U_{PMNS} = U_ell^dagger U_nu

TL;DR

This paper investigates how corrections from charged leptons and neutrinos affect the PMNS matrix, linking observable neutrino mixing angles and CP violation, and introduces sum-rules for these parameters.

Contribution

It provides a detailed analysis of corrections to neutrino mixing parameters from charged lepton and neutrino sectors, including new sum-rules independent of parametrization.

Findings

|U_{e3}| can be sizable and close to current experimental limits.

The solar mixing angle is linked to CP violation magnitude.

Both correction scenarios align with current observations.

Abstract

We consider corrections to vanishing U_{e3} and maximal atmospheric neutrino mixing originating from the relation U = U_ell^dagger U_nu, where U is the PMNS mixing matrix and U_ell (U_nu) is associated with the diagonalization of the charged lepton (neutrino) mass matrix. We assume that in the limit of U_ell or U_nu being the unit matrix, one has U_{e3} = 0 and theta_{23} = pi/4, while the solar neutrino mixing angle is a free parameter. Well-known special cases of the indicated scenario are the bimaximal and tri-bimaximal mixing schemes. If U_{e3} \neq 0 and theta_{23} \neq pi/4 due to corrections from the charged leptons, |U_{e3}| can be sizable (close to the existing upper limit) and we find that the value of the solar neutrino mixing angle is linked to the magnitude of CP violation in neutrino oscillations. In the alternative case of the neutrino sector correcting U_{e3} = 0 and theta_{23} = pi/4, we obtain a generically smaller |U_{e3}| than in the first case. Now the magnitude of CP violation in neutrino oscillations is connected to the value of the atmospheric neutrino mixing angle theta_{23}. We find that both cases are in agreement with present observations. We also introduce parametrization independent "sum-rules" for the oscillation parameters.