Suppressing Flavor Anarchy

TL;DR

The paper proposes that the observed pattern of fermion masses and mixing angles can arise when Standard Model fields couple to a near-conformal sector, producing large anomalous dimensions that renormalize Yukawa couplings toward small IR values. The mechanism yields Yukawa matrices of the form $Y_{ij} \simeq \epsilon^L_i \epsilon^R_j Y^{(0)}_{ij}$, with suppression factors $\epsilon$ set by anomalous dimensions and the scales $M_0$ and $M_c$, and provides generic predictions for CKM and neutrino mixing without imposing explicit flavor symmetries. It develops several explicit SUSY-based and GUT-compatible models, discusses graceful exit, proton decay, Landau poles, and the SUSY flavor problem, and shows that coupling constant unification can be preserved in these scenarios. The approach offers testable consequences for the superpartner spectrum and flavor-violating processes, while remaining compatible with unification and neutrino oscillation data, and it also informs string theory and non-supersymmetric extensions. Overall, it provides a unified framework for generating fermion mass hierarchies via IR conformal dynamics with limited input parameters and clear phenomenological implications.

Abstract

We present a new mechanism, which does not require any flavor symmetry, to explain the small Yukawa couplings and CKM mixing angles. The Yukawa matrices are assumed to be random at short distances and the hierarchical structure is generated in the infrared by renormalization group flow. The generic qualitative predictions of this mechanism are in good agreement with observation. We give several simple examples in supersymmetric theories. We show that our mechanism can also ameliorate the supersymmetric flavor problem, and make predictions for the superpartner mass spectrum. The mechanism is fully consistent with grand unification, and in SU(5)-based models of neutrino mass, predicts a large mixing angle for muon neutrino to tau neutrino oscillations.