$\mu$-$\tau$ reflection symmetry and radiative corrections

TL;DR

This paper investigates how $$-tau reflection symmetry in neutrino physics, which predicts specific mixing angles and phases, is affected by radiative corrections, leading to testable deviations at low energies.

Contribution

The authors analytically derive the radiative corrections to neutrino mixing parameters under $$-tau reflection symmetry and perform numerical analysis within the MSSM framework.

Findings

Deviations in $ heta_{23}$ depend on mass ordering: above 45° for normal, below for inverted.

Sizable correction to $$ phase favors negative values.

Predicted deviations are testable in future neutrino oscillation experiments.

Abstract

The $\mu$-$\tau$ reflection symmetry is compatible with current neutrino oscillation data and easily realized under family symmetries. We prove that this symmetry preserves $\theta_{23}=45^\circ$, $\delta=\pm90^\circ$, $\rho,\sigma=0,90^\circ$, and can be embedded into the seesaw mechanism. The $\mu$-$\tau$ reflection symmetry preserved at a high energy scale $\Lambda_\text{FS}$ will be broken by radiative corrections and result in deviations of $\theta_{23}$ from $45^\circ$ and $\delta$ from $\pm90^\circ$ at the electroweak scale. We develop an analytical method to derive the corrections to all the mixing parameters. We perform a numerical analysis in the MSSM for $\delta=-90^\circ$ at $\Lambda_\text{FS}$, and observe that $\theta_{23}>45^\circ$ in the normal mass ordering, $\theta_{23}<45^\circ$ in the inverted mass ordering, and the sizable correction to $\delta$ prefers a negative sign. These deviations have definite directions and can be tested in the future neutrino oscillation experiments.