Neutrino mass, mixing and muon $g-2$ explanation in $U(1)_{L_\mu-L_\tau}$ extension of left-right theory

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 the muon anomalous magnetic moment. We get sizeable contribution from the interaction of the new light gauge boson $Z_{\mu\tau}$ of the $U(1)_{L_\mu-L_\tau}$ symmetry with muons which can individually satisfy the current bounds on muon $(g-2)$ anomaly ($\Delta a_\mu$). The other positive contributions to $\Delta a_\mu$ come from the interactions of singly charged gauge bosons $W_L$, $W_R$ with heavy neutral fermions and that of neutral CP-even scalars with muons. The interaction of $W_L$ with heavy neutrino is facilitated by inverse seesaw mechanism which allows large light-heavy neutrino mixing and explains neutrino mass in our model. CP-even scalars with mass around few hundreds GeV can also satisfy the entire current muon anomaly bound. 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. We have briefly presented a comparative study for symmetric and asymmetric left-right symmetric model in context of various contribution to $\Delta a_\mu$. We also discuss how the generation of neutrino mass is affected when left-right symmetry breaks down to Standard Model symmetry via various choices of scalars.