Light neutral $CP$-even Higgs boson within the next-to-minimal supersymmetric standard model at the Large Hadron Electron Collider

We analyze the prospects of observing the light charge parity ($CP$)-even neutral Higgs bosons ($h_1$) in their decays into $b\overline{b}$ quarks, in the neutral and charged current production processes $e{h}_{1}q$ and $\nu h_{1}q$ at the upcoming Large Hadron Electron Collider (LHeC), with $\sqrt{s}\approx 1.296\mathrm{TeV}$. Assuming that the intermediate Higgs boson ($h_2$) is Standard Model (SM)-like, we study the Higgs production within the framework of next-to-minimal supersymmetric Standard Model (NMSSM). We consider the constraints from dark-matter, sparticle masses, and the Higgs boson data. The signal in our analysis can be classified as three jets, with electron (missing energy) coming from the neutral (charged) current interaction. We demand that the number of $b$-tagged jets in the central rapidity region be greater or equal to two. The remaining jet is tagged in the forward regions. With this forward jet and two $b$-tagged jets in the central region, we reconstructed three jets invariant masses. Applying some lower limits on these invariant masses turns out to be an essential criterion to enhance the signal–to–background rates, with slightly different sets of kinematical selections in the two different channels. We consider almost all reducible and irreducible SM background processes. We find that the non-SM like Higgs boson, $h_1$, would be accessible in some of the NMSSM benchmark points, at approximately the $0.4\sigma$ ($2.5\sigma$) level in the $e+3\mathrm{j}$ channel up to Higgs boson masses of 75 GeV, and in the ${\cancel{E}}_T+3\mathrm{j}$ channel could be discovered with the $1.7\sigma$ ($2.4\sigma$) level up to Higgs boson masses of 88 GeV with $100{\mathrm{fb}}^{-1}$ of data in a simple cut-based (with optimization) selection. With ten times more data accumulation at the end of the LHeC run, and using optimization, one can have $5\sigma$ discovery in the electron (missing energy) channel up to 85 (more than 90) GeV.

Figure 1

Left panel: the dark matter relic density (${\mathrm{\Omega }}_{{\tilde{\chi }}_1^0}{h}^2$) as a function of the lightest neutralino masses ($m_{{\tilde{\chi }}_1^0}$) within the standard cosmology. The two lines represent the upper (${\mathrm{\Omega }}_{{\tilde{\chi }}_1^0}{h}^2=0.131$) and lower (${\mathrm{\Omega }}_{{\tilde{\chi }}_1^0}{h}^2=0.107$) bounds from the Planck measurements [41]. The first deep dip around 45 GeV is due to the Z-boson exchange (annihilation diagram) and the second around 63 GeV, from the Higgs-boson ($h_2$-SM) exchange annihilation within the NMSSM parameter spaces. The green points within the strips satisfy the direct and indirect dark matter search results and are termed as “All-DM”. Right panel: we only show the relic density allowed parameter space together with various other constraints (in the legends), see the text for details.

Figure 2

Left panel: the singlet component ($N_{15}$) of the lightest neutralino (${\tilde{\chi }}_1^0$) consistent with the dark matter relic density (${\mathrm{\Omega }}_{{\tilde{\chi }}_1^0}{h}^2$) and various other constraints (see text for details). Right panel: the masses of the Higgs boson masses, $h_1$, $h_2$, $h_3$, $a_2$, and $h^{\pm }$ (“Hpm”) as a function of the lightest $CP$-odd Higgs boson masses ($m_{a_1}$). The mass of the $a_2$ is shown up to 1600.0 GeV and extends, however, even beyond this point in these allowed NMSSM model parameter spaces.

Figure 3

Left panel: the Higgs boson masses, $h_1$, $h_2$, and $h^{\pm }$ as a function of the lightest $CP$-odd Higgs bosons mass ($m_{a_1}$) for the $h_2$-SM scenario and consistent with all other constraints (see details in the text). Right panel: we show the branching ratio of the $h_1$ in different channels, and it is clear that in the large region of allowed parameter space the branching ratio of $h_1\to b\overline{b}$ is above 90%.

Figure 4

The coupling $g_{hWW}$ (for $h=h_1$ and $h_2$) is shown as a function of the Higgs boson mass. The top right corner (with populated green points) shows the masses of the $h_2$ and the corresponding coupling constraints (that we imposed following Table 2) from the recent LHC measurements.

Figure 5

Number of events in $e+3$-jets (left panel) and ${\cancel{E}}_T+3$-jets (right panel) channels at LHeC with integrated luminosity of $100f{b}^{-1}$.

