The light MSSM neutral Higgs boson production associated with an electron and a jet at the LHeC

We study the light CP-even neutral Higgs boson production in association with an electron and a jet at the possible CERN large hadron-electron collider within the minimal supersymmetric standard model. We investigate the possible supersymmetric effects on this process and compare our standard model numerical results with those in previous work. We present the leading-order and QCD next-to-leading-order corrected total cross sections and the distributions of the transverse momenta of the final electron, the light neutral Higgs boson, and jet in the minimal supersymmetric standard model. Our results show that the scale dependence of the leading-order cross section is obviously reduced by the QCD next-to-leading-order corrections. The K factor of the QCD correction to the total cross section at the large hadron-electron collider varies from 0.893 to 1.048 when the factorization/renormalization scale $\mu$ goes up from $0.2 m_Z$ to $3.8 m_Z$ in our chosen parameter space.