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

Abstract

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 ($\Delta m_{21}^2$ and $\Delta m_{32}^2$ ), three mixing angles ($\theta_{12}$, $\theta_{13}$, $\theta_{23}$) and three phases i.e. one Dirac CP violating phase ($\delta_{CP}$) and two Majorana phases ($\alpha$ and $\beta$). 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 3$\sigma$ bound are allowed in both normal hierarchy (NH) and inverted hierarchy (IH) consistent with the latest Planck cosmological upper bound, $\sum\vert m_i\vert<0.12$ eV. This latest cosmological upper bound is allowed only in three cases of zero texture for $m_{11}=0$; $m_{11},m_{12}=0$ and $m_{11},m_{13}=0$ in normal hierarchy whereas none of zero texture is allowed in inverted hierarchy. We also study effective neutrino masses $m_{\beta}$ in tritium beta decay and $m_{\beta\beta}$ in neutrinoless double beta decay.