Thermal Leptophilic Light Vector Dark Matter with Spinor Mediator and Muon (g-2) Anomaly

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 $\rm M_{DM}\sim 10^{-1}-10^{1}~\rm GeV$.