Neutrino mass matrices with one texture zero and a vanishing neutrino mass

Abstract

Assuming Majorana nature of neutrinos, we investigate the singular one texture zero neutrino mass matrices in the flavor basis. We find that for the normal mass ordering with $m_1=0$, all the six one texture zero classes are now ruled out at 3$\sigma$ confidence level, whereas for inverted mass ordering with $m_3=0$ only four classes out of total six can accommodate the latest neutrino oscillation data at 3$\sigma$ confidence level. Moreover, only two classes can accommodate the present data at 1$\sigma$ confidence level. We examine the phenomenological implications of the allowed classes for the effective Majorana mass, Dirac and Majorana CP-violating phases. Working within the framework of type-I seesaw mechanism, we present simple discrete Abelian symmetry models leading to all the phenomenologically allowed classes.

Comments: 11 pages, 3 figures, 5 tables