Unified Theories with U(2) Flavor Symmetry

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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 9 relations among the fermion masses and mixings, 5 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.