matrix elements, to the extent that the effective theory accurately reproduces the low-momentum behavior of the full theory. Hence, in a cutoff factorization scheme, the short-distance coefficients are free of a given IR renormalon ambiguity, provided that the effective action retains enough powers of the small scale in the calculation to reproduce the low-momentum behavior that is characteristic of such a renormalon. The absence of renormalons in a cutoff factorization scheme has been discussed in a number of publications. Some of the earliest discussions are in Refs. [@novikov-et-al; @david].

In a dimensional-regularization factorization scheme, it is conventional to integrate the IR-finite parts of the short-distance coefficients down to zero momentum. Consequently, the short-distance coefficients contain renormalon ambiguities. The IR-finite parts of the short-distance coefficients correspond to the power-UV-divergent parts of the operator matrix elements. Thus, because of the constraints imposed by the matching conditions, the integration of the IR-finite parts of the short-distance coefficients down to zero momentum demands, for consistency, that the UV-power-divergent parts of the matrix elements be set to zero. As we will explain in Sec. \[sec:dim-reg-prescrip\], there is a prescription for regulating the operator matrix elements dimensionally in which such power UV divergences [*are*]{} set to 