Chiral Hierarchies and Flavor-Changing Neutral Currents in Hypercolor

Dynamical chiral-symmetry breaking in asymptotically free theories with a slowly running coupling is analyzed. When the confinement scale Λ is much less than the cutoff M beyond which the theory cannot be used in isolation, the dynamical mass Σ(p) starts from a value ≈Λ for momenta pΛ and falls slowly for a significant range p>Λ. It then takes on the asymptotic form (lnp)ᵃp² where $a>1$. In hypercolor theories this behavior generates sufficiently large fermion masses for a higher value of M than naively expected. This in turn could allow for an adequate suppression of flavor-changing neutral currents.