The signatures of the new particles h${}_2$ and Z${}_{\mu \tau }$ at e-p colliders in the U(1)${}_{L_{\mu }\text{â}\text{ˆ}\text{’}{L}_{\tau }}$ 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${}_2$ and the light gauge boson Z${}_{\mu \tau }$, which are predicted by the U(1)${}_{L_{\mu }-L_{\tau }}$ model. Taking into account the experimental constraints on the relevant free parameters, we consider all possible production channels of h${}_2$ and Z${}_{\mu \tau }$ 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 5σ of h${}_2$ as well as Z${}_{\mu \tau }$ detecting can be achieved via e${}^{-}$p $\to$ e${}^{-}$ jh${}_2$ ($\to$ Z${}_{\mu \tau }$ Z${}_{\mu \tau }$) $\to$ e${}^{-}$ j+ $\text{⧸}{E}_{\tau }$ process and a 5σ sensitivity of Z${}_{\mu \tau }$ detecting can be gained via e${}^{-}$p $\to$ e${}^{-}$ jh${}_1$ ($\to$ Z${}_{\mu \tau }$ Z${}_{\mu \tau }$) $\to$ e${}^{-}$ j+ $\text{⧸}{E}_{\tau }$ 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.