Dihedral flavor group as the key to understand quark and lepton flavor mixing

Abstract

We have studied the lepton and quark mixing patterns which can be derived from the dihedral group D n in combination with CP symmetry. The left-handed lepton and quark doublets are assigned to the direct sum of a singlet and a doublet of D n. A unified description of the observed structure of the quark and lepton mixing can be achieved if the flavor group D n and CP are broken to Z 2 × CP in neutrino, charged lepton, up quark and down quark sectors, and the minimal group is D 14. We also consider another scenario in which the residual symmetry of the charged lepton and up quark sector is Z 2 while Z 2 ×CP remains preserved by the neutrino and down quark mass matrices. Then D 7 can give the experimentally favored values of CKM and PMNS mixing matrices.

Modular S4 and A4 symmetries and their fixed points: new predictive examples of lepton mixing

“…[2][3][4][5][6][7] for review. Moreover, the leptonic CP violation phases can be predicted and the precisely measured quark CKM mixing matrix can be accommodated if the discrete flavour symmetry is combined with generalized CP symmetry [8][9][10][11].…”

Neutrino masses and mixing from double covering of finite modular groups

“…Discrete flavor symmetry in combination with generalized CP symmetry can give rise to rather predictive models [2][3][4][5][6][7][8][9][10], see [11] for a detailed list of references. In particular, the observed flavor mixing patterns of quark and lepton can be explained simultaneously by the same flavor symmetry group in combination with CP symmetry [12][13][14]. The flavor symmetry group is usually broken down to different subgroups in the neutrino and charged lepton sectors by the vacuum expectation values (VEVs) of a set of scalar flavon fields.…”

Fermion mass hierarchies from modular symmetry

“…[5][6][7][8][9][10][11]). Moreover, the leptonic CP violation phases can be predicted and the precisely measured quark CKM mixing matrix can be accommodated if the discrete flavour symmetry is combined with generalized CP symmetry [12][13][14][15]. However the main drawback of all such approaches that the flavour symmetry must be broken down to different subgroups in the neutrino and charged lepton sectors at low energy and this requires flavon fields to obtain vacuum expectation values (VEVs) along specific directions in order to reproduce phenomenologically viable lepton mixing angles.…”