the NMSSM are two SU(2) doublets H u , H d , anda gauge singlet S . The parameters in the Higgs sector of the general Z -invariant NMSSMinclude two dimensionless Yukawa couplings λ (proportional to a term SH u H d in the su-perpotential) and κ (a trilinear singlet self coupling in the superpotential), correspondingsoft Susy breaking terms A λ , A κ , and three soft Susy breaking mass terms for H u , H d , and S . The three soft Susy breaking mass terms can be traded for the known value of M Z andthe two variables tan β ≡ h H u i / h H d i , µ eff ≡ λ h S i (for more details see [31]). Hence we areleft with the free variables λ, κ, A λ , A κ , tan β and µ eff . (1)A mass of about 125 GeV of a mostly SM-like Higgs boson H is obtained naturally forlarger values of λ and relatively low values of tan β . The results below are obtained from ascan over these parameters in the ranges λ = 0 . − . , κ = 0 . − . ,A λ = 300 − , A κ = − − , tan β = 1 . − , µ eff = 120 −
300 GeV . (2)Since we confine ourselves to the leading stop/top quark induced radiative correctionsto the Higgs potential, we only have to specify the stop masses and mixing parameter. Wechoose 1 TeV for the stop masses (allowing to safely neglect stop contributions to Higgsproduction in gluon fusion) and A top = 0 for the mixing parameter. (Large values for A top are not necessary in order to obtain a mostly SM-like Higgs boson at 125 GeV throughradiative corrections.)The Higgs spectrum in the above range of parameters contains no light CP-odd states.Together with the relatively low values of tan β , the constraints from B -physics implementedin NMSSMTools are always satisfied. More relevant are the constraints we impose on theCP-even Higgs sector.First, we require a CP-even Higgs boson H of a mass of 125 . ± b -quarks and τ -leptons are within the95% confidence limits obtained in [58] from a combination of the measurements at ATLAS,CMS and the Tevatron. (In the NMSSM at low tan β one can safely assume that the Higgscouplings to b -quarks and τ -leptons are rescaled by the same amount with respect to theSM, so that the corresponding measurements can be combined.)3hese bounds imply that, within the above parameter space of the NMSSM, the cou-plings of the Higgs boson near 125 GeV to electroweak gauge bosons and fermions cannotdeviate dramatically from the SM values, just the loop-induced coupling to photons can besignificantly larger (depending on the production mode, see [58]).On the mass of the lightest CP-even Higgs boson H we impose M H >
65 GeV. Oth-erwise H → H + H decays (with H nearly on shell) would be possible with much largersignal rates than the Higgs pair production considered here, allowing to detect H in single H production channels. Subsequently we assume that such on-shell Higgs-to-Higgs decayswill not be observed.The code NMSSMTools provides us with all required parameters (including the trilinearHiggs self couplings) for the calculation of the Higgs pair production cross sections in gluonfusion of all possible combinations of H and H states. For the calculation of the Higgs pairproduction cross sections we use the public code HPAIR [62] which includes QCD correctionsand a low energy theorem for the top quark loop. We modified this code according to ourneeds and verified that, in cases where H or H are SM-like and the other state is omitted,a SM-like pair production cross section is obtained. (For a 125 GeV SM Higgs boson, HPAIR gives a production cross section of about 32 . First we show our results for the trilinear Higgs couplings obtained from NMSSMTools fromthe scan described in Section 2. These are defined in the convention where the the trilinearterms in the effective potential are written as V eff = 13! X i,j,k g ( H i , H j , H k ) H i H j H k + ... , (3)in which the trilinear Higgs coupling of the SM has a value of about 190 GeV. Our sub-sequent results will be shown as function of M H which we study in the range M H ∼ −
125 GeV (always below the SM-like M H ). In Fig. 1 we show scatter plots of g ( H , H , H ), g ( H , H , H ), g ( H , H , H ) and g ( H , H , H ).We see that the trilinear coupling of the SM-like state H (top left) is typically close to itsSM value, except for a possible reduction if M H > ∼
100 GeV. The couplings g ( H , H , H )and g ( H , H , H ) are smaller, just g ( H , H , H ) can assume similar values as g ( H , H , H )for M H > ∼
100 GeV. The coupling g ( H , H , H ) can vary from small up to SM-like values,with no specific dependence on M H . Values significantly larger than in the SM are notobserved.Next we turn to the Higgs pair production cross sections in gluon fusion at the LHC at14 TeV. As stated in the Introduction, we make the conservative assumptions that neitherlight stops nor the heavy state H contribute to the cross sections. Since observations ofHiggs pair production will certainly require large integrated luminosities of at least 300-600 fb − , these particles should otherwise have been observed by then in which case the4 M H1 [GeV] g ( H , H , H ) [ G e V ]
