Probing for chiral $Z^\prime$ gauge boson through scattering measurement experiments

Motivated by the observation of tiny neutrino mass can not be explained within the framework of Standard Model (SM), we consider extra gauge extended scenarios in which tiny neutrino masses are generated through seesaw mechanism. These scenarios are equipped with beyond the standard model (BSM) neutral gauge boson called $Z^\prime$ in the general $U(1)_X$ symmetry which is a linear combination of $U(1)_Y$ and $U(1)_{B-L}$. In this case, left and right handed fermions interact differently with the $Z^\prime$. The $Z^\prime$ gives rise to different processes involving neutrino-nucleon, neutrino-electron, electron-nucleus and electron-muon scattering processes. By comparing with proton, electron beam-dump experiments data, recast data from searches for the long-lived and dark photon at BaBaR, LHCb and CMS experiments, the electron and muon $g-2$ data, and the data of the dilepton and dijet searches at the LEP experiment, we derive bounds on the gauge coupling and the corresponding gauge boson mass for different $U(1)_X$ charges and evaluate the prospective limits from the future beam-dump scenarios at DUNE, FASER(2) and ILC. We conclude that large parameter regions could be probed by scattering, beam-dump and collider experiments in future.