Fermionic decays of NMSSM Higgs bosons under LHC 13 TeV constraints

This paper investigates the impact of the recent LHC constraints on the Higgs sector in the semi-constrained version of the Next-to-Minimal Supersymmetric Standard Model. Our analysis focuses on the parameter space for which the value of the Higgs doublet-singlet coupling, $\lambda$, is large as possible, while the ratio between the vacuum expectation values of the two Higgs doublets, $\tan\beta$, is small as possible. Under the current constraints, we present the possible fermionic decay channels and reduced cross-section into fermions final states for the lightest neutral Higgs bosons in the NMSSM, $(h_{1}$, $h_{2}$, and $a_{1})$. We found that the branching ratios of the non SM-like Higgs ($a_{1}$ and $h_{2}$) into a pair of bottom quarks are near 90\% level when the Higgs mass below 400 GeV. Moreover, the branching ratio of $h_{2}/a_{1}\rightarrow t\bar{t}$ can reach unity for all mass ranges when these bosons are mostly singlet.


Introduction
In 2012, ATLAS and CMS at the Large Hadron Collider announced the detection of a Higgs-like particle with a mass of around 125 GeV and its measurements consistent with the Standard Model's prediction [1,2]. However, several new physics models with extended Higgs sector can also accommodate 125 GeV Higgs boson, such as the Minimal Supersymmetric Standard Model (MSSM) [3,4]. The Higgs sector in the MSSM involves two Higgs doublets, which the mixing of their components leads to five Higgs states, one of them is the SM-like Higgs. To obtain a 125 GeV Higgs, the MSSM needs large quantum corrections from the third generation of squark loops [5,6]. Also, in the MSSM Lagrangian, there is a supersymmetric term, the μ-term. This term should be of a scale of the electroweak scale to ensure that the two Higgs doublets get a non-zero vacuum after EWSB; this leads to the well-known "μ problem" [7]. However, in the Next-to-minimal supersymmetric standard model (NMSSM) [8,9], these issues can be fixed. This model was proposed as an extension of MSSM with an additional Higgs singlet field, Ŝ , that generates a μ parameter dynamically of the SUSY breaking scale, solving the "μ-problem" [10,11]. Moreover, this new singlet scalar gives the NMSSM particle spectrum additional degrees of freedom. In the Higgs sector of the NMSSM, there are seven massive states: three CP-even h i (i = 1, 2, 3), two CP-odd a j (j = 1, 2), two charged h ± . Furthermore, the introduction of an extra Higgs singlet in the NMSSM has many implications that cause interesting phenomena. Thus, the NMSSM was widely proposed to interpret the results of the LHC . The singlet components' presence causes all Higgs bosons measurements to deviate from the Higgs boson's expected values in the SM, which may change the particle (and sparticle) decay width and signals at the LHC [35,36]. Based on this observation, the constraints of the recent LHC Higgs data on the lightest neutral Higgs states' properties are discussed in this paper. This method was used in a previous paper to investigate the effect of the latest LHC constraints on bosonic decays of possible lightest neutral Higgs bosons in the semi-constrained NMSSM (scNMSSM) with Grand unification boundary conditions [37] and will be shortly described in Section "Scan strategy". In this paper, we will apply this method to predict the effect of the recent constraints of the LHC on fermionic decays of neutral Higgs particles in scNMSSM.
The structure of this paper is as follows. Section "Higgs Sector in the NMSSM" briefly introduces the Higgs sector in the NMSSM model. Section "Scan Strategy" is devoted to present the analyzed parameter space of the NMSSM at the GUT scale and the imposed theoretical and experimental constraints. In Section "Results", our results are derived and analyzed. Finally, Section "Conclusion" contains brief conclusions of our findings.

Higgs sector in the NMSSM
The NMSSM represents the simplest extension of the MSSM by additional gauge chiral superfield which is singlet under SU(3) c × SU(2) L × U(1) Y . To solve the μ-problem of the MSSM, Z 3 -symmetry is imposed. Thus, the scale-invariant NMSSM superpotential reads [8], (1) The most general NMSSM soft Lagrangian is consists of mass terms for all scalars, the Higgs and sfermion fields (m 2 L and m 2 E ), the gauginos mass terms (m 1 , m 2 and m 3 ), and finally, the trilinear soft SUSY breaking interaction between the sfermions and Higgs fields.
To present the tree-level mass matrices of the Higgs fields physically, the expansion of the full scalar potential around the vacuum expectation values (VEVs), υ d ,υ u , and s, is required. Thus, the neutral Higgs doublets and singlet components are labeled by, The CP-even Higgs bosons (h 1 , h 2 , h 3 )are acquired from the mixing between a real part of S with real parts of H 0 d and H 0 u , while the CP-odd Higgs states (a 1 , a 2 , a 3 ) are obtained from the mixing between the imaginary parts of Higgs fields.
One of the advantages of this model is the prediction of the Higgs-like particle, at tree level, with mass around 125 GeV, where the following expression gives the upper bound on the lightest CP-even Higgs mass, The maximum tree-level enchantment is achieved when the ratio between the VEVs of the two Higgs doublets, tanβ ≡ υ u /υ d , is small, and the coupling constant between the singlet and two Higgs doublet fields, λ, is large. In scNMSSM, we assume that the soft SUSY breaking terms (the gauginos mass, sfermions mass, and the trilinear couplings) are equal at the GUT scale.
In addition, the Higgs soft mass terms m 2 H d , m 2 Hu , and m 2 HS are computed at the GUT scale but can vary from m 0 , and the trilinear couplings A λ , A κ are allowed also to differ from A 0 . Thus, at tree-level, the behavior of the scNMSSM Higgs sector is controlled by these parameters, Here, the first five parameters are given at the GUT scale, while the last four parameters are electroweak scale parameters.

