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

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.

13 pages, 5 figures

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• The Muon Magnetic Moment and Physics Beyond the Standard Model