Grand Unification with Anomalous U(1) Symmetry and Non-abelian Horizontal Symmetry

Non-abelian horizontal symmetry has been considered to solve potentially SUSY flavor problem, but simple models are suffering from various problems. In this talk, we point out that (anomalous) U(1)A gauge symmetry solves all the problems in a natural way, especially, in the E6 grand unified theories. Combining the GUT scenario with anomalous U(1)A gauge symmetry, in which doublet-triplet splitting and natural gauge coupling unification are realized, and realistic quark and lepton mass matrices are obtained including bi-large neutrino mixings, complete E6 × SU(3)H (or E6 × SU(2)H ) GUTs can be obtained, in which all the three generation quarks and leptons are unified into a single multiplet (27,3) (or two multiplets (27,2+ 1)). This talk is based on Ref. [1]. e-mail: [email protected] 1 Problems of Simple Models with Horizontal Symmetry First of all, we recall the basic features and the problems of non-abelian horizontal symmetry,[2, 3] considering a simple model with a horizontal symmetry U(2)H , under which the three generations of quarks and leptons, Ψi = (Ψa,Ψ3) (a = 1, 2) (Ψ = Q,U,D, L,E,N), transform as 2 + 1 and the Higgs fields H and H̄ are singlets. Such a horizontal symmetry is interesting because only the Yukawa couplings for the third generation are allowed by the horizontal symmetry, that accounts for the large top Yukawa coupling, and because the U(2)H symmetric interaction ∫ dθΨΨaZ Z, where Z has a non-vanishing vacuum expectation value (VEV) given by 〈Z〉 ∼ θm̃, leads to the equal first and second generation sfermion masses, which may realize suppression of flavor changing neutral currents (FCNC). However, the U(2)H symmetry must be broken to obtain realistic mass hierarchical structure of quarks and leptons. Therefore, we introduce a doublet Higgs F̄ a and an anti-symmetric tensor A, whose VEVs | 〈