# Natural Fermion Hierarchies from Random Yukawa Couplings

## TL;DR

This paper proposes a novel explanation for the hierarchical structure of fermion masses and quark mixing in the Standard Model, using products of random matrices to naturally generate the observed hierarchies without fine-tuning.

## Contribution

It introduces a mechanism based on random matrix products to explain fermion mass hierarchies and quark mixing without small or large parameters.

## Key findings

- Random matrix products produce hierarchical eigenvalues.
- The mechanism accounts for quark mixing hierarchies.
- No fine-tuning required for 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.