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

TL;DR

This paper uses an Adaptive Monte Carlo method to generate and analyze a complex symmetric Majorana neutrino mass matrix, extracting oscillation parameters and phases, and examining compatibility with cosmological bounds and decay experiments.

Contribution

It introduces a novel application of Adaptive Monte Carlo to generate neutrino mass matrices and systematically extract oscillation parameters and phases.

Findings

Oscillation parameters within 3σ bounds are consistent with Planck data.

Certain zero textures are compatible with normal hierarchy but not inverted hierarchy.

Effective neutrino masses are evaluated for decay experiments.

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.