# 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

## TL;DR

This paper explores the potential to detect new particles predicted by the ${U(1)}_{L_-L_}$ model at future electron-proton colliders, focusing on their production channels and observability under experimental constraints.

## Contribution

It provides a detailed analysis of the production and detection prospects of the scalar $h_2$ and gauge boson $Z_{}$ at e-p colliders, considering beam polarization and parameter constraints.

## Key findings

- Signal significance above 5$$ can be achieved for $h_2$ and $Z_{}$ detection.
- $Z_{}$ detection sensitivity reaches 5$$ at certain parameter values.
- Detection of $h_2$ decays into SM particles is challenging.

## Abstract

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 5$\sigma$ of $h_{2}$ as well as $Z^{}_{\mu\tau}$ detecting can be achieved via $e^{-}p\to{e^{-}jh_{2}(\to{Z_{\mu\tau}Z_{\mu\tau}})}\to~e^{-}j+/\!\!\!\!{E}^{}_{T}$ process and a 5$\sigma$ sensitivity of $Z^{}_{\mu\tau}$ detecting can be gained via $e^{-}p\to{e^{-}jh_{1}(\to{Z^{}_{\mu\tau}Z^{}_{\mu\tau}})\to}~e^{-}j+/\!\!\!\!{E}^{}_{T}$ 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.