the inverse transform in Eq. (\[borel-inverse\]).

Another potential source of renormalons in the short-distance coefficients is the UV renormalization procedure that is applied to full QCD. If the renormalization counterterms involve loop integrations down to zero momentum, then the counterterms can contain renormalons. In this paper, we assume that a minimal-subtraction procedure ($MS$) or modified minimal-subtraction procedure ($\overline{MS}$) is used, so that the renormalization counterterms are poles in $\epsilon$ or constants and contain no IR renormalons.

Factorization-Scheme Dependence of Renormalons {#sec:factorization}
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In a factorization formalism, the domain of integration of a loop integral in full QCD is partitioned between the operator matrix elements and the short-distance coefficients. This partitioning allocates the low-momentum part of the loop integral, including the IR divergences, to the operator matrix elements and allocates the remaining high-momentum part of the loop integral to the short-distance coefficients, which contain no IR divergences.

The partitioning arises in the matching of the effective theory to full QCD. For example, in the on-shell matching procedure, on-shell quark and gluon amplitudes in the full theory are equated to the same amplitudes in the effective theory. Each amplitude in the effective theory can be written as a sum of products of 