Pandax-4T limits on $Z^\prime$ mass in 3-3-1LHN model

The framework of the so-called 3-3-1LHN model may accommodate two different, but viable, scenarios of dark matter: one involving a heavy Dirac neutrino , $N_1$, or another having a scalar, $\phi$, as dark matter candidate. In both cases the dark matter phenomenology, relic abundance and scattering cross section off of nuclei, is controlled by exchange of $Z^{\prime}$. We then investigate the impact on the parameter space $(M_{Z^{\prime}}\,,\,M_{(N_1\,,\, \phi)})$ due to the recent Pandax-4T experimental result in both scenarios. First, the Pandax-4T experiment excludes scenarios with dark matter mass below $1.9$ TeV. Concerning $Z^{\prime}$, we find the lower bound $M_{Z^{\prime}}> 4.1$ TeV for the case when $N_1$ as the dark matter and $M_{Z^{\prime}}>5.7$ TeV for the other case. This implies that the 3-3-1 symmetry is spontaneously broken above $10$ TeV scale. We also comment on the contributions to the relic abundance of processes involving flavor changing neutral current mediated by $Z^{\prime}$.