Search for a lighter Higgs Boson in the Next-to-Minimal Supersymmetric Standard Model

After the discovery of the Higgs boson with mass at approximately 125 $GeV$ at the LHC, many studies both from the theoretical and experimental sides have been performed to search for a new Higgs Boson lighter than the 125 $GeV$ Higgs boson. We explore the possibility of constraining a lighter neutral scalar Higgs boson $h_{1}$ and a lighter pseudo-scalar Higgs boson $a_{1}$ in the Next-to-Minimal Supersymmetric Standard Model by restricting the next-to-lightest scalar Higgs boson $h_{2}$ to be the LHC observed Higgs boson after the phenomenological constraints and the constraints from experimental measurements. Such lighter particles are not yet completely excluded by the latest results of the search for a lighter Higgs boson with the diphoton decay channel from LHC data. Our results show that for a lighter scalar Higgs boson some new constraints on the Next-to-Minimal Supersymmetric Standard Model could be obtained at the LHC if such a search is performed by the experimental collaborations with more data. The discovery potential of other interesting decay channels of such a lighter neutral scalar and a pseudo-scalar particle are also discussed.


Introduction
The Standard Model (SM) of particle physics has been very successful in explaining high-energy experimental results. A Higgs boson with mass at approximately 125 GeV was discovered at the LHC with its properties consistent with the SM predicted Higgs boson [1][2][3][4]. However, the observed signal strength of the Higgs boson is somewhat biased against the SM prediction within 1 or 2 times of the experimental uncertainty in each final state. Many important questions dealing with the nature and the origin of the Higgs boson discovered at the LHC remain unanswered. The Higgs boson can be embedded in some beyond standard model (BSM) such as Supersymmetric models which can easily accommodate the discovered Higgs boson and address the deficiencies of the Standard Model.
Supersymmetry (SUSY) [5][6][7][8] is one of the theoretical options for BSM physics. It introduces a new symmetry between fermions and bosons. The most com-mon framework and minimal realisation of SUSY is the Minimal Supersymmetric Standard Model (MSSM) [9][10][11] which keeps the number of new fields and couplings to the minimum. In the MSSM, the Higgs sector contains two Higgs doublets, which leads to a spectrum including two CP-even, one CP-odd and two charged Higgs bosons. The Lagrangian of MSSM contains a supersymmetric mass term, the µ-term. This mass term is invariant under supersymmetry and therefore it seems unrelated to the electroweak scale, although it is phenomenologically required to be in this scale. This leads to the well known "µ problem" [12,13] in the MSSM. Additionally the MSSM suffers from another serious flaw, the little hierarchy problem [14,15]. The simplest solution is the so-called Next-to-Minimal Supersymmetric Standard Model (NMSSM) by introducing a new gauge singlet superfield which only couples to the Higgs sector in a similar way as the Yukawa coupling and can generates dynamically a µ parameter of the order of the SUSY breaking scale to solve the "µ problem" and the little hierarchy problem without much fine-tuning [16][17][18][19][20][21][22][23]. Meanwhile, this new singlet adds additional degrees of freedom to the NMSSM particle spectrum. In CP conserving case, which is assumed in this paper, the seven observable states in the Higgs sector can be classified as three CP-even Higgs bosons h i (i = 1,2,3), two CP-odd Higgs bosons a j (j = 1,2) and two charged Higgs bosons h ± .
The extended parameter space of the NMSSM gives rise to a rich and interesting phenomenology. The lightest CP-even Higgs bosons (h 1 ) in the mass range down to approximately 80 GeV , by assuming the next-tolightest CP-even Higgs boson h 2 as the new particle at m ∼125 GeV , was studied with the diphoton (γγ) final state in [24]. Higgs decaying into γγ is one of the two most promising channels for the Higgs discovery at the LHC. Discovery prospects of a light scalar in the NMSSM [25] and Two Higgs Doublet Models (2HDM) [26] In this paper, we explore the possibility of constraining a lighter neutral scalar Higgs boson h 1 and a lighter pseudo-scalar Higgs boson a 1 in the NMSSM by restricting the next-to-lightest scalar Higgs boson h 2 to be the observed 125 GeV state by comparing the lighter particles in NMSSM with the latest CMS results with the full 2016 dataset at √ s = 13 TeV, after the constraints from the experimental measurements and other sources. The structure of this paper is organized as follows. In section 2, we introduce the Higgs sector of the NMSSM briefly, the details of different constraints and the parameter ranges we choose. Section 3 shows the results of the study for the lighter scalar Higgs boson a 1 . Section 4 is dedicated to the study of the case where the lighter resonance is the pseudo-scalar particle a 1 . Finally the conclusions are presented in section 5.

