Further study on the textures of neutrino mass matrix for maximal atmospherical mixing angle and Dirac CP phase

TL;DR

This paper explores specific neutrino mass matrix textures that can produce maximal atmospheric mixing and CP violation, deriving sum rules to determine unknown parameters and discussing model realizations.

Contribution

It introduces a novel approach to identify neutrino mass matrix textures leading to maximal mixing and CP phases, including sum rules and model implications.

Findings

Derived textures lead to maximal atmospheric mixing and CP phase.

Established neutrino mass sum rules relating masses and mixing.

Discussed model realizations and symmetry breakings of textures.

Abstract

In this paper, we derive in a novel approach the possible textures of neutrino mass matrix that can lead to maximal atmospherical mixing angle ($\theta^{}_{23} = \pi/4$) and Dirac CP phase ($\delta = - \pi/2$) in two phenomenologically appealing scenarios: (1) one neutrino mass matrix element being vanishing (2) one neutrino mass being vanishing. For the obtained textures, some neutrino mass sum rules which relate the neutrino masses and mixing parameters will emerge. With the help of these sum rules, the unknown absolute neutrino mass scale and Majorana CP phases can be determined. Some discussions about the possible textures of neutrino mass matrix that can lead to $\theta^{}_{23} = \pi/4$, $\delta = - \pi/2$ and maximal Majorana CP phases ($\rho, \sigma = \pi/4$ or $3\pi/4$) as well as the model realization and breakings of the obtained textures are also given.