Neutrino phenomenology in a Standard Model extension with $\mathbf{T^\prime\times Z_{10} \times Z_2}$ symmetry

TL;DR

This work presents a Standard Model extension with $T^{\prime}\times Z_{10} \times Z_2$ symmetry to realize a Majorana neutrino mass texture where $(M_\nu)_{13}=(M_\nu)_{31}=-\frac{1}{2}(M_\nu)_{22}$ through a combination of Type-I seesaw and Weinberg-type operators. The authors derive a diagonalization framework for $M_\nu$, show that the model effectively depends on six input parameters reduced to two free quantities $\mathrm{Re}\,G$ and $J$, and construct a concrete scalar sector with 12 scalars and specific VEV alignments to produce the desired mass matrices. Numerical analysis fixes the standard oscillation parameters and yields distinct NO and IO predictions for $\delta m^2$, $\Delta m^2$, neutrino masses, $\sum m_ν$, $m_{ee}$, Majorana phases, and heavy-light mixing, all compatible with current constraints; the inferred Yukawa couplings naturally reproduce charged-lepton and neutrino hierarchies and predict heavy neutrinos at $\mathcal{O}(10^5)$ GeV with tiny mixings. The results offer testable late-time predictions for $0\nu 2\beta$ decay and future neutrino mass measurements, and illustrate a streamlined approach to flavor model building with reduced scalar content. $M_\nu$ textures and their phenomenological consequences are tightly linked to the chosen discrete symmetries and scalar sector structure, highlighting the role of group theory in shaping neutrino physics.

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 $(M_ν)_{13}=(M_ν)_{31}=-\frac{1}{2}(M_ν)_{22}$ 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 $δm^2\in (69.360, 79.220)\, \mathrm{meV}^2$ and $Δm^2\in (2.484, 2.490)10^3\,\mathrm{meV}^2$ for normal ordering (NO) while $δm^2\in (69.450, 79.160)\, \mathrm{meV}^2$ and $Δm^2\in (-2.464, -2.456)10^3\,\mathrm{meV}^2$ 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 $\sum m_ν\in (136.700,\, 136.800)$ meV for NO and $\sum m_ν\in (221.400,\, 221.600)$ meV for IO. Two Majorana phases are predicted to be $α\in (6.367, 6.380)^\circ$ and $β\in (6.936, 6.946)^\circ$ for NO while $α\simeq 358.800^\circ$ and $β\simeq 0.600^\circ$ 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.