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 (b) over bar quarks, in the neutral and charged current production processes eh(1)q and nu h(1)q at the upcoming Large Hadron Electron Collider (LHeC), with root s approximate to 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 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 0.4s (2.5s) level in the e + 3j channel up to Higgs boson masses of 75 GeV, and in the is not an element of(T) + 3j channel could be discovered with the 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.