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 × 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.And 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 µ − τ reflection symmetry.Accordingly, elements of S 3 group algebras are equivalent to Z 2 × CP. Comments on S 4 group algebras are given. And the predictions of Z 2 × CP broken from the group S 4 with the generalized CP symmetry are also obtained from elements of S 4 group algebras.

The Geometric Correlations of Leptonic Mixing Parameters

“…Another method introduces a generalized CP transform on the basis of a discrete flavor symmetry, i.e., a finite flavor group G f and a CP symmetry are combined [23][24][25][26][27]. Furthermore, a novel mathematical structure called group algebra was introduced [28,29]. In this scenario, a specific leptonic mixing pattern could correspond to a set of equivalent elements of a group algebra.…”