  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.

High Energy Physics - Phenomenology