Muon (g-2) anomaly in extended left-right symmetric model

We consider a gauged $U(1)_{L_\mu-L_\tau}$ extension of the left-right symmetric theory in order to simultaneously explain neutrino mass, mixing and muon anomalous magnetic moment. We get sizeable contribution from the interaction of the new light gauge boson $Z_{\mu\tau}$ of $U(1)_{L_\mu-L_\tau}$ symmetry with muons which can individually satisfy the current bounds on muon $(g-2)$ anomaly . The other positive contributions to $\Delta a_\mu$ come from the interactions of neutral CP-even scalars with muons and that of singly charged gauge boson $W_L$ with heavy neutrinos which is facilitated by inverse seesaw mechanism that explains neutrino mass in our model. The results show that the model gives a small but non-negligible contribution to $\Delta a_\mu$ thereby eliminating the entire deviation in theoretical prediction and experimental result of muon $(g-2)$ anomaly.