Relating the neutrino mixing angles to a lepton mass hierarchy

TL;DR

This paper introduces two phenomenological models linking lepton mass hierarchies to neutrino mixing angles, predicting specific relations and a normal neutrino mass hierarchy, with testable implications for upcoming experiments.

Contribution

It presents novel lepton mass matrix scenarios that exactly relate neutrino mixing angles to charged lepton masses, with implications for neutrino mass hierarchy and CP violation.

Findings

Predicts an^2 heta_{13} = m_e/(m_e + 2m_mu)

Predicts an^2 heta_{23} = m_mu/(m_e + m_mu)

Estimates heta_{13}  approximately 2.8 and J  about 1.1%

Abstract

We propose two phenomenological scenarios of lepton mass matrices and show that either of them can exactly give rise to \tan^2\theta_{13} = m_e/(m_e + 2m_\mu), \tan^2\theta_{23} = m_\mu/(m_e + m_\mu) and \tan^2\theta_{12} = (m_e m_2 + 2m_\mu m_1)/(m_e m_1 + 2m_\mu m_2) in the standard parametrization of lepton flavor mixing. The third relation, together with current experimental data, predicts a normal but weak hierarchy for the neutrino mass spectrum. We also obtain \theta_{13} \approx 2.8^\circ for the smallest neutrino mixing angle and J \approx 1.1% for the Jarlskog invariant of leptonic CP violation, which will soon be tested in the long-baseline reactor and accelerator neutrino oscillation experiments. A seesaw realization of both scenarios is briefly discussed.