Chiral hierarchies from slowly running couplings in technicolor theories

Chiral-symmetry breaking in asymptotically free theories with slowly running couplings 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 p≲Λ and falls slowly for a significant range p>Λ. It then takes on the asymptotic form (lnp${)}^a$/$p^2$ where a>1. This behavior leads to an enhancement of the fermion condensate defined with the ultraviolet cutoff M, while the Goldstone-boson decay constant F remains essentially unaltered. In technicolor theories, with four-fermion interactions of strength ≃1/$M^2$ that explicitly break some chiral symmetries, the technifermion condensate determines the values of fermion masses and pseudo-Goldstone-boson masses while F determines W and Z masses. An enhancement of the technifermion condensate will then generate fermion and pseudo-Goldstone-boson masses for higher values of M than naively expected, keeping W and Z masses nearly fixed. This could allow for an adequate suppression of the flavor-changing neutral currents that have plagued technicolor theories. Explicit gauge theories that exhibit slow running are tabulated and the results of a numerical study are reported.