# LHC Signals of the Next-to-Lightest Scalar Higgs State of the NMSSM in the4τ Decay Channel

Authors: M. M. Almarashi
Journal: Advances in High Energy Physics
 (2021)

---

## Abstract

We study thea1a1 and Za1 decay channels of the next-to-lightest CP-even Higgs boson h2 of the NMSSM at the LHC, where the h2 is produced in gluon fusion. It is found that while the h2 discovery is impossible through the latter channel, the former one in the 4τ final state is a promising channel to discover the h2 with masses up to around 250 GeV at the LHC. Such a discovery of the h2 is mostly accompanied with a light a1, which is a clear evidence for distinguishing the NMSSM from the MSSM since such a light a1 is impossible in the MSSM.


---

## Body

## 1. Introduction

The discovery of the standard model- (SM-) like Higgs boson with a mass around 125 GeV at the LHC [1–4] can be accommodated in the framework of the next-to-minimal supersymmetric standard model (NMSSM) [5–16] without much fine tuning and as a consequence, it has acquired increasing attention. In this model, one Higgs singlet field is added to the two MSSM-type Higgs doublets in order to give a natural explanation of the μ-problem of the MSSM [17]. So, the Higgs sector of the NMSSM is phenomenologically richer than that of the MSSM due to the existence of this extra Higgs singlet.The Higgs spectrum of the NMSSM after electroweak symmetry breaking contains seven Higgs mass states, assuming CP conservation: two pseudoscalar Higgsesa1,2ma1<ma2, three scalar Higgses h1,2,3mh1<mh2<mh3, and a pair of charged Higgses h±. Following the discovery of the SM-like Higgs boson in 2012, the observation of additional Higgs bosons, if they exist, would point to the existence of supersymmetric extensions of the SM. In the NMSSM framework, the search for light Higgs bosons has been done by many authors, aiming to establish the so-called “no-lose theorem” of the NMSSM stating that one or more of the Higgs bosons of the NMSSM should be discovered at the LHC throughout the entire NMSSM parameter space [18–27]. All these studies were performed before the discovery of the Higgs boson at the LHC in 2012. Many studies have also been done on the discovery potential of other Higgs bosons of the NMSSM following the 2012 discovery [28–51].One of the interesting features of the NMSSM is that Higgs-to-Higgs decays are dominant over large regions of parameter space if they are kinematically allowed. The importance of such decays in the framework of the NMSSM has long been emphasized in the literature (see, e.g., Ref. [52]). It was found that Vector Boson Fusion (VBF) could be a suitable production channel to detect h1,2⟶a1a1 at the LHC, in which the Higgs pair decays into jjτ+τ− [19]. Both the Vector Boson Fusion and Higgs-Strahlung production mechanisms could also be useful to discover such Higgses in the 4τ final states [53]. Furthermore, some scope could be afforded by 4μ and 2τ2μ signatures in the gluon-fusion production channel [22, 54]. Higgs production in association with a bb¯ pair could also be a good means to search for the h1,2⟶Za1 at the LHC [55]. All these studies were performed prior to the Higgs discovery in 2012.In this paper, we study the LHC discovery potential for the next-to-lightest CP-even Higgs bosonh2, which is not a SM-like Higgs, decaying either into two light CP-odd Higgs bosons a1a1 or into a light a1 and a gauge boson a1Z through the gluon fusion gg⟶h2 in the 4τ final state in the NMSSM framework. We calculate the signal rates of the two processes gg⟶h2⟶a1a1⟶4τ and gg⟶h2⟶Za1⟶4τ to examine whether or not there are some regions of NMSSM parameter space where the h2 and a1 states can simultaneously be observed at the LHC (we do not consider the case of both bb¯bb¯ and bb¯τ+τ− final states because these channels are burdened by large SM backgrounds). We perform a partonic signal-to-background analysis of the h2 production. It is found that there are parameter regions of the NMSSM where the h2 and a1 signals may be found at the LHC through the process gg⟶h2⟶a1a1⟶4τ.The paper is planned as follows. In the next section, we briefly discuss the Higgs sector of the NMSSM, describing the NMSSM parameter space scans performed under current constraints. In Section3, we present the inclusive production rates of the h2 at the LHC in the 4τ final states as well as signal-to-background analysis for some benchmark points. Finally, conclusions are given in Section 4.


