Unified theories with U(2) flavor symmetry Original Research Article

A general operator expansion is presented for quark and lepton mass matrices in unified theories based on a U(2) flavor symmetry, with breaking parameter of order Vcb ≈ ms/mb ≈ √mc/mt. While solving the supersymmetric flavor-changing problem, a general form for the Yukawa couplings follows, leading to nine relations among the fermion masses and mixings, five of which are precise. The combination of grand unified and U(2) symmetries provides a symmetry understanding for the anomalously small values of mu/mc and mc/mt. A fit to the fermion mass data leads to a prediction for the angles of the CKM unitarity triangle, which will allow a significant test of these unified U(2) theories. A particular SO(10) model provides a simple realization of the general operator expansion. The lighter generation masses and the non-trivial structure of the CKM matrix are generated from the exchange of a single U(2) doublet of heavy vector generations. This model suggests that CP is spontaneously broken at the unification scale—in which case there is a further reduction in the number of free parameters.