Light neutral CP-even Higgs boson within Next-to-Minimal Supersymmetric   Standard model (NMSSM) at the Large Hadron electron Collider (LHeC)
  We analyze the prospects of observing the light CP-even neutral Higgs bosons ($h_1$) in their decays into $b \bar b$ quarks, in the neutral and charged current production processes $e h_1 q$ and $\nu h_1 q$ at the upcoming LHeC, with $\sqrt s \approx 1.296$ TeV. Assuming that the intermediate Higgs boson ($h_2$) is Standard Model (SM)-like, we study the Higgs production within the framework of 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 0.4$\sigma$ (2.5$\sigma$) level in the $e$+3j channel up to Higgs boson masses of 75 GeV and in the $E\!\!\!\!/_T$+3j channel could be discovered with 1.7$\sigma$ (2.4$\sigma$) level up to Higgs boson masses of 88 GeV with 100 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. 
Siba Prasad Das and Marek Nowakowski
hep-ph hep-ex