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 m1 = 0, all the six one texture zero classes are now ruled out at 3σ confidence level, whereas for inverted mass ordering with m3 = 0 only four classes out of total six can accommodate the latest neutrino oscillation data at 3σ confidence level. Moreover, only two classes can accommodate the present data at 1σ 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.

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The latest data from Planck collaboration has presented an improved sensitivity limit of the sum of neutrino masses (Σ), Σ < 0.17eV at 95% confidence level (CL). On the other hand, the updated global fits of neutrino oscillation have shown a refined range of atmospheric mixing angle θ 23 at the same CL. In the light of these observations, we have re-investigated the five viable cases ( B 1,2,3,4 and C) of texture two zero Majorana mass matrix in the flavor basis. Using the present Planck's data, we have demonstrated that only cases B 2 and B 4 are now viable for normal mass ordering, while remaining three cases does not meet the present experimental constraints at 2σ CL. The viable cases are also found to be in agreement with the latest T2K, Super-Kamiokande and NOνA results, indicating the preference for normal neutrino mass ordering (m 1 < m 2 < m 3 ), a maximal Dirac CP-violating phase (δ ≃ 270 0 ), and upper octant of neutrino mixing angle (θ 23 > 45 0 ). In addition, the implication of Σ on neutrinoless double beta decay is studied for viable cases.

In the light of non-zero and relatively large value of rector mixing angle (θ 13 ), we have performed a detailed analysis of texture one zero neutrino mass matrix M ν in the scenario of vanishing determinant/trace conditions , assuming the Dirac nature of neutrinos. In both the scenarios, normal mass ordering is ruled out for all the six possibilities of M ν , however for inverted mass ordering, only two are found to be viable with the current neutrino oscillation data at 3σ confidence level. Numerical and some approximate analytical results are presented.

We have studied that the implication of a large value of the effective Majorana neutrino mass in case of neutrino mass matrices has either two equal elements and one zero element (popularly known as hybrid texture) or two equal cofactors and one zero minor (popularly known as inverse hybrid texture) in the flavor basis. In each of these cases, four out of sixty phenomenologically possible patterns predict near maximal atmospheric neutrino mixing angle in the limit of large effective Majorana neutrino mass. This feature remains irrespective of the experimental data on solar and reactor mixing angles. In addition, we have also performed the comparative study of all the viable cases of hybrid and inverse hybrid textures at 3 CL.