Anarchy with Hierarchy: A Probabilistic Appraisal

TL;DR

This paper presents probabilistic models based on SU(5) symmetry that explain the hierarchical structure of quark and charged fermion masses and mixing angles, while accounting for the anarchical nature of neutrino parameters, using Monte Carlo simulations.

Contribution

It introduces a unified SU(5)-based probabilistic framework with random Yukawa couplings to reproduce fermion mass hierarchies and mixing patterns, extending to a flavor U(1) model with Froggatt-Nielsen mechanism.

Findings

Monte Carlo simulations successfully reproduce observed fermion spectra.

Random Yukawa couplings with hierarchical parameters match experimental data.

The SU(5) and U(1) models provide a probabilistic explanation for fermion mass structures.

Abstract

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.