Lepton mixing from Δ(3n2)Δ(3n2) and Δ(6n2)Δ(6n2) and CP

We perform a detailed study of lepton mixing patterns arising from a scenario with three Majorana neutrinos in which a discrete flavor group Gf=Δ(3n2)Gf=Δ(3n2) or Gf=Δ(6n2)Gf=Δ(6n2) and a CP symmetry are broken to residual symmetries Ge=Z3Ge=Z3 and Gν=Z2×CPGν=Z2×CP in the charged lepton and neutrino sectors, respectively. While we consider all possible Z3Z3 and Z2Z2 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 GeGe and GνGν, it is sufficient to discuss only three types of combinations. One of them requires as flavor group Δ(6n2)Δ(6n2). 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 phase as well as one of the Majorana phases are trivial, whereas the other two types of combinations 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≤11n≤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 Δ(3n2)Δ(3n2) and Δ(6n2)Δ(6n2).