General theory of virtual heavy-particle effects in renormalizable field theories (I)

We develop a systematic method of isolating the effects of virtual heavy particles in renormalizable field theories. With a φ⁴-type field-theory model involving two real scalar fields (one with a heavy mass M, and the other light), we show in detail, that up to order $\text{1}\text{M}{}^2$ (but to all orders in renormalized coupling), effects of virtual heavy particles can be completely incorporated into pure light-particle theory via effective local vertices which involve operators of canonical dimension at most six. All the coupling strengths for such effective local interactions are of order $\text{1}\text{M}{}^2$ (the decoupling theorem) and are systematically calculable in renormalized perturbation theory. We also derive a closed set of Callan-Symanzik equations which are satisfied by these coupling strengths. Using these equations, we explicitly sum all the leading logarithms (i.e., log M ～ O(1)) which appear in the perturbative calculations of the effective coupling strengths.