Inspired by the recently new measurement of $(g-2)_{ \mu}$ at FermiLab and reported upper bound for electron-dark matter (DM) recoil by the XENON1T collaboration, we revisited phenomenology of a light MeV scale vector dark matter in a leptophilic extension of standard model while a new spinor field plays the role of mediator. A viable parameter space is considered to discuss the possibility of light dark matter relic density as well as anomalous magnetic moment of the muon. We study DM-electron direct detection and cosmological bounds on the parameters space of the model. It is shown that although new bound of $(g-2)_{ \mu}$ anomaly greatly confines the parametric space of the model, the thermal light dark matter can exist for $\rm M_{ DM}\sim 10^{ -1}-10^{ 1}~\rm GeV$.
Categories: hep-ph
