Gauged $U(1)_{L_{\mu}-L_{\tau}}$ Symmetry and two-zero Textures of Inverse Neutrino Mass Matrix in light of Muon ($g-2$)

TL;DR

This paper explores an anomaly-free $U(1)_{L_{}-L_{ au}}$ model linking muon g-2 and neutrino mass textures, identifying specific inverse neutrino mass matrix structures that fit experimental data and constrain model parameters.

Contribution

It introduces two zero textures of the inverse neutrino mass matrix within a $U(1)_{L_{}-L_{ au}}$ framework that simultaneously explain muon g-2 and neutrino phenomenology.

Findings

Muon g-2 explained with $Z_{}$ mass in 0.035-0.100 GeV range.

Model constrains neutrino mixing angles and CP invariants.

Consistent with experimental bounds from CCFR, COHERENT, BABAR, NA62, NA64.

Abstract

In the framework of anomaly free $U(1)_{L_{\mu}-L_{\tau}}$ model, charged scalar fields give rise to massive gauge boson ($Z_{\mu\tau}$) through spontaneous symmetry breaking. $Z_{\mu\tau}$ leads to one loop contribution to the muon anomalous magnetic moment. These scalar fields may, also, appear in the structure of right-handed neutrino mass matrix, thus, connecting the possible explanation of muon ($g-2$) and low energy neutrino phenomenology through $vevs$ associated with the scalar fields. In the present work, we consider textures of inverse neutrino mass matrix ($M_{\nu}^{-1}$) wherein any two elements of the mass matrix are zero. In this ansatz, with Dirac neutrino mass matrix diagonal, the zero(s) of right-handed Majorana neutrino mass matrix correspond to zero(s) in the low energy effective neutrino mass matrix (within Type-I seesaw). We have realized two such textures of $M_{\nu}^{-1}$ accommodating the muon ($g-2$) and low energy neutrino phenomenology. The requirement of successful explanation of muon ($g-2$), further, constrain the allowed parameter space of the model and results in sharp correlations amongst neutrino mixing angles, $CP$ invariants and effective Majorana mass ($M_{ee}$). The model explains muon ($g-2$) for $M_{Z_{\mu\tau}}$ in the range ($0.035$ GeV-$0.100$ GeV) and $g_{\mu\tau}\approx\mathcal{O}(10^{-4}$) which is found to be consistent with constraints coming from the experiments like CCFR, COHERENT, BABAR, NA62 and NA64.