Natural Fermion Hierarchies from Random Yukawa Couplings

Abstract

The Standard Model of particle physics requires Yukawa matrices with eigenval- ues that differ by orders of magnitude. We propose a novel way to explain this fact without any small or large parameters. The mechanism is based on the observation that products of matrices of random order one-numbers have hierarchical spectra. The same mechanism can easily account for the hierarchical structure of the quark mixing matrix.

Comments: 9 pages. v2: Extended and improved discussion on CKM matrix. References added. Matches published version