Finite flavour groups of fermions

Abstract

We present an overview of the theory of finite groups, with regard to their application as flavour symmetries in particle physics. In a general part, we discuss useful theorems concerning group structure, conjugacy classes, representations and character tables. In a specialized part, we attempt to give a fairly comprehensive review of finite subgroups of SO(3) and SU (3), in which we apply and illustrate the general theory. Moreover, we also provide a concise description of the symmetric and alternating groups and comment on the relationship between finite subgroups of U (3) and finite subgroups of SU (3). Though in this review we give a detailed description of a wide range of finite groups, the main focus is on the methods which allow the exploration of their different aspects. *

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

“…For recent reviews of model building and relevant group theory aspects (see for example [10][11][12][13][14]). Three different model building approaches have been identified, known as "direct", "semi-direct" and "indirect" [13,14].…”

Leptonic dynamical Yukawa couplings

“…This is in contrast to the simplest quark case -which yields a vanishing mixing angle -and it leads to a strong correlation between neutrino mass hierarchy and mixing pattern: a novelty in the field (see refs. [34][35][36][37][38] for recent reviews on lepton flavour models).…”

Repressing anarchy in neutrino mass textures

“…Thus one is naturally led to discrete flavour groups. Models based on discrete flavour symmetries, like A 4 or S 4 , have been proposed in this context and widely studied [56][57][58][59][60][61][62]. In these models the starting Leading Order (LO) approximation is completely fixed (no chance), but the Next to LO (NLO) corrections still introduce a number of undetermined parameters, although in general much less numerous than for U(1) FN models.…”