Scan strategy
In this work, the NMSSM parameter space was extensively scanned with GUT boundary conditions using the NMSSMTools (v.5.5.2) package [38][39][40][41][42]. To date, over 70 theoretical and experimental constraints are implemented in this package. All theoretical and experimental constraints, except for (g − 2) μ , were considered during this study. To study in detail the effect of current constraints on the Higgs sector in this model, we allowed the passage of points with problems related to the limits imposed on the Higgs while we ruled out the other ones. After that, we analyzed the points and divided them into categories according to the problems that were excluded because of them. All these points were represented in different colors. Then, we investigated the possibility of observing one of the lightest neutral Higgs bosons (h 1 , h 2 , and a 1 ) for the surviving points. It is worth mentioning that the constraints from ATLAS and CMS are taken into account represent data of protonproton collisions at ̅̅ s √ = 13 TeV, corresponding to the luminosity of ∼ 36 fb − 1 and ∼ 80 fb − 1 [43][44][45][46][47][48][49][50][51][52][53][54][55].
In a previous study, we showed the effect of the recent constraints on the properties of the neutral Higgs bosons, such as the mass spectrum, the singlet and doublets components, the reduced couplings of such particles, and their decays and reduced cross-section to bosons [37]. This paper will show the rest of the results of the possible decays of these particles and the reduced cross-section of them to fermions. Note that the reduced cross-section represents an insightful approximation of the signal strength. It is computed from the multiplication of the relevant coupling squared (e.g. effective coupling of the Higgs to gluons) relative to the SM with the branching ratio of the Higgs decays to XX in the NMSSM relative to the SM, and given by the following expression (see for e.g. [21]) The NMSSMTools package provides the reduced cross-section for each decay mode for all Higgs bosons.
Because there are many free parameters for the NMSSM, in order to simplify our analysis, we assumed the scNMSSM. With this assumption, we randomly scan scanned up to 10 8 points to get a complete picture of this model. Moreover, we ensure that λ at the SUSY scale is smaller than < 0.7 to avoid any Landau singularities below the GUT scale. The free parameters ranged between the following values:

Branching Ratios
Lightest CP-even Higgs (h 1 )   orange and red points, respectively. Finally, the blue dots express the surviving points that exceeded all recent constraints. Please note that the deviations from the SM predictions are computed with the assumption that there is only one underlying state at 125 GeV (h SM ). According to the results shown in this figure, this boson represents the SM-like Higgs with a mass ranging from 122 GeV to 128 GeV. Therefore, the branching ratios and the reduced cross-sections of this particle are supposed to be close to what was expected in the SM. As seen from this figure (in the top panels), for the allowed range mass, the branching ratio of h 1 →bb, h 1 →ττ, and h 1 →Jets may vary from 0.4 to 0.7, 0.05 to 0.08, and 0.06 to 0.12, respectively. Next, the bottom panels shows Br (h 1 →cc) runs from 0.02 to 0.03, while for h 1 →μμ, the allowed band indicates the expected branching ratio at 0.00025. This figure also shows that some points violate the LHC constraints. The constraints with the most considerable impact are h→aa→4l/2l +2b and B BSM (h SM ), with the branching ratios below the accepted value in the SM. It should be noted that, in the scanned parameter space, if a region contains both good points and ruled-out points, then we plot the good points on top of the bad points since such a region is still valid given the presence of good solutions. However, if only bad points are shown in the plot, then this means we could not find good solutions in the associated region. Fig. 2 shows the permitted fermionic decays of the second lightest CP-even Higgs boson, h 2 . The results illustrate that the dominant decay mode is to tt for mass values above 300 GeV for this boson. On the other hand, when the Higgs mass below 300 GeV, h 2 →bb can be dominant with a branching ratio of about 0.9. The branching ratio of the channels h 2 →ττ, h 2 →Jets are about 0.1 for m h2 < 300 GeV, then decreases to 0.01 and 0.001, respectively, as m h2 →2 TeV. For m h2 below 200 GeV, the branching ratio of h 2 is to cc is around 0.01, then sharply decreases to 10 − 5 . Finally, for the low mass range (m h2 < 200 GeV), the value of the Higgs's branching ratio to →μμ can not exceed 0.001. Moreover, the region where m h2 ⩽250 GeV and branching ratios below 0.01, the impact of the constraints are more visible due to violating the constraint on C t (h SM ) (as clearly shown for h 2 →ττ/μμ), B BSM , C γ (h SM ), and from h→aa→4l/2l +2b (as shown for h 2 →Jets/cc).

