Relating Lepton Mixing Angles with Lepton Mass Hierarchy

Abstract

We revisit the possibility of relating lepton mixing angles with lepton mass hierarchies in a model-independent way. Guided by the existence of such relations in the quark sector, we first consider all the mixing angles, both in charged lepton and neutrino sectors to be related to the respective mass ratios. This allows us to calculate the leptonic mixing angles observed in neutrino oscillations as functions of the lightest neutrino mass. We show that for both normal and inverted hierarchical neutrino masses, this scenario does not give rise to correct leptonic mixing angles. We then show that correct leptonic mixing angles can be generated with normal hierarchical neutrino masses if the relation between mixing angle and mass ratio is restricted to 1-2 and 1-3 mixing in both charged lepton and neutrino sectors leaving the 2-3 mixing angles as free parameters. We then restrict the lightest neutrino mass as well as the difference between 2-3 mixing angles in charged lepton and neutrino sectors from the requirement of producing correct leptonic mixing angles. We constrain the lightest neutrino mass to be around $0.002$ eV and leptonic Dirac CP phase $\delta_{CP}$ such that $\sin^2{\delta_{CP}}\sim(0.35-0.50)$. We also construct the leptonic mass matrices in terms of $2-3$ mixing angles and lightest neutrino mass and briefly comment on the possibility of realizing texture zeros in the neutrino mass matrix.