Geometric Mean Neutrino Mass Relation

Abstract

Present experimental data from neutrino oscillations have provided much information about the neutrino mixing angles. Since neutrino oscillations only determine the mass squared differences $\Delta m_{ij}^2=m_i^2-m_j^2$, the absolute values for neutrino masses $m_i$ can not be determined using data just from oscillations. In this work we study implications on neutrino masses from a geometric mean mass relation $m_2=\sqrt{m_1{m}_3}$ which enables one to determined the absolute masses of the neutrinos. We find that the central values of the three neutrino masses and their $2\sigma$ errors to be $m_1=(1.58\pm 0.18)meV$, $m_2=(9.04\pm 0.42)meV$, and $m_3=(51.8\pm 3.5)meV$. Implications for cosmological observation, beta decay and neutrinoless double beta decays are discussed.

7 pages. Talk given at COSPA06. A reference added