Predictions for the Dirac CP Violation Phase in the Neutrino Mixing Matrix

TL;DR

This paper investigates how the Dirac CP violation phase in the neutrino mixing matrix can be predicted using sum rules derived from discrete flavor symmetries and minimal charged lepton corrections, aligning with current neutrino data.

Contribution

It derives specific sum rules for the Dirac phase based on the structure of the neutrino and charged lepton mixing matrices influenced by discrete flavor symmetries.

Findings

Predicted ranges for the Dirac CP phase δ consistent with current data.

Relations between mixing angles and CP phase derived from symmetry considerations.

Constraints on flavor symmetry models based on phase predictions.

Abstract

Using the fact that the neutrino mixing matrix $U = U^\dagger_{e}U_{\nu}$, where $U_{e}$ and $U_{\nu}$ result from the diagonalisation of the charged lepton and neutrino mass matrices, we analyse the predictions based on the sum rules which the Dirac phase $\delta$ present in $U$ satisfies when $U_{\nu}$ has a form dictated by, or associated with, discrete flavour symmetries and $U_e$ has a "minimal" form (in terms of angles and phases it contains) that can provide the requisite corrections to $U_{\nu}$, so that the reactor, atmospheric and solar neutrino mixing angles $\theta_{13}$, $\theta_{23}$ and $\theta_{12}$ have values compatible with the current data.