Lepton Mixing from Delta (3 n^2) and Delta (6 n^2) and CP

Abstract

We perform a detailed study of lepton mixing patterns arising from a scenario with three Majorana neutrinos in which a discrete flavor group Gf=Delta (3 n^2) or Gf=Delta(6 n^2) and a CP symmetry are broken to residual symmetries Ge=Z3 and Gnu=Z2 x CP in the charged lepton and neutrino sectors, respectively. While we consider all possible Z3 and Z2 generating elements, we focus on a certain set of CP transformations. The resulting lepton mixing depends on group theoretical indices and one continuous parameter. In order to study the mixing patterns comprehensively for all admitted Ge and Gnu, it is sufficient to discuss only three types of combinations. One of them requires as flavor group Delta (6 n^2). Two types of combinations lead to mixing patterns with a trimaximal column, while the third one allows for a much richer structure. For the first type of combinations the Dirac as well as one Majorana phase are trivial, whereas the other two ones predict in general all CP phases to be non-trivial and also non-maximal. Already for small values of the index n of the group, n <= 11, experimental data on lepton mixing can be accommodated well for particular choices of the parameters of the theory. We also comment on the relation of the used CP transformations to the automorphisms of Delta (3 n^2) and Delta (6 n^2).

60 pages, 12 tables and 10 figures. v2: typos corrected, references updated, some minor improvement of the text, matches version accepted for publication in Nuclear Physics B

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