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

Abstract

The $\mu$-$\tau$ reflection symmetry $({\nu }_e,{\nu }_{\mu },{\nu }_{\tau })\to ({\overline{\nu }}_e,{\overline{\nu }}_{\tau },{\overline{\nu }}_{\mu })$ 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 (${\theta }_{12}\approx 34^{\circ }$), 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.

Comments: 12 pages, comments added, version to appear in PRD