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 $\mathrm{CP}$-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. Once can then show qualitatively that the hierarchy is such that $logm$ varies linearly with respect to the generation index.

• Received 15 August 1983

DOI:https://doi.org/10.1103/PhysRevD.29.1504