Lightest CP-odd Higgs (a 1 )
The branching ratios of allowed fermionic decays of a 1 are presented in Fig. 3. As shown in the right top panel, with m a1 above 350 GeV, the dominant decay mode is to tt. For m a1 < 400 GeV, the branching ratio of a 1 →bb reaches a maximum value of 0.9 then decreases with mass increasing to about 0.45. Moving now to a 1 →cc, when the mass below 400 GeV, this decays also has a maximum value of 0.01 then sharply drops to about 10 − 5 for the allowed range mass. Next, The decay of a 1 → Jets is possible for mass below 350 GeV with branching ratios dramatically increases from 0 to about 0.6 at m a1 ∼ 350 GeV. Finally, for the allowed range mass of the lightest CP-odd, m a1 , the expected value of the branching ratios to ττ and μμ can reach about 0.1 and 1.5 × 10 − 4 , respectively. There are some points that are excluded due to the LHC constraints on C t (h SM ) and C γ (h SM ), with m a1 < 300 GeV and BR below 10 − 5 (as shown for a 1 →cc/μμ). Fig. 4 shows the reduced cross-section of the lightest CP-even and CPodd Higgs bosons (h 1 ,h 2 , and a 1 ) into bottom quarks via ttH production mode (top panels), and via VBF and VH production modes (bottom panels). While the reduced cross-sections of the these neutral Higgs bosons into ττ via ggF production mode (top panels) and via VBF and VH production modes (bottom panels) are presented in Fig. 5.

Reduced cross-sections
As we mentioned before, the results showed that the SM-like Higgs is the lightest of CP-even Higgs boson during this range of the scan. Therefore, the left panels in Figs. 4 and 5 show that the permissible values for the reduced cross-section of h 1 into bb and ττ via various production modes are near unity. These plots also show that when the cross-section values are between 0.1 and 0.0012, there are points that were excluded due to their violation of the restrictions of LHC (specifically from B BSM (h SM ) and h→aa→4l/2l + 2b), while near the permissible values there are points that were excluded due to the constraints on C t (h SM ), C g (h SM ), and C V (h SM ). Fig. 3. The branching ratios of a 1 →tt, a 1 →bb, a 1 →cc, a 1 →Jets, a 1 →ττ, and a 1 →μμ plotted aginest the lightest CP-odd Higgs mass M a1 From the middle panels of Figs. 4 and 5, the results show that when the mass of h 2 < 200 GeV, the reduced cross-section into bb and ττ is around the unity. With mass increasing, the reduced cross-section may get enhanced by over 100 via ttH production mode and get decreased to below 0.5 via VBF or VH. We noted that when the reduced cross-section is between 10 − 4 and 10 − 6 , some points were excluded due to the constraints from h→aa→4l/2l + 2b, B BSM (h SM ), C γ (h SM ), and C t (h SM ). Moreover, R(ggF→h 2 →ττ) and R(VBF/VH→h 2 →ττ) have similar properties of R(ttH→h 2 →bb) and R(VBF/VH→h 2 →bb), respectively.
The reduced cross-section of a 1 into bb, via ttH, and ττ, via VBF or  Higgs boson (right panel) into ττ via ggF, VBF, and VH production modes. The color-coding is the same as Fig. 3. VH, is presented in the right panel in Figs. 4 and 5, respectively. As shown here, when the mass of a 1 < 200 GeV, the reduced cross-section to down-type fermions via different production modes has tiny values, and whenever the mass increases, these values get increased. Finally, We also noted that when the mass of a 1 above 400 GeV, there are excluded points, with huge value of the reduced cross-section, due to the limitations on C t (h SM ), C g (h SM ), C V (h SM ), and from h→aa→γγ.

Conclusion
For the lightest neutral Higgs bosons in the NMSSM (h 1 , h 2 , and a 1 ), we examined the reduced cross-section and possible decay modes to the fermions in a region where λ is large as possible, and tanβ is small. The results show that in future searches the following channels could be most promising. For example, the decays of h 2 →bb, and a 1 →bb, can be dominant with a branching ratio of 0.9 when the Higgs mass below 300 GeV and 400 GeV, respectively, due to the high values of the doublet components of h 2 and a 1 . Thus, the coupling between these Higgs states and b quarks will get enhanced. Moreover, the branching ratio of h 2 and a 1 to a pair of top quarks, if kinematically allowed, would be dominant. This is because the doublet component of h 2 and singlet component of a 1 have high values, which leads to a strong coupling between these particles and the top quarks. The results also showed a similar behavior of a reduced cross-section of the neutral Higgs bosons into bb and ττ final states.
In summary, the discovery of a SM-like Higgs boson with a mass of about 125 GeV may indicate the existence of extended Higgs sectors predicted by new physics models, such as the NMSSM. The measured couplings of the SM-like Higgs can indirectly affect the parameter space of the other non-SM Higgs bosons in the model as is shown by the findings of this paper, which can provide a deeper insight into the model and suggest new directions for future research.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. proton-proton collisions at