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

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.