sufficient accuracy in the underlying effective field theory [@LMS94].

Let us explain more fully what we mean by sufficient accuracy in the underlying effective field theory. Generally, an operator matrix element scales, in its leading behavior, as a power of the small scale in the two-scale problem. For example, in the NRQCD factorization formalism for heavy-quarkonium decay and production [@bbl], matrix elements scale as powers of $p=mv$, where $p$ and $v$ are the typical heavy-quark-antiquark relative momentum and velocity, and $m$ is the heavy-quark mass. To achieve the cancellation of a renormalon at given value of $u$, it is crucial to retain matrix elements of sufficiently high order in the small scale to reproduce the IR power behavior that gives rise to that renormalon. Furthermore, if one is computing a matrix-element renormalon ambiguity in the context of an effective field theory, it is necessary to retain terms in the effective action of sufficiently high accuracy in the small scale to reproduce the corresponding IR power behavior. The action of an effective theory may depend on both the cutoff and the large scale. For example, in HQET and NRQCD, the action depends on $m$, as well as the cutoff. Hence, the 