We investigate the prospects for neutrinoless double beta decay, texture zeros. and equalities between neutrino mass matrix elements in scenarios with vanishing determinant mass matrices for vanishing and finite ${\theta }_{13}$ mixing angles in normal and inverse mass hierarchies. For normal hierarchy and both zero and finite ${\theta }_{13}$ it is found that neutrinoless double beta decay cannot be observed by any of the present or next generation experiments, while for inverse hierarchy it is, on the contrary, accessible to experiments. Regarding texture zeros and equalities between mass matrix elements, we find that in both normal and inverse hierarchies with ${\theta }_{13}=0$ no texture zeros nor any such equalities can exist apart from the obvious ones. For ${\theta }_{13}\ne 0$ some texture zeros become possible. In normal hierarchy two texture zeros occur if $8.1\times {10}^{-2}\le |\sin {\theta }_{13}|\le 9.1\times {10}^{-2}$ while in inverse hierarchy three are possible, one with $|\sin {\theta }_{13}|\ge 7\times {10}^{-3}$ and two others with $|\sin {\theta }_{13}|\ge 0.18$. All equalities between mass matrix elements are impossible with ${\theta }_{13}\ne 0$.

• Received 19 December 2005

DOI:https://doi.org/10.1103/PhysRevD.73.053003