Implications of ${\delta }_l^{CP}\sim 270^{\circ }$ and ${\theta }_{23}\gtrsim 45^{\circ }$ for texture specific lepton mass matrices and $0\nu \beta \beta$ decay

Abstract

We study the phenomenological consequences of recent results from atmospheric and accelerator neutrino experiments, favoring normal neutrino mass ordering $m_1<m_2<m_3$, a near maximal lepton Dirac CP phase ${\delta }_l\sim 270^{\circ }$ along with ${\theta }_{23}\gtrsim 45^{\circ }$, for possible realization of natural structure in the lepton mass matrices characterized by $(M_{ij})\sim O(\sqrt{m_i{m}_j})$ for $i,j=1,2,3$. It is observed that deviations from parallel texture structures for $M_l$ and $M_{\nu }$ are essential for realizing such structures. In particular, such hierarchical neutrino mass matrices are not supportive for a vanishing neutrino mass $m_{\nu 1}\to 0$ characterized by Det$M_{\nu }\ne 0$ and predict $m_{\nu 1}\simeq (0.1-8.0)$ $meV$ , $m_{\nu 2}\simeq (8.0-13.0)$ $meV$, $m_{\nu 3}\simeq (47.0-52.0)$ $meV$, $\Sigma \simeq (56.0-71.0)$ $meV$ and $⟨m_{ee}⟩\simeq (0.01-10.0)$ $meV$, respectively, indicating that the task of observing a $0\nu \beta \beta$ decay may be rather challenging for near future experiments.

Comments: 12 pages, 10 figures, 2 tables