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

The present manuscript studies a recently proposed new neutrino mixing scheme with a neutrino mass selection rule, $m_{\nu }^{13}+m_{\nu }^{22}+m_{\nu }^{31}=0$, among a neutrino mass matrix elements. The neutrino mass matrix texture is achieved by means of $T^{\mathrm{\prime }}$ 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 ${\alpha }_2\approx 2\pi$ (best fit), $m_{\text{lightest}}\approx 3-4\times {10}^{-4}\text{eV}$, and $m_{ee}^{0\nu \beta \beta }\approx 3\times {10}^{-3}\text{eV}$ for normal neutrino mass ordering; ${110}^{\circ }<{\alpha }_1<{170}^{\circ }$, $40(220{)}^{\circ }<{\alpha }_2<60(240{)}^{\circ }$, ${240}^{\circ }<{\delta }_{\text{Dirac}}<{310}^{\circ }$, and $m_{\text{lightest}}\approx 2\times {10}^{-5}-7\times {10}^{-3}\text{eV}$ for inverted neutrino mass ordering.