Anarchy with Hierarchy: A Probabilistic Appraisal

The masses of the charged fermion and the mixing angles among quarks are observed to be strongly hierarchical, while analogous parameters in the neutrino sector appear to be structure-less or anarchical. We develop a class of unified models based on SU(5) symmetry that explains these differing features probabilistically. With the aid of three input parameters that are hierarchical, and with the assumption that all the Yukawa couplings are uncorrelated random variables described by Gaussian distributions, we show by Monte Carlo simulations that the observed features of the entire fermion spectrum can be nicely reproduced. We extend our analysis to an SU(5)-based flavor U(1) model making use of the Froggatt-Nielsen mechanism where the order one Yukawa couplings are modeled as random variables, which also shows good agreement with observations.