Effective gauge theories

A method is described for dealing with gauge field theories that contain very heavy particles, by constructing a gauge-invariant effective field theory, in which the heavy particles do not appear. For theories in which a simple group is spontaneously broken to the strong and electroweak gauge groups, the running strong and electroweak effective couplings become equal to the original gauge coupling at different renormalization scales, given as weighted geometric averages of the super-heavy particle masses. The method is also applied to quantum chromodynamics with heavy quarks.