Neutrino mixing and CP violation from Dirac-Majorana mixing

TL;DR

This paper predicts the lepton mixing angle θ13 using a minimal condition related to Dirac-Majorana mixing, aligning well with experimental data for normal mass ordering and exploring CP violation implications.

Contribution

It introduces a minimal condition linking θ13 to the Cabibbo angle and provides improved predictions, along with a model-independent measure of CP violation.

Findings

Predicted θ13 ≈ 8.6° for normal ordering, matching global fits.

Predicted θ13 ≈ 9.7° for inverted ordering, inconsistent with current data.

Shows that CP phase δ_CP can vary widely with fine tuning, but is generally small without tuning.

Abstract

We consider a minimal condition that predicts the 1-3 lepton mixing angle $\theta_{13} \simeq \theta_{\rm C}/\sqrt{2}$ with $\theta_{\rm C}$ the Cabibbo angle, and give the improved prediction of $\theta_{13}$. In the case of normal mass ordering, the theoretical value of $\theta_{13}$ is predicted as $\theta_{13}=8.6^\circ$, which is in good agreement with the current global best fit. In the case of inverted mass ordering, the theoretical value is predicted as $\theta_{13}=9.7^\circ$, which is far from the current global best fit. We also study the leptonic CP violation. We show that any values of the leptonic Dirac CP phase $\delta_{\rm CP}$ can be obtained by fine tuning. Without fine tuning, $|\sin\delta_{\rm CP}|$ should be very small, typically of ${\cal O}(\lambda^2)$ where $\lambda\equiv \sin\theta_{\rm C}$. Furthermore, a model-independent measure of CP violation is proposed, which is applicable to any flavor models.