Solving the flavour problem with hierarchical fermion wave functions

TL;DR

The paper investigates whether flavor-changing effects in SM extensions can be suppressed by hierarchical fermion wave functions, rather than by a flavor symmetry, by treating higher-dimensional couplings as ${\mathcal{O}}(1)$ in a basis with hierarchical kinetic terms. It demonstrates that quark-sector FCNCs can be kept within experimental bounds with a TeV-scale NP (\Lambda ~ 10 TeV) thanks to suppressions $X_{AB}^{ij}\sim z_A^{(i)} z_B^{(j)}$, while kaon observables (ε_K, ε'/ε) require mild tuning of LR operators; the lepton sector faces a much stiffer challenge from LFV, notably μ → e γ, which pushes the required scale or demands additional suppression of dipole operators. Compared with MFV, the framework relaxes some RR/LR suppressions and yields distinctive kaon- and lepton-flavor signatures, potentially testable in near-future experiments and naturally realized in extra-dimensional setups where fermion profiles generate the needed hierarchies. The results highlight a viable but nuanced alternative path to addressing the flavor problem, with clear experimental handles in kaon CP violation and LFV searches.

Abstract

We investigate the flavour structure of generic extensions of the SM where quark and lepton mass hierarchies and the suppression of flavour-changing transitions originate only by the normalization constants of the fermion kinetic terms. We show that in such scenarios the contributions to quark FCNC transitions from dimension-six effective operators are sufficiently suppressed without (or with modest) fine tuning in the effective scale of new physics. The most serious challenge to this type of scenarios appears in the lepton sector, thanks to the stringent bounds on LFV. The phenomenological consequences of this scenarios in view of improved experimental data on quark and lepton FCNC transitions, and its differences with respect to the Minimal Flavour Violation hypothesis are also discussed.