Dynamical chiral-symmetry breaking in asymptotically free theories with a slowly running coupling is analyzed. When the confinement scale $\Lambda$ is much less than the cutoff $M$ beyond which the theory cannot be used in isolation, the dynamical mass $\Sigma \mathrm{}\left(p\right)\mathrm{}$ starts from a value $\approx \Lambda$ for momenta $p\lesssim \Lambda$ and falls slowly for a significant range $p>\mathrm{}\Lambda$. It then takes on the asymptotic form $\frac{{\left(\ln p\right)}^a}{p^2}$ where $a>\mathrm{}1\mathrm{}$. 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.

• Received 2 June 1986

DOI:https://doi.org/10.1103/PhysRevLett.57.957