Brief description of the NMSSM
The general NMSSM includes two Higgs superfieldŝ H u ,Ĥ d and one additional gauge singlet chiral superfield S. We consider the NMSSM with a scale invariant superpotential W N M SSM and the corresponding soft SUSYbreaking masses and couplings L sof t , both of which are limited to the R-parity and CP-conserving case. The superpotential W N M SSM depending on the Higgs super-fieldsĤ u ,Ĥ d andŜ is [16] In the right-hand side of the above formula, the first three terms are the Yukawa couplings of the quark and lepton superfields. The fouth term replaces the µ-term µĤ uĤd of the MSSM superpotential. The last term, cubic in the singlet superfield, is introduced to avoid the appearance of a Peccei-Quinn axion, tightly constrained by cosmological observation [16]. The corresponding soft SUSY-breaking masses and couplings are given in the SLHA2 [29] conventions by [16] −L sof t = m 2 In Eq. 1 and Eq. 2, clearly the non-zero vacuum expectation value s of the singletŜ of the order of the weak or SUSY-breaking scale gives rise to an effective µ-term with µ ef f = λs. ( which solves the "µ problem" of the MSSM. Meanwhile, the three SUSY-breaking mass-squared terms for H u , H d and S appearing in L sof t can be expressed in terms of their VEVs (Vacuum Expectation Value) through the three minimization conditions of the scalar potential. Therefore, the Higgs sector of the NMSSM is described by the following six parameters in which each pair of brackets denote the VEV of the respective field inside them. In addition to these six parameters of the Higgs sector, during the studies as described below we need to specify the squark and slepton soft SUSY-breaking masses and the trilinear couplings as well as the gaugino soft SUSY-breaking masses to describe the model completely.

Constraints on NMSSM and its parameters
For the studies in this paper, the program package N M SSM T ools (version 5.2.0) [30] is used for the calculation of the SUSY particle and NMSSM Higgs boson spectrum and branching ratios (BR), and the reduced couplings of NMSSM Higgs bosons. N M SSM T ools contains four subpackages: N M HDECAY , N M SDECAY , N M SP EC and N M GM SB. The Fortran code N M HDECAY provides the Higgs boson masses, decay widths, branching ratios and reduced couplings to particles which will be used in this paper. In this paper, we consider the four Higgs production modes, including the gluon-gluon fusion through a heavy quark loop (ggh), the vector boson fusion proces (vbf), the associate production of Higgs with vector boson (vh) and the associated production of a Higgs with a pair of top quarks (tth). The cross section for different production modes of each NMSSM Higgs boson are obtained from a linear interpolation of the 5 GeV per step cross section values taken from the handbook of LHC Higgs Cross Section Working Group [31] for a SM-like BSM Higgs boson, and multiplied it by the reduced couplings of each NMSSM Higgs boson to gluons κ 2 g , gauge bosons κ 2 V and fermions κ 2 f , which are given by the output of NMSSMTools. The N M SSM T ools package applies all phenomenological constraints including the absence of Landau singularities below the GUT scale and the constraints from flavour physics, dark matter relic density Ωh 2 , anomalous magnetic moment of the muon (g − 2), Higgs searches in various channels and direct searches of SUSY particles at LEP, Tevatron and LHC, with details described in [30].
The six NMSSM specific parameters as described above are varied in the following ranges 0.55 < λ < 0.75, 0.05 < κ < 0.3, 3 < tan β < 6, We are more interested in large values of λ, κ (but small enough to avoid Landau pole below GUT scale) and low values of tan β, which naturally keep the amount of finetuning as low as possible.We found that wider ranges of the trilinear couplings A κ , A λ , and µ ef f have practically no impact on our results. The With the N M SSM T ools package and the general NMSSM model, we have performed random scans with about 10 billion points in the specific parameter space described above. For each point in the parameter space satisfying the phenomenological constraints, we require that a SM-like Higgs state, the next-to-lightest scalar Higgs boson h 2 in NMSSM, must be within the allowed theoretical uncertainties 3 GeV around the measured mass 125.1 GeV at the LHC using the whole Run1 data [32] (125.1 ± 3 GeV ) and couplings of h 2 to gauge bosons and fermions in the 3σ ranges of the best-fit values given in [33,34]. After these constraints, about 1.40 million points remain. Fig. 1 show the mass distributions of the two lightest scalar Higgs bosons h 1 and h 2 , and the signal strengths of h 2 → γγ versus the signal strengths of

