Permutation symmetry and the origin of fermion mass hierarchy

A realization of the ``flavor-democracy'' approach to quark and lepton masses is provided in the context of the standard model with a horizontal S₃ permutation symmetry. In this model, t and b quarks pick up mass at the tree level, c, s-quark and {τ}-lepton masses arise at the one-loop level, u, d, and {μ} masses at the two-loop level, and the electron mass at the three-loop level, thus reproducing the observed hierarchial structure without fine tuning of the Yukawa couplings. The pattern of quark mixing angles also emerges naturally, with Vᵤₛ,Vcb{}O({ε}), Vub{}O(ε²), where {ε} is a loop expansion parameter.