elements are controlled with a regulator, such as lattice regularization, that has an explicit cutoff in the loop momenta [@novikov-et-al; @david]. In contrast, in a dimensional-regularization scheme, both the short-distance coefficients and the operator matrix elements contain renormalon ambiguities, but they cancel in physical observables [@LMS94]. We give a prescription for calculating the renormalon ambiguities in the dimensionally-regulated operator matrix elements, and we apply this method to the computation of the renormalon ambiguities in the NRQCD matrix elements that appear in the decays of S-wave quarkonia in the leading and first subleading orders in the expansion in the heavy-quark velocity. Comparing with a calculation of the ambiguities in the short-distance coefficients for the decays of S-wave quarkonia [@braaten-chen], we find that the renormalon ambiguities cancel in the physical decay rates, as expected.

The remainder of this paper is organized as follows. In Sec. \[sec:renormalons\], we review the bubble-chain model and Borel transformation and discuss, in general, the origins of renormalons in short-distance coefficients. Here we present a concise argument to show that renormalon ambiguities in the short-distance coefficients arise from the low-momentum regions of loop integrals. Sec. \[sec:factorization\] contains a discussion of the interplay between the factorization scheme and the 