Results for a lighter scalar Higgs boson
In this section we will explore the possibility that the signal may be given by the lightest scalar Higgs boson h 1 in NMSSM. We make a detailed comparison with the sensitivity of the CMS search at 13 TeV. About 1.25 million points are selected from the random scans passing the phenomenological constraints, the mass and signal strength constraints on h 2 , and also the mass constraint on h 1 with mass range from 60 GeV to 120 GeV .
The left panel of Fig. 2 shows the signal strengths of h 1 decaying into diphoton µ h 1 →γγ plotted against the mass of Higgs boson h 1 (M h 1 ). It can be seen that a sizable enhancement over the SM-like Higgs rate is possible for the Higgs boson h 1 , with the largest strength ∼ 2.2 at an h 1 mass of ∼85 GeV . We note that for the mass ranges M h 1 < ∼80 GeV and M h 1 > ∼110 GeV the allowed signal strengths µ h 1 →γγ are rather lower than 1. Especially for M h 1 < ∼75 GeV , the signal strengths are below ∼0.2. The production rates in femtobarn (f b) of h 1 decaying into γγ versus M h 1 are also plotted in Fig. 2 for the combined ggh and tth production mode ((σ × BR) ggh+tth h 1 →γγ ) in the middle panel, and for the combined vbf and vh production mode ((σ × BR) vbf +vh h 1 →γγ ) in the right panel, superimposed on the public observed exclusion limits of CMS collaboration with the full 2016 dataset at √ s = 13 TeV [28] in red line. The comparisons show that there is no sensitivity in the vbf+vh production mode but many points are above the CMS observed upper limit in the ggh+tth production mode for a light Higgs boson with mass M h 1 > ∼80 GeV . For vbf+vh production mode, it's possible to obtain points above the CMS observed upper limit in near future with more proton-proton collision data accumulated at the LHC. As the points above the observed CMS upper limit are excluded at 95% Confidence Level, we can expect to exclude some NMSSM region in the parameter space thanks to this analysis. To illustrate this point, in Fig. 3 we compared several sensitivity parameters for two dif-  (color online) Two-dimensional scatter plots of the input parameters tan β vs λ, λ vs κ and µ ef f vs κ for all selected points passing the phenomenological constraints, the mass and signal strength constraints on h2, and also the mass constraint on h1 with mass range from 60 GeV to 120 GeV are shown in the top panels. The corresponding Two-dimensional scatter plots of the input parameters for the selected points further excluded by the observed upper limits of the CMS 13 T eV low-mass diphoton analysis with mass range from 70 GeV to 110 GeV are shown in the bottom panels.
Additionally we also checked the production rates of other interesting decay channels including bb, τ + τ − , W + W − , ZZ, Zγ and µ + µ − , to investigate the discovery potential of h 1 in these channels. Fig. 4 shows the production rates in picobarn (pb) for h 1 decaying into bb, τ + τ − , W + W − , ZZ, Zγ and µ + µ − , as functions of its mass M h 1 . For h 1 → bb, h 1 → τ + τ − and and h 1 → µ + µ − decays, they have tight correlations on the branching ratios although different values. So the shapes of their production rates as functions of M h 1 are similar. Also the similar shapes of production rates of h 1 → W + W − , h 1 → ZZ and h 1 → Zγ are due to the tight correlations on the branching ratios. Among these decay channels, the signal rate of h 1 → bb is quite large, as the rates can reach to 18 pb with M h 1 at around 95 GeV . For h 1 → W + W − , h 1 → ZZ and h 1 → Zγ channels, signal rates decrease with decreasing M h 1 . For bb and τ + τ − final states in the investigated mass range, the signal rates are large enough that it's much possible to detect h 1 by the experiments at the LHC via these two channels.