## 2. The Higgs Sector of the NMSSM

The scale invariant superpotential of the NMSSM in terms of the usual two MSSM-type Higgs doublet superfieldsH^u and H^d as well as the singlet one S^ is given by [8, 9].
(1)WNMSSM=MSSMYukawaterms+λS^H^uH^d+13κS∧3,where both λ and κ are dimensionless couplings. The term λS^H^uH^d is introduced to solve the μ-problem of the MSSM superpotential. When the singlet superfield develops a vacuum expectation value (VEV) S=1/2υs upon spontaneous symmetry breaking, an “effective” μ-parameter given by μeff=λS of the order of the electroweak scale will be automatically generated. The last term of the above equation is introduced to avoid the Peccei-Quinn symmetry [56, 57]. The soft breaking terms for both the doublet and singlet fields read
(2)VNMSSM=mHu2Hu2+mHd2Hd2+mS2S2+λAλSHuHd+13κAκS3+h.c.,where Aλ and Aκ are the trilinear coupling parameters of the order of SUSY mass scale mSUSY.The physical Higgs bosons arise after the Higgs fields acquire vacuum expectation values (VEVs),Hu=1/2υu, Hd=1/2υd, and S=1/2υs, and eliminating the Goldstone boson states. As a result, the potential has terms for the nonzero mass modes for the scalar fields Sii=1,2,3, pseudoscalar fields Pii=1,2, and charged fields h± given by
(3)Vmass=12S1S2S3MSS1S2S3+12P1P2MPP1P2+mh±2h+h−.One can obtain physical mass eigenstates with tree-level masses as follows. First, the elements of the mass matrix for the CP-even Higgs states at tree-level are given by [58]
(4)MS11=mA2+mZ2−12λυ2sin22β,MS12=−12mZ2−12λυ2sin4β,MS13=−12mA2sin2β+2κμeff2λλυ2μeffcos2β,MS22=mZ2cos22β+12λυ2sin22β,MS23=124μeff2−mA2sin22β−2κμeff2sin2βλλυ2μeff,MS33=18mA2sin22βλ2υ2μeff2+4κ2μeff2λ2+κAκμeffλ−14λκυ2sin2β,where mA2=2μeff/sin2βAλ+κμeff/λ, tanβ=υu/υd, and υ2=υu2+υd2.Second, the elements of the mass matrix for the CP-odd Higgs states at tree-level are [58]
(5)MP11=mA2,MP12=12mA2sin2β−6κμeff2λλυ2μeff,MP22=18mA2sin2β+6κμeff2λλ2υ2μeff2sin2β−3κμeffAκλ.Third, the mass of charged Higgs fields at tree level is given by [58]
(6)mh±2=mA2+mW2−12λυ2.It is clear from the above equations that the Higgs sector of the NMSSM at the tree level is described by the six parameters:λ, κ, tanβ, μeff, Aλ, and Aκ. Assuming CP conservation, the upper mass bound for the lightest CP-even Higgs boson of the NMSSM, if it is the SM-like Higgs, at the tree level is given by [8, 9]
(7)mh12<mZ2cos22β+λ2υ22sin22β.The last term in this expression can liftmh1 with up to 10-15 GeV higher than the corresponding one of the MSSM. So, less loop corrections are required to get the lightest Higgs, h1, to be SM-like with a mass around 125 GeV. Clearly, large values of λ and low values of tanβ are preferred to obtain a large value of the h1 at the tree level. The scenarios with mh1<125 GeV mean that the h1 is highly singlet-like so it can escape the constraints coming from LEP, the Tevatron, and the LHC. In this case, the next-to-lightest CP-even Higgs boson h2 is the SM-like Higgs of a mass around 125 GeV.In this paper, we are interested in the production of the next-to-lightest scalar Higgs bosonh2, which is not the SM-like Higgs, and its decays into either two light CP-odd Higgs bosons, a1a1, or a light CP-odd Higgs and a gauge boson, a1Z, in the mass region mh2≲300 GeV. We use the package NMSSMTools5.1.2 [59–61] which computes the masses, couplings, and decay widths of all the Higgs bosons in addition to the spectrum of supersymmetric particles. This package takes into account various theoretical and experimental constraints such as constraints from negative Higgs searches at LEP, the Tevatron, and the LHC, as well as SUSY mass limits as implemented in the package. Moreover, it takes into account constraints of upsilon, B, and K decays and also the bounds on the mass of the SM-like Higgs and its signal rates. More details about the constraints can be found on the website of the package. We have ignored the constraints on the dark matter because its nature is still unknown. We also do not take into account the constraints on the muon anomalous magnetic moment because such constraints have large theoretical uncertainties.In our parameter space, we scan by varying the tree level parameters of the NMSSM within the following ranges:(8)0.6≤λ≤0.7,−0.65≤κ≤0.65,1.6≤tanβ≤60,100≤μeff≤200GeV,−2000≤Aλ≤2000GeV,−10≤Aκ≤10GeV.Notice that we focus here on scenarios with large values ofλ and small values of both μeff and Aκ to simultaneously obtain the h2 with mh2≲300 GeV and a light a1. Remaining soft mass parameters for the scalars and gauginos in addition to the trilinear soft SUSY coupling parameters, contributing at higher order level, are set to
(i)
mQ=mU=mD=mL=mE=mQ3=mU3=mD3=mL3=mE3=3000GeV(ii)
M1=500 GeV, M2=1000 GeV, M3=3000 GeV(iii)
AU3=AD3=AE3=3000GeVWe randomly perform a scan over the above mentioned parameters and identify the parameter space of the NMSSM that passed all theoretical and experimental constraints. The outcome of our scan contains masses and branching ratios of the NMSSM Higgs bosons for all the surviving data points which have passed the constraints. As mentioned above, we have ignored the constraints on dark matter relic density. To know the effects of these constraints on the NMSSM parameter space, see, for example, Ref. [62] and references therein.