60 70 80 90 100 110 120 130 M H1 [GeV] -50050100150200 g ( H , H , H ) [ G e V ]
60 70 80 90 100 110 120 130 M H1 [GeV] -50050 g ( H , H , H ) [ G e V ]
60 70 80 90 100 110 120 130 M H1 [GeV] -50050100150200250 g ( H , H , H ) [ G e V ] Figure 1: Scatter plots of the trilinear Higgs couplings g ( H , H , H ) (top left), g ( H , H , H ) (top right), g ( H , H , H ) (bottom left) and g ( H , H , H ) (bottom right)as function of M H .present calculations can be correspondingly corrected. Besides the triple Higgs couplingsshown before, also the Higgs top couplings are relevant here.We normalize all Higgs pair production cross sections to the SM value of about 32.6 fbfrom HPAIR . First, this value will certainly be used as “benchmark” by the experimentalcollaborations in order to test the trilinear Higgs coupling of the SM. Second, one can expectthat this ratio should remain approximately invariant under higher order QCD correctionsand the replacement of the heavy top quark limit in
HPAIR by the full matrix element,although the latter may be relevant for specific simulations [19]. In Fig. 2 we show thenormalized Higgs pair production cross sections for the final states H + H , H + H , H + H and the sum over all final states.In Fig. 2 we see no significant enhancement of the cross section for the final state H + H (in agreement with the results obtained in [26] for heavy stops), a possible enhancementfor the final state H + H for M H > ∼
100 GeV, and always below-the-SM values for thefinal state H + H . Unfortunately there exist regions in the parameter space where thecross sections for both final states H + H and H + H are small. Since H has typically5 M H1 [GeV] σ ( H H ) / σ S M
60 70 80 90 100 110 120 130 M H1 [GeV] σ ( H H ) / σ S M
60 70 80 90 100 110 120 130 M H1 [GeV] σ ( H H ) / σ S M
60 70 80 90 100 110 120 130 M H1 [GeV] σ T O T / σ S M Figure 2: The Higgs pair production cross sections relative to the SM for the final states H + H (top left), H + H (top right), H + H (bottom left) and the sum over all finalstates (bottom right).reduced couplings to top quarks, its production has to rely essentially on a virtual mostlySM-like H in the s-channel. However, the then relevant trilinear couplings g ( H , H , H )and g ( H , H , H ) can simultaneously be small leading to a poor production rate for both H + H and H + H final states, which are relevant for the H discovery. The good newsis, on the other hand, that the sum over all final states is never below the SM value, butup to ∼ . M H > ∼
100 GeV.However, Higgs pair production will only be measurable in specific channels. First weconsider the b ¯ b + τ + τ − final state which has been studied in [19]. Since the branchingfractions of both H and H can differ significantly from a SM-like Higgs boson (limited, inthe case of H , by the combinations of the LHC and Tevatron measurements) one shouldweight the production cross sections by the corresponding branching fractions relative tothe SM. In the NMSSM for low tan β one can assume that the relative variations of thebranching fractions into b ¯ b and τ + τ − are practically the same, since both couplings originatefrom the H d component of H and H . Hence, in the case of H + H , these cross sectionsweighted by the branching fractions will be the same for H or H decaying into τ + τ − .6 M H1 [GeV] σ ( H H ) bb + ττ / σ S M , bb + ττ
60 70 80 90 100 110 120 130 M H1 [GeV] σ ( H H ) bb + ττ / σ S M , bb + ττ
60 70 80 90 100 110 120 130M H1 [GeV]00,20,40,60,81 σ ( H H ) bb + ττ / σ S M , bb + ττ
60 70 80 90 100 110 120 130 M H1 [GeV] σ T O T , bb + ττ / σ S M , bb + ττ Figure 3: The Higgs pair production cross sections relative to the SM for the final states H + H → b ¯ b + τ + τ − (top left), H + H → b ¯ b + τ + τ − (top right), H + H → b ¯ b + τ + τ − (bottom left) and the sum over all H i into b ¯ b + τ + τ − (bottom right).In Fig. 3 we show the normalized Higgs pair production cross sections for the final states H + H → b ¯ b + τ + τ − , H + H → b ¯ b + τ + τ − , H + H → b ¯ b + τ + τ − and the sum over all H i into b ¯ b + τ + τ − .Although the cross sections weighted by the branching fractions relative to the SMdiffer in general from the full relative cross sections shown in Fig. 2 for given points inparameter space, the general pattern is similar: the sum over cross sections for all Higgspairs is practically never below the SM value, and can be amplified by a factor ∼ .
