Muon Anomalous Magnetic Moment and Neutrino Mass in  \(U(1)_{L_\mu -L_\tau }\) Extended Scotogenic Model

The value of muon magnetic moment, recently, reported by Fermilab has \(4.2 \sigma \) discrepancy with the theoretical prediction which is a robust signal for physics beyond the SM. In this work, we consider \(U(1)_{L_{\mu }-L_{\tau }}\) extension of the scotogenic model to explain non-zero neutrino mass and muon ( \(g-2\) ), simultaneously. It is known that muon neutrino trident (MNT) process put an upper bound on mass of gauge boson \(M_{Z_{\mu \tau }}<300\) MeV to accommodate muon ( \(g-2\) ) anomaly. We have constrained the vev of scalar singlet responsible for the mass of gauge boson using low energy neutrino data. We find that there exist a range of \(M_{Z_{\mu \tau }}\) above 300 MeV giving consistent neutrino phenomenology. In this case, it is shown that muon ( \(g-2\) ) can be explained by adding a vector like lepton triplet with appropriate \(L_{\mu }-L_{\tau }\) charge such that it only couples to muon through inert doublet \(\eta \) . We have, also, investigated the implication of the model for CP violation and effective Majorana neutrino mass \(m_{ee}\) appearing in neutrinoless double beta ( \(0\nu \beta \beta \) ) decay process.