A randomly generated Majorana neutrino mass matrix using Adaptive Monte Carlo method

A randomly generated complex symmetric matrix using Adaptive Monte Carlo method, is taken as a general form of Majorana neutrino mass matrix, which is diagonalized by the use of eigenvectors. We extract all the neutrino oscillation parameters i.e. two mass-squared differences (Δ m₂₁² and Δ m₃₂² ), three mixing angles (θ₁₂, θ₁₃, θ₂₃) and three phases i.e. one Dirac CP violating phase (δCP) and two Majorana phases (α and β). The charge-parity (CP) violating phases are extracted from the mixing matrix constructed with the eigenvectors of the Hermitian matrix formed by the complex symmetric matrix. All the neutrino oscillation parameters within 3σ bound are allowed in both normal hierarchy (NH) and inverted hierarchy (IH) consistent with the latest Planck cosmological upper bound, ∑ mᵢ<0.12 eV. This latest cosmological upper bound is allowed only in three cases of zero texture for m₁₁=0; m₁₁,m₁₂=0 and m₁₁,m₁₃=0 in normal hierarchy whereas none of zero texture is allowed in inverted hierarchy. We also study effective neutrino masses mβ in tritium beta decay and mββ in neutrinoless double beta decay.