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

A randomly generated complex symmetric matrix using the 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 ([Formula: see text] and [Formula: see text]), three mixing angles ([Formula: see text], [Formula: see text], [Formula: see text]) and three phases, i.e. one Dirac CP violating phase ([Formula: see text]) and two Majorana phases ([Formula: see text] and [Formula: see text]). 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 mass matrix. All the latest neutrino oscillation parameters within 3[Formula: see text] bound are only allowed in Normal Hierarchy (NH) consistent with the latest Planck cosmological upper bound, [Formula: see text][Formula: see text]eV. Three cases of one-zero texture i.e. [Formula: see text], [Formula: see text], [Formula: see text] and two cases of two-zero texture, i.e. [Formula: see text] and [Formula: see text] are allowed in normal hierarchy whereas none of zero texture is allowed in inverted hierarchy. We also study effective neutrino masses [Formula: see text] in tritium beta decay and [Formula: see text] in neutrinoless double beta decay and calculate numerically the allowed range of mass elements of Majorana mass matrix.