Neutrino masses from an approximate mixing matrix with $\theta_{13}\neq 0$

TL;DR

This paper develops an approximate neutrino mixing matrix based on experimental data, constrains the neutrino mass matrix with zero textures, and predicts neutrino masses consistent with observed mass differences.

Contribution

It introduces a method to derive neutrino masses from an approximate mixing matrix with a non-zero $ heta_{13}$ and zero textures, providing specific mass predictions.

Findings

Predicted neutrino masses are consistent with experimental mass differences.

The approach accurately reproduces the solar neutrino squared mass difference.

Neutrino masses depend on the mixing angle $ heta_{13}$ and hierarchy assumptions.

Abstract

An approximate neutrino mixing matrix is formutated by using the standard neutrino mixing matrix as a basis and experimental data of neutrino oscillations as inputs. By using the resulted approximate neutrino mixing matrix to proceed the neutrino mass matrix and constraining the resulted neutrino mass matrix with zero texture: $M_{\nu}(1,1)=M_{\nu}(1,3)=M_{\nu}(3,1)=0$, we can have neutrino masses as function of mixing angle $\theta_{13}$ with normal hierarchy: $m_{1}<m_{2}<m_{3}$. By taking the central value of mixing angle $\theta_{13}=9^{o}$ that gives $\epsilon=0.16$ and using the squared mass difference: $\Delta m_{32}^{2}$ for normal hierarchy, we then obtained neutrino masses: $m_{1}=0.00847$ eV, $m_{2}=0.01215$ eV, and $m_{3}=0.05062$ eV which can predict the squared mass difference for solar neutrino precisely with the experimental result: $\Delta m_{21}^{2}=7.59\times 10^{-5}~{\rm eV^{2}}$