## 3. Higgs Boson Signal Rates

In this section, we discuss the discovery potential of theh2 produced in the gluon fusion gg⟶h2 at the LHC in the mass region mh2≲300 GeV. The region with mh2≳300 GeV is less promising since the cross sections for the h2 production fall quickly with increasing h2 masses. For the surviving data points obtained from the random scan, we calculate the inclusive cross sections for the h2 production by using CalcHEP [63] for the following processes:
(9)gg⟶h2⟶a1a1⟶τ+τ−τ+τ−andgg⟶h2⟶Za1⟶τ+τ−τ+τ−.Here, we consider a center-of-mass energys=14 TeV for the LHC.In Figure1, we present the mass of the next-to-lightest CP-even Higgs boson mh2 against the tree-level parameters of the NMSSM. One finds that for the surviving points, the mh2 decreases by increasing λ whereas it increases by increasing both κ and μeff. Also, it is found that for our parameter space, most of the surviving points correspond to the region with 2≲tanβ≲7 and 200≲Aλ≲800 while the distribution in Aκ is quite uniform.Figure 1
The next-to-lightest CP-even Higgs massmh2 as a function of λ and κ (a), tanβ and μeff (b), and Aλ and Aκ (c).
(a)(b)(c)Looking at Figures2 and 3, showing the correlations between mh2 and the lightest CP-even Higgs mass mh1 and between mh2 and the lightest CP-odd Higgs mass ma1 for the surviving points, it is clear that in most regions of our parameter space, the h1 is the SM-like Higgs and the h2 can only play the role of the SM-like Higgs in a small region of the parameter space. The h2 is a mixture of doublet and singlet components for the majority of points selected in our parameter space. Figure 3 shows that the smaller the ma1, the smaller the mh2. Since the surviving points have small values of Aκ, only small values of ma1 are allowed. One noteworthy feature of the figure is that the h2 can be the SM-like Higgs with mass around 125 GeV, which corresponds to a light a1 with ma1≲90 GeV.Figure 2
The mass distribution for the next-to-lightest CP-even Higgs,mh2, versus the lightest CP-even Higgs mass, mh1.Figure 3
The mass distribution for the next-to-lightest CP-even Higgs,mh2, versus the lightest CP-odd Higgs mass, ma1.Due to the mixing between the Higgs doublets and singlet, Higgs-to-Higgs decays are kinematically allowed for large area of the NMSSM parameter space, even for small masses of Higgs bosons. Also, one distinguished landmark of the NMSSM is that the existence of the lightest CP-odd Higgs bosona1 with mass values less than mZ is quite natural, which is impossible in the context of the MSSM. In Figure 4, we display the correlations between mh2 and the h2 decays into light CP-odd Higgs pairs h2⟶a1a1 (a) and into an a1 and a gauge boson Z (b). It is clear from panel (a) of the figure that the decay h2⟶a1a1 is the dominant one whenever it is kinematically open. It is found that the BR(h2⟶a1a1) ranges from around 40% to 100% see panel (a) of the figure), while the maximum BR(h2⟶Za1) is 0.1% (see the panel (b) of the figure). In fact, the dominance of a1a1 decay channel causes a suppression to other decay channels such as bb¯ and other channels.Figure 4
The next-to-lightest CP-even Higgs massmh2 plotted against both BRh2⟶a1a1 (a) and BRh2⟶Za1 (b).
(a)(b)Figure5 illustrates the inclusive h2 production rates ending up with a1a1⟶τ+τ−τ+τ− (a) and Za1⟶τ+τ−τ+τ− (b) as functions of mh2. It is shown from the figure that the h2 production rates decrease rapidly with increasing mh2. It is clear that the production rates σgg⟶h2⟶a1a1⟶τ+τ−τ+τ− are sizable, reaching up to 100 fb for small values of mh2, while the production rates σgg⟶h2⟶Za1⟶τ+τ−τ+τ− is quite small, reaching around 0.5 fb at the most. The latter production rates are clearly not enough to detect the h2 at the LHC, taking into account that leptonic tau decays are around 17.5%. In short, the inclusive production rates for h2 decaying into a1a1⟶τ+τ−τ+τ− are promising and could allow discovery of both h2 and a1 at the LHC while the production rates for h2 decaying into Za1⟶τ+τ−τ+τ− are quite small. So, we will analyze signal-to-background for the former channel as the latter channel is useless.Figure 5
The production rates in fb forσgg⟶h2·BRh2⟶a1a1⟶τ+τ−τ+τ− (a) and σgg⟶h2·BRh2⟶Za1⟶τ+τ−τ+τ− (b) as functions of mh2.
(a)(b)To claim discovery at the LHC, we have done a partonic signal-to-background (S/B) analysis based on CalcHEP. The dominant standard model backgrounds are the irreducible background coming frompp⟶τ+τ−τ+τ−(via γ and Z exchange). Here, we assume the double leptonic decay channels of the τ’s. In Table 1, we give 4 points as benchmark points for various masses of the h2 to do our analysis. Here, we assume that the tagging efficiency is 50% for tau jets, by scaling of the total cross sections. As it is shown in the table ,we have calculated the cross sections for both the signal and background processes and also the significance S/B at a center-of-mass energy s=14 TeV for the LHC. We have done that for 300 fb−1 and 1000 fb−1 of accumulated luminosity (we do such analysis without assuming any cuts. Of course, the proper cuts could improve the signal to background ratio, which we leave for the experimentalist to do). It is obvious that there is a good potential to detect the h2 decaying into a1a1⟶τ+τ−τ+τ− at the LHC in the mass region 140≲mh2≲220 GeV. The corresponding signal events are quite large of order 31680 events for mh2=140 GeV and 2364 events for mh2=220 events with 300 fb−1 of integrated luminosity. Again, these results are given without assuming any cuts, which of course is reducing the number of signal rates. Thus, we conclude that the LHC with integrated luminosity of 1000 fb−1 has the potential to discover the h2, if it is not a SM-like Higgs, with masses up to around 250 GeV. Such a discovery of the h2 is mostly accompanied with a light a1. The existence of such a light a1 is a direct evidence for distinguishing the NMSSM from the MSSM.Table 1
Four benchmark points P1, P2, P3, and P4 used in theS/B analysis.
P1P2P3P4λ0.6157060.6508280.6375900.617789κ0.2612870.2647250.3391340.387478tanβ5.22473.787383.825143.70979μeff (GeV)153.678198.766198.201199.224Aλ (GeV)646.778517.464464.215426.835Aκ (GeV)-8.009375.1126-9.723449.09329mh2 (GeV)140180220260ma1 (GeV)66649967S (fb) with 300 fb−13.168×1048.61×1032.364×1033.21×102B (fb) with 300 fb−13.9×1043.9×1043.9×1043.9×104S/B with 300 fb−1160.443.6121.6S/B with 1000 fb−1292.979.621.93


