Narrow Results

In the framework of anomaly free $U{(1)}_{L_{\mu }-L_{\tau }}$ model, singlet scalar field with nonzero $L_{\mu }-L_{\tau }$ charge gives 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 this 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, constrains the allowed parameter space of the model and results in sharp correlations amongst neutrino mixing angles and CP invariants. The model explains muon $(g-2)$ for $M_{Z_{\mu \tau }}$ in the range (0.035–0.100 GeV) and $g_{\mu \tau }\approx {𝒪}(10^{-4})$ which is found to be consistent with constraints coming from the current experiments CCFR, COHERENT, BABAR while being within sensitivities of future experiments such as NA62 and NA64.