Generating $\theta_{13}$ from sterile neutrinos in $\mu - \tau$ symmetric models

TL;DR

This paper explores how sterile neutrinos can induce the small $ heta_{13}$ mixing angle in neutrino oscillations within $ ext{mu}- au$ symmetric models, linking experimental data with theoretical symmetry breaking.

Contribution

It proposes a sterile neutrino as a perturbative source of $ ext{mu}- au$ symmetry breaking, explaining the observed $ heta_{13}$ without violating existing bounds.

Findings

Sterile neutrinos can generate the observed $ heta_{13}$ angle.

Conditions for $ ext{mu}- au$ breaking via sterile neutrinos are established.

Impact on the effective $m_{ee}$ Majorana mass is analyzed.

Abstract

The smallness of the $\theta_{13}$ mixing angle as observed in neutrino oscillation experiments can be understood through an approximated $\mu - \tau$ exchange symmetry in the neutrino mass matrix. Using recent oscillation neutrino data, but assuming no \textit{CP} violation, we study $\mu-\tau$ breaking parameter space to establish the conditions under which such a breaking could have a perturbative origin. According to the so-obtained conditions, we suggest that a sterile neutrino, matching LSND/MiniBooNE neutrino oscillation results, could provide the necessary ingredients to properly fix atmospheric and $\theta_{13}$ mixing angles to observable values, without exceeding the sterile neutrino fraction bound in solar oscillations. In such a scenario, we analyze the general effect of a fourth neutrino on the prediction for the effective $m_{ee}$ majorana mass parameter.