Comprehensive Bayesian Exploration of Froggatt-Nielsen Mechanism

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.