Electron and Muon \({(g-2)}_{e,\mu }\) Anomalous Magnetic Moment in  \({U(1)}_{L_e-L_{\mu }}\) Symmetry Model

The nature of neutrino (whether Majorana or Dirac), and the origin of neutrino masses are still mysteries to be resolved. Also, the recent results of \(\text {(g-2)}_{e,\mu }\) measurements deviate from the Standard Model (SM) predictions and motivate towards the new physics beyond the SM. In this work, we propose a model with the minimal field content in the framework of anomaly free extension of Standard Model; i.e. \(\text {U(1)}_{L_{e}-L_{\mu }}\) symmetry model. We find this model capable of explaining the low energy neutrino phenomenology and anomalous magnetic moment \(\text {(g-2)}_{e,\mu }\) of electron and muon, simultaneously. The field content is extended by a \(\text {SU(2)}_{L}\) singlet scalar field \(\phi \) and three right handed neutrinos \(\text {N}_{R}\) (R = 1, 2, 3). The neutrino masses are generated using the Type-I seesaw mechanism. The extended model leads to the results, which are in consistency with the experimental values of \(\text {(g-2)}_{e,\mu }\) and also satisfy all relevant experimental data.