Exploring neutrino masses, $(g-2)_{\mu, e}$ in type I+II seesaw in ${L^{}_e-L^{}_{\alpha}}$ gauge extended model

This paper aims to explore the implications of $U(1)_{L_e-L_{\alpha}}$ gauge symmetries, where $\alpha=\tau, \mu$, in the neutrino sector through the type-(I+II) seesaw mechanisms. To achieve such a hybrid framework, we include a scalar triplet and three right-handed neutrinos. The model can successfully account for the active neutrino masses, mixing angles, mass squared differences, and the CP-violating phase within the $3 \sigma$ bounds of NuFit v5.2 neutrino oscillation data. The presence of new gauge boson at the MeV scale provides an explanation for the muon and electron $(g-2)$ within the confines of their experimental limits. Furthermore, we scrutinize the proposed models in the context of upcoming long-baseline neutrino experiments such as DUNE, P2SO, T2HK, and T2HKK. The findings reveal that P2SO and T2HK have the ability to probe both the models in their $5 \sigma$ allowed oscillation parameter region, whereas DUNE and T2HKK can conclusively test only model with $U(1)_{L_e-L_\mu}$- symmetry within their $5 \sigma$ parameter space if the true values of the oscillation parameters remain consistent with NuFit v5.2.