Toward a model of quarks and leptons

Abstract

We propose an extra-dimension framework on the orbifold $S^1/Z_2$ for understanding the origin of the fermion mass and mixing hierarchies. Introducing the flavor symmetry $G_F(=${\it non-Abelian}$\times${\it Abelian}) as well as the extra gauged $U(1)$ symmetries through the bulk, we regard the $SU(2)$ singlet and doublet fermions in the Standard Model (SM) to be localized at the separate 3-branes and let the extra $SU(2)$ singlet flavored fermions in the bulk couple to the SM fermions at the 3-branes. The extra $U(1)$ symmetries satisfy the $U(1)$ gravitational anomaly-free condition, playing a crucial role in achieving the desirable fermion mass and mixing hierarchies and making the flavored axion naturally light. The singlet scalar fields, the flavon fields, are responsible for the spontaneous breaking of $G_F$ on the two 3-branes, while the $SU(2)$ singlet flavored fermions are integrated out to give rise to the effective Yukawa couplings for the SM fermions, endowed with the information of $G_F$ breaking in the two sectors. The flavored axion from the PQ symmetry is also proposed for solving the strong CP problem and being a dark matter candidate in our model.