New partial symmetries from group algebras for lepton mixing

Abstract

Recent stringent experiment data of neutrino oscillations induces partial symmetries such as $Z_2$, $Z_2\times CP$ to derive lepton mixing patterns. New partial symmetries expressed with elements of group algebras are studied. A specific lepton mixing pattern could correspond to a set of equivalent elements of a group algebra. The transformation which interchanges the elements could express a residual $CP$ symmetry. Lepton mixing matrices from $S_3$ group algebras are of the trimaximal form with the $\mu -\tau$ reflection symmetry. Accordingly, elements of $S_3$ group algebras are equivalent to $Z_2\times CP$. Comments on $S_4$ group algebras are given. The predictions of $Z_2\times CP$ broken from the group $S_4$ with the generalized $CP$ symmetry are also obtained from elements of $S_4$ group algebras.

Comments: 15 pages, 1 figure. More refs. are added