Majorana neutrino textures from numerical considerations: The CP conserving case

Phenomenological bounds on the neutrino mixing matrix U are used to determine numerically the allowed range of real elements (CP conserving case) for the symmetric neutrino mass matrix M-nu (Majorana case). For this purpose an adaptive Monte Carlo generator has been used. Histograms are constructed to show which forms of the neutrino mass matrix M-nu are possible and preferred. We confirm results found in the literature which are based on analytical calculations, though a few differences appear. These cases correspond to some textures with two zeros. The results show that, actually, both normal and inverted mass hierarchies are still possible at the 3 sigma confidence level.