Comprehensive Bayesian Exploration of Froggatt-Nielsen Mechanism

TL;DR

This paper employs Bayesian analysis to systematically explore and evaluate viable Froggatt-Nielsen charge assignments in the Standard Model, revealing new viable configurations and their experimental implications.

Contribution

It introduces a comprehensive Bayesian framework to analyze FN charge assignments, including negative charges and large generational differences, across neutrino mass generation scenarios.

Findings

Wide range of FN charges consistent with data

Negative charges and large differences are viable

Predictions for neutrino masses and nucleon decay vary with charges

Abstract

The Froggatt-Nielsen (FN) mechanism successfully explains the hierarchical structure of fermion Yukawa couplings by introducing a U(1) flavor symmetry with distinct charge assignments for different fermion generations. While some FN charge assignments have been proposed, their evaluation has largely relied on heuristic approaches. This paper systematically investigates viable FN charge assignments within the Standard Model, including both the quark and lepton sectors, using Bayesian statistical analysis. The study explores scenarios involving both the seesaw mechanism and dimension-five operators for neutrino mass generation. A comprehensive parameter scan over FN charges reveals a wide range of charge assignments consistent with observed fermion masses and mixing angles. Interestingly, negative FN charges and significant generational differences in charges are found to be viable, contrary to conventional assumptions. The analysis also compares the seesaw mechanism and dimension-five operator scenarios, finding no strong preference between them for optimal charge assignments. Furthermore, predictions for the lightest neutrino mass and effective Majorana mass relevant for neutrinoless double-beta decay are presented, highlighting regions of parameter space accessible to upcoming experiments. Finally, implications for nucleon decay are studied, demonstrating that different FN charge assignments predict significantly different nucleon decay lifetimes and branching ratios, providing a potential experimental probe for FN models.