Lepton mixing fromΔ(3n2)andΔ(

Abstract

We perform a detailed study of lepton mixing patterns arising from a scenario with three Majorana neutrinos in which a discrete flavor group G f = (3n 2 ) or G f = (6n 2 ) and a CP symmetry are broken to residual symmetries G e = Z 3 and G ν = Z 2 × CP in the charged lepton and neutrino sectors, respectively. While we consider all possible Z 3 and Z 2 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 G e and G ν , it is sufficient to discuss only three types of combinations. One of them requires as flavor group (6n 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 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 ≤ 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 (3n 2 ) and (6n 2 ).

Generalised CP and Δ(6n 2) family symmetry in semi-direct models of leptons

“…Where the results overlap for ∆(6n 2 ) they appear to be broadly in agreement, although the case that the residual symmetry Z 2 × CP is preserved by the charged lepton sector was not considered in [59]. The present paper focuses exclusively on ∆(6n 2 ), and, apart from considering extra cases not previously considered, presents the numerical results in a quite different and complementary way.…”

“…While this paper was being prepared, a study of generalised CP within the semi-direct approach appeared based on the infinite series of finite groups ∆(6n 2 ) and ∆(3n 2 ) [59]. Where the results overlap for ∆(6n 2 ) they appear to be broadly in agreement, although the case that the residual symmetry Z 2 × CP is preserved by the charged lepton sector was not considered in [59].…”

Lepton sector phases and their roles in flavor and generalized CP symmetries

“…Eq. (14). Such a global phase redefinition changes the traces of the X Diag ν thereby affecting their group character when θ ν = 0, cf.…”

“…The CP symmetry should of course be defined consistently together with the discrete flavor symmetry [9]. Many such models of CP and flavor symmetries have been proposed and investigated, including models based on A 4 [10,11]/∆(3n 2 ) [12][13][14][15], A 5 [16][17][18][19], S 4 [21][22][23][24][25][26]/∆(6n 2 ) [14,[27][28][29][30], Σ(nφ) [31,32], T ′ [33], and D (1) 9n,3n [34]. 1 With these studies in mind, is also worthwhile to take a bottom-up perspective, in which the goal is not to construct a specific top-down model, but instead to elucidate how and when preserving different residual CP and flavor symmetry elements affects the predictions for the lepton mixing parameters.…”

Neutrino masses and mixing from flavour antisymmetry

“…See [39][40][41] for earlier studies of neutrino mixing using the groups ∆(3N 2 ) and ∆(6N 2 ) and neutrino symmetry rather than antisymmetry.…”