Predictions for the Leptonic Dirac CP Violation Phase: a Systematic Phenomenological Analysis

TL;DR

This paper predicts the leptonic Dirac CP violation phase using a systematic analysis of neutrino mixing matrices, exploring how symmetry-based forms influence the phase and its measurement's potential to reveal lepton sector symmetries.

Contribution

It provides a comprehensive framework for predicting the Dirac CP phase based on various symmetry-inspired neutrino mixing models and current and future experimental sensitivities.

Findings

Likelihood functions for cos δ constructed from global fit data.

Measurement of δ can reveal underlying lepton sector symmetries.

Analysis confirms the importance of precision in mixing angles for CP violation insights.

Abstract

We derive predictions for the Dirac phase $\delta$ present in the $3\times 3$ unitary neutrino mixing matrix $U = U_e^{\dagger} \, U_{\nu}$, where $U_e$ and $U_{\nu}$ are $3\times 3$ unitary matrices which arise from the diagonalisation, respectively, of the charged lepton and the neutrino mass matrices. We consider forms of $U_e$ and $U_{\nu}$ allowing us to express $\delta$ as a function of three neutrino mixing angles, present in $U$, and the angles contained in $U_{\nu}$. We consider several forms of $U_{\nu}$ determined by, or associated with, symmetries, tri-bimaximal, bimaximal, etc., for which the angles in $U_{\nu}$ are fixed. For each of these forms and forms of $U_e$ allowing one to reproduce the measured values of the neutrino mixing angles, we construct the likelihood function for $\cos \delta$, using i) the latest results of the global fit analysis of neutrino oscillation data, and ii) the prospective sensitivities on the neutrino mixing angles. Our results, in particular, confirm the conclusion, reached in earlier similar studies, that the measurement of the Dirac phase in the neutrino mixing matrix, together with an improvement of the precision on the mixing angles, can provide unique information as regards the possible existence of symmetry in the lepton sector.