Fine-tuning and naturalness issues in the two-zero neutrino mass textures

In this paper we analyze the compatibility of two-zero neutrino Majorana textures with the recent experimental data. Differently from previous works, we use the experimental data to fix the values of the non-vanishing mass matrix entries and study in detail the correlations and degree of fine-tuning among them, which is also a measure of how naturally a given texture is able to describe all neutrino data. This information is then used to expand the textures in powers of the Cabibbo angle; extracting random O(1) coefficients, we show that only in few cases such textures reproduce the mixing parameters in their 3σ ranges.