Sterile Neutrinos in E_6 and a Natural Understanding of Vacuum Oscillation Solution to the Solar Neutrino Puzzle

TL;DR

This paper shows that in E_6-based models with sterile neutrinos, the tiny mass differences needed for solar neutrino oscillations naturally emerge, linking them to known lepton mass ratios and atmospheric neutrino data.

Contribution

The paper demonstrates that E_6 models with sterile neutrinos naturally produce the small mass differences required for the vacuum oscillation solution to the solar neutrino puzzle.

Findings

Mass difference squared for solar neutrinos is proportional to (m_e/m_μ)^3 times atmospheric neutrino mass difference.

The model predicts the solar neutrino oscillation parameters based on known lepton masses and atmospheric data.

Provides a natural theoretical framework for the vacuum oscillation solution to the solar neutrino problem.

Abstract

If Nature has chosen the vacuum oscillation solution to the Solar neutrino puzzle, a key theoretical challenge is to understand the extreme smallness of the $\Delta m^2_{\nu_e-\nu_X}$ ($\sim 10^{-10} eV^2$) required for the purpose. We find that in a class of models such as [SU(3)]^3 or its parent group E_6, which contain one sterile neutrino, $\nu_{is}$ for each family, the $\Delta m^2_{\nu_i-\nu_{is}}$ is proportional to the cube of the lepton Yukawa coupling. Therefore fitting the atmospheric neutrino data then predicts the $\nu_e-\nu_{es}$ mass difference square to be $\sim (\frac{m_e}{m_{\mu}})^3 \Delta m^2_{atmos}$, where the atmospheric neutrino data is assumed to be solved via the $\nu_{\mu}-\nu_{\mu s}$ oscillation. This provides a natural explanation of the vacuum oscillation solution to the solar neutrino problem.