Abstract
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.
Highlights
Discoveries of neutrino oscillation [1,2,3] opened a window to physics beyond the standard model
The residual symmetry is expressed by an element of group algebras
A specific lepton mixing pattern corresponds to a set of equivalent residual symmetries which are expressed by elements of group algebras Xi
Summary
Discoveries of neutrino oscillation [1,2,3] opened a window to physics beyond the standard model. For Z2 symmetries, an unfixed unitary rotation is contained in the mixing matrix Even so, they may predict some mixing angle, Dirac CP phase, or correlation of them. The partial symmetry is expressed by an element of a group algebra. Similar to the residual symmetry Z2 × CP, the elements of a group algebra with continuous superposition coefficients may describe partial symmetries of leptons. They may be used to predict the lepton mixing pattern. We cannot prove that the equivalence holds for X in a general algebra, we may have more choices in the realization of partial symmetries.
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