Fermion Masses and Mixings from a Minimum Principle

We analyze the structure of quark and lepton mass matrices under the hypothesis that they are determined from a minimum principle applied to a generic potential invariant under the $\left[U(3)\right]^5\otimes {\mathcal O}(3)$ flavor symmetry, acting on Standard Model fermions and right-handed neutrinos. Unlike the quark case, we show that hierarchical masses for charged leptons are naturally accompanied by degenerate Majorana neutrinos with one mixing angle close to maximal, a second potentially large, a third one necessarily small, and one maximal relative Majorana phase. The scheme presented here could be tested in the near future via neutrino-less double beta decay and cosmological measurements.