Lepton Mass Hierarchy and Neutrino Mixing

Abstract

We speculate that the mass spectrum of three neutrinos might have a normal hierarchy as that of three charged leptons or that of three up-type (or down-type) quarks. In this spirit, we propose a novel parametrization of the $3\times 3$ lepton flavor mixing matrix. Its mixing angles ${\theta }_l$ and ${\theta }_{\nu }$ can be related to the mass ratios $m_e/m_{\mu }$ and $m_1/m_2$ in a specific texture of lepton mass matrices with vanishing (1,1) elements: $\tan {\theta }_l=\sqrt{m_e/m_{\mu }}$ and $\tan {\theta }_{\nu }=\sqrt{m_1/m_2}$. The latter relation, together with solar and atmospheric neutrino oscillation data, predicts 0.0030 eV $\lesssim m_1\lesssim$ 0.0073 eV, 0.009 eV $\lesssim m_2\lesssim$ 0.012 eV and 0.042 eV $\lesssim m_3\lesssim$ 0.058 eV. The smallest neutrino mixing angle is found to be ${\theta }_{13}\approx {\theta }_l/\sqrt{2}\approx 3^{\circ }$, which is experimentally accessible in the near future.

RevTex 10 pages, 2 figures