Modifications to the neutrino mixing from the mu-tau reflection symmetry

TL;DR

This paper investigates how to modify the neutrino mixing matrix derived from mu-tau reflection symmetry to better align with precise experimental measurements, using specific rotation-based adjustments.

Contribution

It introduces a framework for modifying the neutrino mixing matrix via real orthogonal rotations to account for deviations from mu-tau reflection symmetry.

Findings

Provides a method to adjust the mixing matrix with rotations

Analyzes the impact of modifications on mixing angles and phases

Offers insights into potential deviations from symmetry predictions

Abstract

The $\mu$-$\tau$ reflection symmetry serves as a unique basis for understanding the observed neutrino mixing as it can lead us to the interesting results $\theta^{}_{23} = \pi/4$ and $\delta = -\pi/2$ which stand close to the current experimental results. But a precise measurement for $\theta^{}_{23}$ and $\delta$ will probably force us to modify the neutrino mixing $U^{(0)}$ from such a symmetry. Here we perform a study for modifications to $U^{(0)}$ in the forms of $U^{(1)\dagger} U^{(0)}$ and $U^{(0)} U^{(1)}$ where $U^{(1)}= R^{(1)}_{ij}$ (for $ij = 12, 23$ and 13) with $R^{(1)}_{ij}$ denoting a real orthogonal rotation on the $ij$ plane.