The signatures of the new particles $h_2$ and $Z_{μτ}$ at e-p colliders in the $U(1)_{L_μ-L_τ}$ model
Considering the superior performances of the future e-p colliders, LHeC and FCC-eh, we discuss the feasibility of detecting the extra neutral scalar $h_{2}$ and the light gauge boson $Z^{}_{μτ}$, which are predicted by the ${U(1)}_{L^{}_μ - L^{}_τ}$ model. Taking into account the experimental constraints on the relevant free parameters, we consider all possible production channels of $h_{2}$ and $Z^{}_{μτ}$ at e-p colliders and further investigate their observability through the optimal channels in the case of the beam polarization P($e^{-}$)= -0.8. We find that the signal significance above 5$σ$ of $h_{2}$ as well as $Z^{}_{μτ}$ detecting can be achieved via $e^{-}p\to{e^{-}jh_{2}(\to{Z_{μτ}Z_{μτ}})}\to~e^{-}j+/\!\!\!\!{E}^{}_{T}$ process and a 5$σ$ sensitivity of $Z^{}_{μτ}$ detecting can be gained via $e^{-}p\to{e^{-}jh_{1}(\to{Z^{}_{μτ}Z^{}_{μτ}})\to}~e^{-}j+/\!\!\!\!{E}^{}_{T}$ process at e-p colliders with appropriate parameter values and a designed integrated luminosity. However, the signals of $h_{2}$ decays into pair of SM particles are difficult to be detected.