Two-zero Majorana textures in the light of the Planck results

The recent results of the Planck experiment put a stringent constraint on the sum of the light neutrino masses, Σᵢmᵢ<0.23 eV (95% C.L.). On the other hand, two-zero Majorana mass matrix textures predict strong correlations among the atmospheric angle sin²θ₂₃ and Σ. We use the Planck result to show that, for the normal hierarchy case, the texture with vanishing (2, 2) and (3, 3) elements is ruled out at a high confidence level; in addition, we emphasize that a future measurement of the octant of θ₂₃ (or the 1σ determination of it based on a recent fit to neutrino data) will put a severe constraint on the possible structure of the Majorana mass matrix. The implication of the above-mentioned correlations for neutrinoless double β decay are also discussed, for both normal and inverted orderings.