Figure 6

The cross section multiplied with the Higgs branching ratios in units of $[fb]$ in the $e^{+}{e}^{-}$ LEP collider with center-of-mass energy 209 GeV, for the $\sigma (e^{+}{e}^{-}\to e^{+}{h}_1{e}^{-})$ and $\sigma (e^{+}{e}^{-}\to {\nu }_e{h}_1{\overline{\nu }}_e)$ in the left and right panels, respectively.

Figure 7

Left panel: the cross section with Higgs branching ratios in units of [fb] at the Tevatron $(\sigma (p\overline{p}\to j{h}_{1}j))$ with center-of-mass energy 1.96 TeV. Right panel: $\sigma (pp\to j{h}_{1}j)$ at LHC collider with center-of-mass energy 14 TeV, where $j=\mathrm{u},\mathrm{d},\mathrm{c},\mathrm{s},\mathrm{b},\mathrm{g}$ and their charge conjugation.

Figure 8

Left panel: number of jet distributions for the $e1$ benchmark ($\nu 5$ benchmark) in the $e+3$-jets (${\cancel{E}}_T+3$-jets) channel using the thick (thin) black lines. Right panel: the number of $b$-tagged jet distribution is shown. Both of the distributions depend mainly upon the masses of the Higgs boson in two signal channels, i.e., the more massive the Higgs, the higher the number of jet peaks toward higher values. For all other signal benchmarks, the distributions follow a similar pattern and can be understood from the numerics in the corresponding columns in Tables 4 and 6.

Figure 9

Number of electron ($N_e$) distribution for the $e1$ benchmark ($\nu 1$ benchmark) using thick (thin) black line in the left panel. The distribution of missing energy (${\cancel{E}}_T$) for the $e1(\nu 1)$ benchmark using thick (thin) black line in the right panel.

Figure 10

Left panel: the di-$b$-tagged invariant masses, $M_{bb}$, distribution for the $e+3$-jets channel, for the $e1$, $e3$, and $e5$ benchmark points from left to right (thick to thinner), respectively. Right panel: similar to the ${\cancel{E}}_T+3$-jets channel, with the mass peaks for $\nu 1$, $\nu 3$, and $\nu 5$ from left to right (thick to thinner), respectively. See Table 3 for the corresponding Higgs boson masses.

Figure 11

Left panel: the rapidity of the forward jet (${\eta }_{jf}$) for the $e1$ and $\nu 5$ signal benchmark points. The distributions for other benchmarks lie between these distribution profiles. Right panel: the rapidity of the forward lepton (${\eta }_{ef}$) for the $e1$ and $e5$ benchmark points (somewhat similar for other benchmarks).

Figure 12

Left panel: the transverse momentum ($P_T$) of forward jet ($P_{Tjf}$) for the $e1$ and $\nu 5$ signal benchmarks. Right panel: the same for the forward lepton ($P_{Tef}$) only in the electron channel for the $e1$ and $e5$ signal benchmarks.

Figure 13

Left panel: the rapidity differences between forward jet ($j_f=jf$) and forward lepton ($e_f=ef$), i.e., $\mathrm{\Delta }{\eta }_{jf-ef}$ only for the $e1$ and $e5$ signal benchmarks in the electron channel. The signal shows a large rapidity gap. Right panel: The invariant masses of the Higgs candidate jets, $M_{bb}$ shown in Fig. 10, together with the forward jet, i.e., $M_{bb{j}_f}=m_{h_1{j}_f}$ for both the signal channels for the $e1$ benchmark ($\nu 5$ benchmark) using thick(thin) black lines. The signal distributions in both channels do not differ as the electron and ${\cancel{E}}_T$ do not have a direct big role in reconstructing the three-jet invariant mass. The distributions for other signal benchmarks in both of the channels are somewhat identical.

Figure 14

Left panel: $H_T=\sum |P{t}_j|$ distribution for the $e1$ benchmark and the $\nu 5$ benchmark. The distributions for other signal benchmarks in both of the channels are somewhat identical. Right panel: ${\overrightarrow{H}}_T=|\sum \overrightarrow{P}{t}_j|$ defined (in the figure, the magnitude of the vector is naturally implied) in kinematical selection (i), for the leptonic and missing energy channels (the presence of the lepton or ${\cancel{E}}_T$ do not matter directly for the ${\overrightarrow{H}}_T$ distribution; however, the number of jets does.) for the $e1$ and $\nu 5$ benchmark points. The distributions for other benchmarks in both of the signal channels are somewhat similar.