Seesaw-I and II Hybrid $T^{\prime}$ Symmetric Neutrino Masses with Mass Selection Rule

TL;DR

The paper tackles realizing a neutrino-mass texture that satisfies the selection rule $m_nu^{13} + m_nu^{22} + m_nu^{31} = 0$ using a $T'$ flavor-symmetry extension of the Standard Model. A UV-complete model is proposed that combines type-I and type-II seesaw contributions, with scalar triplets and SM-singlet neutrinos to generate the texture and break degeneracies. Numerical analysis imposes current oscillation, cosmological, and neutrinoless double beta decay constraints for normal and inverted ordering, yielding concrete predictions: for normal ordering, alpha2 near $2 ext{π}$ best fit, alpha1 in $[110^ extcirc,170^ extcirc]$, alpha2 in $[40^ extcirc,60^ extcirc]$ (or $[220^ extcirc,240^ extcirc]$), delta_Dirac in $[240^ extcirc,310^ extcirc]$, m_lightest in $(3-4) imes 10^{-4}$ eV, and $m_{ee}^{0 uetaeta}$ in $ ext{around }3 imes 10^{-3}$ eV; for inverted ordering, alpha1 in $[110^ extcirc,170^ extcirc]$, alpha2 in $[40^ extcirc,60^ extcirc]$ (and also $[220^ extcirc,240^ extcirc]$), delta_Dirac in $[240^ extcirc,310^ extcirc]$, and m_lightest in $(2 imes 10^{-5}, 7 imes 10^{-3})$ eV. These results reveal distinct correlations among Majorana phases, Dirac CP phase, and the lightest-neutrino mass, providing clear targets for upcoming neutrinoless double beta decay and cosmological measurements.

Abstract

The present manuscript studies a recently proposed new neutrino mixing scheme with a neutrino mass selection rule, $m_ν^{13} + m_ν^{22} + m_ν^{31} = 0$, among a neutrino mass matrix elements. The neutrino mass matrix texture is achieved by means of $T^{\prime}$ flavor discrete symmetry extension of the Standard Model gauge group. The model realizing the neutrino mixing pattern consists of a combination of type-I and II seesaw mechanisms in the minimal possible extension of the Standard Model. Stringent predictions are obtained for normal and inverted neutrino mass orderings. Some important predictions include $α_2 \approx 2π$ (best fit), $m_{\text{lightest}} \approx 3 - 4 \times 10^{-4}\,\text{eV}$, and $m_{ee}^{0νββ} \approx 3 \times 10^{-3}\,\text{eV}$ for normal neutrino mass ordering; $110^\circ < α_1 < 170^\circ$, $40(220)^\circ < α_2 < 60(240)^\circ$, $240^\circ < δ_{\text{Dirac}} < 310^\circ$, and $m_{\text{lightest}} \approx 2 \times 10^{-5} - 7 \times 10^{-3}\,\text{eV}$ for inverted neutrino mass ordering.

Figures (11)

• Figure 1: $\alpha_1$ vs $\alpha_2$ correlation.
• Figure 2: Inverted neutrino mass ordering. $\alpha_{1,2}$ vs $\delta_{\text{Dirac}}$ correlation. Color labeling is identical to that of plot in the Fig. \ref{['fig:alpha1_alpha2_IO']}.
• Figure 3: Normal neutrino mass ordering. $\theta_{12}$ vs $\delta_{\text{Dirac}}$ and $\theta_{12}$ vs $\theta_{13}$ correlations. Color labeling is identical to that of plot in the Fig. \ref{['fig:alpha1_alpha2_NO']}.
• Figure 4: Normal neutrino mass ordering. $\theta_{13}$ vs $\delta_{\text{Dirac}}$ and $\theta_{23}$ vs $\delta_{\text{Dirac}}$ correlations. Color labeling is identical to that of plot in the Fig. \ref{['fig:alpha1_alpha2_NO']}.
• Figure 5: $m_{\text{lightest}}$ vs $m_{ee}^{0\nu\beta\beta}$ correlations for normal and inverted neutrino mass ordering. Color labeling is identical to that of plots in the Fig. \ref{['fig:alpha1_alpha2_plots']}.