The signatures of the new particles $$h_{2}$$ and $$Z^{}_{\mu \tau }$$ at e-p colliders in the $${U(1)}_{L^{}_{\mu } - L^{}_{\tau } }$$ 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 $$h_{2}$$h2 and the light gauge boson $$Z^{}_{\mu \tau }$$Zμτ, which are predicted by the $${U(1)}_{L^{}_{\mu } - L^{}_{\tau }}$$U(1)Lμ-Lτ model. Taking into account the experimental constraints on the relevant free parameters, we consider all possible production channels of $$h_{2}$$h2 and $$Z^{}_{\mu \tau }$$Zμτ at e-p colliders and further investigate their observability through the optimal channels in the case of the beam polarization $$\hbox {P}(e^{-})= -0.8$$P(e-)=-0.8. We find that the signal significance above $$5\sigma $$5σ of $$h_{2}$$h2 as well as $$Z^{}_{\mu \tau }$$Zμτ detecting can be achieved via "Equation missing" process and a $$5\sigma $$5σ sensitivity of $$Z^{}_{\mu \tau }$$Zμτ detecting can be gained via "Equation missing" process at e-p colliders with appropriate parameter values and a designed integrated luminosity. However, the signals of $$h_{2}$$h2 decays into pair of SM particles are difficult to be detected.