4. Thisoriginates from possible H + H → b ¯ b + τ + τ − processes, whose cross sections can reachbeyond-the-SM values by itself.Unfortunately the production of the lighter Higgs boson H in either the H + H → b ¯ b + τ + τ − or H + H → b ¯ b + τ + τ − final state does not always have a cross section ofthe order the SM Higgs pair production. Hence the detection of H in this channel is aspectacular possibility, but not guaranteed.Another potential Higgs pair discovery channel is the b ¯ b + γγ final state [17]. Again weconsider the production cross sections multiplied by the branching fractions relative to the7 M H1 [GeV] σ ( H H ) bb + γγ / σ S M , bb + γγ
60 70 80 90 100 110 120 130M H1 [GeV]00,511,522,533,544,55 σ ( H bb H γγ ) / σ S M , bb + γγ
60 70 80 90 100 110 120 130 M H1 [GeV] σ ( H γγ H bb ) / σ S M , bb + γγ
60 70 80 90 100 110 120 130 M H1 [GeV] σ ( H H ) bb + γγ ) / σ S M , bb + γγ
60 70 80 90 100 110 120 130 M H1 [GeV] σ T O T , bb + γγ / σ S M , bb + γγ Figure 4: The Higgs pair production cross sections relative to the SM for the final states H + H → b ¯ b + γγ (top left), ( H → b ¯ b ) + ( H → γγ ) (top right), ( H → γγ ) + ( H → b ¯ b )(middle left), H + H → b ¯ b + γγ (middle right) and the sum over all H i into b ¯ b + γγ (bottom).ones of a 125 GeV SM-like Higgs boson, which would be the target once such searches will beperformed. In this case the final states ( H → b ¯ b ) + ( H → γγ ) and ( H → b ¯ b ) + ( H → γγ )8ave to be considered separately. The relative cross sections times branching fractions forall possible distinct final states together with their sum are shown in Fig. 4.In Fig. 4 we see cases of spectacular enhancements with respect to the SM cross sectionin this channel. In the final state ( H → b ¯ b ) + ( H → γγ ) (up to a factor ∼ .
5, top right)these originate from an enhancement of the branching fraction for H → γγ by a factorup to ∼ .
3, consistent with the present measurements of signal rates at the LHC due to aslightly reduced H production cross section, together with enhancements of the branchingfraction for H → b ¯ b and the production cross section into H + H . Due to the absence ofthe latter factors and a reduction of the branching fraction for H → b ¯ b , the enhancementsof the cross sections in the final state H + H → b ¯ b + γγ for the same points in the top leftof Fig. 4 are less spectacular, but lead to relative signal rates up to a factor ∼ . H + H and H + H . (These final states differ, however,in the invariant mass of the b ¯ b system corresponding to M H or M H , respectively.)Also in the distinguishable final state ( H → γγ ) + ( H → b ¯ b ) enhancements up to afactor ∼ . H → γγ , a possibility pointed out in [63]. On the other hand, as before it is not guaranteedthat any cross section involving H is measurably large; one just ends up with a “no-losetheorem” stating that at least the cross section for the sum over all H , H final statesnever falls below the SM cross section. The regions in the NMSSM parameter space giving rise to another mostly singlet-like Higgsboson H with a mass below 125 GeV are particularly natural, since here mixing effectslead to an increase of the mass of the mostly SM-like state H . In the present work westudied the possible impact of such mixings on the Higgs pair production cross sections ingluon fusion at 14 TeV and the b ¯ b + τ + τ − and b ¯ b + γγ final states. A priori it was not clearwhether, even after summing over the H , H final states, the cross sections are alwaysas large as in the SM for a single 125 GeV Higgs boson. Our results indicate that this isthe case. Cross sections larger than in the SM are possible, notably in the b ¯ b + γγ finalstate involving both H and H . But unfortunately it is not guaranteed that the additionalstate H has always a sufficiently large production rate in Higgs pair production to bedetectable; in this case one would have to rely on either its direct production, or on decaysof the heavier state H into H .On the other hand, given the possibility that H is visible only in Higgs pair productionprocesses, sufficiently flexible cuts should be applied in future analyses in order not to missit even for M H well below 125 GeV. Acknowledgements
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