Discriminating technicolor theories through flavor-changing neutral currents: Slowly varying or fixed coupling constants?

On the basis of the analytical study of the ladder Schwinger-Dyson equation of the technifermion self-energy we find crucial constraints on the running coupling constants in technicolor theories for the flavor-changing neutral currents to be dynamically suppressed. It is unlikely that the slowly varying coupling constants in the asymptotically free technicolor theory can solve the flavor-changing neutral-current problem. Fixed-point theories may be the only viable possibility.