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.