Probing $L$-violating coupling via sbottom resonance production at the LHeC

We investigate the resonant production of the lighter sbottom at the proposed Large Hadron Electron Collider and its subsequent decay into $e^- + jet$ final state, under the single coupling dominance hypothesis in the framework of the $R$-parity-violating minimal supersymmetric standard model. It is concluded that the LHeC running at the high electron beam energy configuration of $E_e = 150 {\rm GeV}$ would provide excellent opportunities to search for the sbottom resonance and probe the lepton-number-violating $\hat{L}\hat{Q}\hat{D}$ $\lambda^{\prime}_{113}$-type Yukawa interaction. With about $1 fb^{-1}$ integrated luminosity expected in $E_e = 150 {\rm GeV}$ $e^-p$ collision at the LHeC, either the lighter sbottom RPV resonance could be directly detected up to $1 {\rm TeV}$, or the $L$-violating coupling $\lambda^{\prime}_{113}$ could be constrained at an unprecedented level of precision compared with all the knowledge derived from indirect measurements.