# Trimaximal $\mu$-$\tau$ reflection symmetry

## TL;DR

This paper explores a highly predictive lepton mixing framework combining $$-$ au$ reflection symmetry and TM1 mixing, analyzing its stability under renormalization in different neutrino mass models.

## Contribution

It introduces a combined $$-$ au$ reflection and TM1 mixing scheme and studies its renormalization stability in the Standard Model and supersymmetric contexts.

## Key findings

- Predicts maximal CP violation and atmospheric mixing angle.
- Shows stability of the framework under renormalization effects.
- Provides constraints on Majorana phases and mixing angles.

## Abstract

The $\mu$-$\tau$ reflection symmetry $(\nu_{e},\thinspace\nu_{\mu},\thinspace\nu_{\tau})\rightarrow(\overline{\nu}_{e},\thinspace\overline{\nu}_{\tau},\thinspace\overline{\nu}_{\mu})$ and the TM1 mixing (a PMNS matrix with the first column fixed to the TBM form) are both well compatible with experiments. If both approaches are simultaneously assumed, all lepton mixing parameters except for $\theta_{13}$ are predicted. In particular, one expects maximal CP violation ($|\delta|=90^{\circ}$), maximal atmospheric mixing ($\theta_{23}=45^{\circ}$), a slightly less-than-TBM solar mixing angle ($\theta_{12}\approx34^{\circ}$), as well as values of $0$ or $\pi$ for the two Majorana phases. We study the renormalization stability of this highly predictive framework when neutrino mass is described by an effective Weinberg operator and by the type I seesaw mechanism, both in the Standard Model and with supersymmetry.