Maximal Abelian flavor symmetries

A bstract A framework, MAFS, is introduced that provides an approximate description of the hierarchies of quark and lepton masses and mixing angles in terms of a set of small parameters, ϵ a , one for each fermion multiplet. MAFS is an alternative to the Froggatt-Nielsen mechanism and has a unique application in any theory, as there are no fermion charges to choose. It becomes more powerful as the number of multiplets is reduced. In SU (5) unified theories, 15 observed mass ratios and mixing angles are described, at the level of factors of 2–3, by five small ϵ a parameters. Even though quarks and leptons are unified, the observed hierarchical pattern of quark masses and mixings requires large neutrino mixing angles and small neutrino mass hierarchies. In an SO (10) unified theory, MAFS successfully describes the 15 observed flavor hierarchies with just three small ϵ a , taking values of 0 . 01 , 0 . 02 and 0 . 002. The observed cosmological baryon asymmetry results approximately from leptogenesis using MAFS in SU (5), without the need for any additional small parameter; while in SO (10), a further small parameter of about 0.2 appears necessary.