Quark mass hierarchies from the universal seesaw mechanism

The paper is an extension of the previous work based on the idea of a universal seesaw mechanism to explain the hierarchies in the fermion mass spectrum. A model is proposed within the framework of left-right symmetry with a minimal Higgs system and an axial U(1) symmetry imposed to distinguish the generations. Previous work was confined, for mathematical simplifications, to the case of nonsingular mass matrices. In the present paper, singular matrices are considered. A systematic perturbative technique is developed to display the mass eigenvalues in terms of the vacuum expectation values of the assumed Higgs multiplets. The model successfully correlates the mass hierarchies among the quarks to the assumed hierarchies in the vacuum expectation values without appealing to a hierarchy in the Yukawa-type fermion--Higgs-boson couplings. By considering a general Higgs potential appropriate to the model, we study its minimization and prove that there exists an open subdomain in the parameter space where the orbit of the lowest minima of the potential corresponds to the kind of hierarchy in the vacuum expectation values needed for the success of the model