Supersymmetric Froggatt-Nielsen Models with Baryon- and Lepton-Number Violation

TL;DR

This work systematically embeds four-dimensional Froggatt–Nielsen models with a single flavon into local supersymmetry, incorporating Green–Schwarz anomaly cancellation and detailed Kahler potential canonicalization. It translates high-energy U(1)_X charge assignments into order-of-magnitude predictions for baryon- and lepton-number violating couplings via the suppression factor $oldsymbol{ig(rac{A}{M_s}ig)^{X_{ ext{sum}}}}$, then runs RGEs to compare with weak- and GUT-scale bounds on Rp-violating and dimension-five operators. The study provides a unified framework and a catalog of models, finding that only a small fraction survive the stringent experimental constraints, with viability often requiring fractional charges or imposed discrete symmetries to suppress dangerous operators. The results underscore the tension between simple FN textures and B/L-violating bounds, and point to future work including the neutrino sector to broaden viable options.

Abstract

We systematically investigate the embedding of U(1)_X Froggatt-Nielsen models in (four-dimensional) local supersymmetry. We restrict ourselves to models with a single flavon field. We do not impose a discrete symmetry by hand, e.g. R-parity, baryon-parity or lepton-parity. Thus we determine the order of magnitude of the baryon- and/or lepton violating coupling constants through the Froggatt-Nielsen mechanism. We then scrutinize whether the predicted coupling constants are in accord with weak or GUT scale constraints. Many models turn out to be incompatible.