Neutrino phenomenology in a Standard Model extension with ${\mathbf{T}}^{\prime }\times {\mathbf{Z}}_{10}\times {\mathbf{Z}}_2$ symmetry

Abstract

We construct a Standard Model (SM) extension with $T^{\prime }\times Z_{10}\times Z_2$ symmetry for generating the expected neutrino mass matrix with the relation $(M_{\nu }{)}_{13}=(M_{\nu }{)}_{31}=-\frac{1}{2}(M_{\nu }{)}_{22}$ via the contributions of the Type-I seesaw and Weinberg-type operators. The proposed model possesses viable parameters capable of predicting the neutrino oscillation parameters being in good agreement with recent constraints. Our analysis reveals the predicted regions for the physical quantities, given as follows. The two mass squared splittings are $\delta m^2\in (69.360,79.220){\mathrm{meV}}^2$ and $\Delta m^2\in (2.484,2.490)10^3{\mathrm{meV}}^2$ for normal ordering (NO) while $\delta m^2\in (69.450,79.160){\mathrm{meV}}^2$ and $\Delta m^2\in (-2.464,-2.456)10^3{\mathrm{meV}}^2$ for inverted ordering (IO). The lightest neutrino mass is $m_{\ell }\in (36.720,36.780)$ meV for NO and $m_{\ell }\in (62.220,62.310)$ meV for IO. The sum of neutrino mass is $\sum m_{\nu }\in (136.700,136.800)$ meV for NO and $\sum m_{\nu }\in (221.400,221.600)$ meV for IO. Two Majorana phases are predicted to be $\alpha \in (6.367,6.380{)}^{\circ }$ and $\beta \in (6.936,6.946{)}^{\circ }$ for NO while $\alpha \simeq 358.800^{\circ }$ and $\beta \simeq 0.600^{\circ }$ for IO. Finally, the effective neutrino mass is $m_{\mathrm{ee}}\in (36.940,36.980)$ meV for NO and $m_{\mathrm{ee}}\in (76.290,76.360)$ meV for IO. Based on these results, the Yukawa-like couplings are estimated, which can naturally explain the charged - lepton as well as neutrino mass hierarchies.

Comments: 21 pages, 7 tables