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.