Neutrino Masses, Leptonic Flavor Mixing and Muon $(g-2)$ in the Seesaw Model with the $U(1)^{}_{L^{}_\mu-L^{}_\tau}$ Gauge Symmetry

The latest measurements of the anomalous muon magnetic moment $a^{}_\mu \equiv (g^{}_\mu - 2)/2$ show a $4.2\sigma$ discrepancy between the theoretical prediction of the Standard Model and the experimental observations. In order to account for such a discrepancy, we consider a possible extension of the type-(I+II) seesaw model for neutrino mass generation with a gauged $L^{}_\mu - L^{}_\tau$ symmetry. By explicitly constructing an economical model with only one extra scalar singlet, we demonstrate that the gauge symmetry $U(1)^{}_{L^{}_\mu - L^{}_\tau}$ and its spontaneous breaking are crucially important not only for explaining the muon $(g - 2)$ result but also for generating neutrino masses and leptonic flavor mixing. Various phenomenological implications and experimental constraints on the model parameters are also discussed.