Results for a lighter pseudo-scalar Higgs boson
As the kinematic behaviour of the two photons coming from the decay of a pseudo-scalar particle is very similar to the the one coming from a scalar particle [35], we can directly apply the CMS study as for the scalar case to constrain a possible light pseudo-scalar. Since the mass of the heavier pseudo-scalar a 2 from NMSSM scans is much larger than the observed Higgs at LHC, we focus on the lightest pseudo-scalar a 1 in the following studies. From the random scans after the phenomenological constraints and the mass and signal strength constraints on h 2 , the mass distributions of the the lightest pseudo-scalar a 1 versus the scalar Higgs bosons h 2 are shown in the top left panel of Fig. 5. Then about 187k points are selected after the constraint of a 1 within the mass range from 60 GeV to 120 GeV . The lightest CP odd Higgs boson a 1 primarily decays to fermions due to the absence of tree level couplings with gauge bosons. As shown in the top right panel of Fig. 5, it decays dominantly to bb with BR ∼90% for the low mass range. For a 1 → γγ with a 1 in the mass range from 60 GeV to 120 GeV , the BR is less than 7 × 10 −4 for all the selected points. The signal rates of a 1 → γγ for all the selected points in the combined ggh and tth production mode, as shown in the bottom left panel, are less than 0.3 f b which are far below the CMS observed upper limits as the red line shown in the middle panel of Fig. 2. Also for the combined vbf and vh production mode, the signal rates of a 1 → γγ with the points shown in the bottom right panel of Fig. 5 are also far below the CMS observed upper limit on production cross-section times branching ratio as the red line shown in the right panel of Fig. 2. We therefore conclude that CMS had no sensitivity to a light pseudo-scalar in the diphoton final state with the data collected in year 2016. Mass spectrum of the lightest pseudo-scalar Higgs bosons a1 versus h2 (top left panel) after the phenomenological constraints and constraints on h2, distributions of the branching ratios of a1 → bb versus a1 → γγ (top right) and the signal rates of a1 → γγ versus the mass of a1 for different combined production modes with (σ × BR) ggh+tth a 1 →γγ for ggh+tth (bottom left) and (σ × BR) vbf +vh a 1 →γγ for vbf+vh (bottom right) after further mass constraint on a1.
We have also checked the production rates of other interesting decay channels of a 1 to investigate the discovery potential of a 1 in these channels. Fig. 6 shows the production rates in femtobarn (f b) for a 1 decaying into bb, τ + τ − , W + W − , ZZ, Zγ and µ + µ − , as functions of its mass M a 1 . As expected, a 1 → bb is the dominant decay channel with signal rates up to about 3800 f b and h 1 → τ + τ − is the sub dominant decay channel with signal rates up to about 300 f b. For bb decay of a 1 , the cross section is large enough to search for a 1 at the LHC if the large backgrounds can be well suppressed. As for the top quark pair final states, it also possible to detect low-mass a 1 in this channel. Considering the BRs of cascade decays of W and Z, it will be difficult to search for a 1 with W + W − and ZZ channels with all LHC Run2 data. It's also difficult to search for a 1 with h 1 → µ + µ − due to the small signal rates and acceptance times selection efficiency of the signal events which is ∼50% for a 125 GeV SM Higgs boson [36,37]. For lower signal rates of Zγ decay, it's impossible to search for a 1 in Zγ channel with all LHC Run2 data. Signal rates as functions of a1 mass for other interesting decay channels : (σ × BR) a 1 →bb (top left), (σ × BR) a 1 →τ + τ − (top middle), (σ × BR) a 1 →W + W − (top right), (σ × BR)a 1 →ZZ (bottom left), (σ × BR)a 1 →Zγ (bottom right) and (σ × BR) a 1 →µ + µ − (bottom right).

Conclusions
The search for an extended Higgs sector is ongoing at the LHC and represents one of the most important avenues for probing the possible structure of physics beyond the Standard Model. We explore the possibility of constraining a lighter neutral scalar Higgs boson h 1 and a lighter pseudo-scalar Higgs boson a 1 in the Nextto-Minimal Supersymmetric Standard Model by restricting the next-to-lightest scalar Higgs boson h 2 to be the LHC observed Higgs boson after the phenomenological constraints and the constraints from experimental mea-surements. Such a lighter particle is not yet completely excluded by the latest results of the search for a lighter Higgs boson with the diphoton decay channel from LHC data. For a lighter neutral scalar h 1 , we can expect to exclude some NMSSM region in the parameter space. While CMS latest results had no sensitivity to a light pseudo-scalar in the diphoton final state. Our results show that some new constraints on the Next-to-Minimal Supersymmetric Standard Model could be obtained at the LHC if such a search is performed by the experimental collaborations with more data. The discovery potential of other interesting decay channels of such a lighter neutral scalar or a pseudo-scalar particle are also discussed. For bb and τ + τ − final states of both h 1 and a 1 in the investigated mass range, it is possible to detect such lighter particles by the experiments at the LHC.