We consider the possibility of identifying the Peccei-Quinn (PQ) symmetry as also the flavor symmetry in multigenerational grand unification schemes. The essential ingredient, a global, axial U(1) symmetry in the PQ mechanism to avoid the strong CP-violation problem provides useful constraints on the fermion —Higgs-boson couplings in the theory, thereby leading to identical "canonical" forms for fermion mass matrices in both the charged sectors. These forms are the conjectured Fritzsch-type matrices exhibiting the "nearest-neighbor" interactions in generation space. From among the popular schemes for grand unification, SO(10) emerges as one which has several advantages over the others for constructing multigenerational grand unification models. Reasonable assumptions regarding the quark masses lead to unique PQ quantum-number assignments for the fermionic generations. These quantum numbers combined with the hierarchy in quark masses lead to a picture in which the lighter generations are composite in nature. One can then show qualitatively that the hierarchy is such that logm varies linearly with respect to the generation index.
Davidson, Aharon; Nair, V. Parameswaran; and Wali, Kameshwar C., "Peccei-Quinn Symmetry as Flavor Symmetry and Grand Unification" (1984). CUNY Academic Works.