Trimaximal μ−τ reflection symmetry

Abstract

The $\ensuremath{\mu}\text{\ensuremath{-}}\ensuremath{\tau}$ reflection symmetry $({\ensuremath{\nu}}_{e},{\ensuremath{\nu}}_{\ensuremath{\mu}},{\ensuremath{\nu}}_{\ensuremath{\tau}})\ensuremath{\rightarrow}({\overline{\ensuremath{\nu}}}_{e},{\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}},{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}})$ and the TM1 mixing (a Pontecorvo--Maki--Nakagawa--Sakata matrix with the first column fixed to the tribimaximal form) are both well compatible with experiments. If both approaches are simultaneously assumed, all lepton mixing parameters except for ${\ensuremath{\theta}}_{13}$ are predicted. In particular, one expects maximal $CP$ violation ($|\ensuremath{\delta}|=90\ifmmode^\circ\else\textdegree\fi{}$), maximal atmospheric mixing (${\ensuremath{\theta}}_{23}=45\ifmmode^\circ\else\textdegree\fi{}$), a slightly less-than-tribimaximal solar mixing angle (${\ensuremath{\theta}}_{12}\ensuremath{\approx}34\ifmmode^\circ\else\textdegree\fi{}$), as well as values of 0 or $\ensuremath{\pi}$ 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.