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

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.