Effective field theories with instantons

Abstract

We explain how nonperturbative effects can be systematically included when constructing an effective field theory. We concentrate in particular on the matching calculation, by which a low-energy theory without a heavy-particle degree of freedom is matched onto the full theory. The matching calculation requires some new formalism, because for a large class of theories, instantons occur in a continuous range of scales for far below the mass of the heavy particle to far above. We show how the complete IR finiteness of the usual matching formalism arises in this new context. As an example, we formally integrate out a heavy quark in QCD.