New Partial Symmetries from Group Algebras for Lepton Mixing

摘要

Recent stringent experiment data of neutrino oscillations induces partial symmetries such as Z2 and Z2×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 S3 group algebras are of the trimaximal form with the μ?τ reflection symmetry. Accordingly, elements of S3 group algebras are equivalent to Z2×CP. Comments on S4 group algebras are given. The predictions of Z2×CP broken from the group S4 with the generalized CP symmetry are also obtained from elements of S4 group algebras.