Fermion mass hierarchy and nonhierarchical mass ratios in SU(5)×U(1)F

We consider a SU(5)×U(1)F grand unified theory (GUT)-flavor model in which the number of effects that determine the charged fermions Yukawa matrices is much larger than the number of observables, resulting in a hierarchical fermion spectrum with no particular regularities. The GUT-flavor symmetry is broken by flavons in the adjoint of SU(5), realizing a variant of the Froggatt-Nielsen mechanism that gives rise to a large number of effective operators. By assuming a common mass for the heavy fields and universality of the fundamental Yukawa couplings, we reduce the number of free parameters to one. The observed fermion mass spectrum is reproduced thanks to selection rules that discriminate among various contributions. Bottom-tau Yukawa unification is preserved at leading order, but there is no unification for the first two families. Interestingly, U(1)F charges alone do not determine the hierarchy, and can only give upper bounds on the parametric suppression of the Yukawa operators.