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

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 $\Delta m_{{\nu }_e-{\nu }_X}^2$ ($\sim 10^{-10}e{V}^2$) 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 $\Delta m_{{\nu }_i-{\nu }_{is}}^2$ 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 $\sim (\frac{m_e}{m_{\mu }}{)}^3\Delta m_{atmos}^2$, 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.

Comments: 7 pages, UMD-PP-99-109; new references added; no other change