## 4. Conclusions

In this paper, we have explored the discovery prospects of the next-to-lightest CP-even Higgs state,h2, at the LHC with s=14 TeV. We have studied the detectability of the h2 in the two processes gg⟶h2⟶a1a1⟶τ+τ−τ+τ− and gg⟶h2⟶Za1⟶τ+τ−τ+τ−. We have shown that while the h2 discovery of the latter channel is impossible due to smallness of the inclusive production rates, the former channel is promising as the σgg⟶h2⟶a1a1⟶τ+τ−τ+τ− is sizable and should help discovering the h2 signals with masses up to around 250 GeV at the LHC with integrated luminosity of 1000 fb−1.After doing some analysis for signals and dominant backgrounds in the partonic level, we have proven that the discovery of both theh2 and a1 is possible at the LHC. Such a discovery of the h2 is mostly accompanied with a light a1 with ma1≲mZ. The existence of such a light a1 is a direct evidence for the NMSSM as such a light a1 is impossible in the MSSM. Of course, more experimental analyses including τ-decays, detector effects, parton shower, and hadronization are needed to claim the actual discovery potential of such Higgses at the LHC. However, we believe that our results are valuable for scientists interested in determining the NMSSM Higgs signals at the LHC.The discovery of Higgs states through the processgg⟶h2⟶a1a1⟶τ+τ−τ+τ− has in fact two merits. On the one hand, it can be a good alternative to discover both h2 and a1 that could be difficult to be discovered in a direct production. On the other hand, it can be exploited to measure the trilinear Higgs self-coupling h2a1a1.



---

*Source: 5569862-2021-06-14.xml*