[@doria-et-al]. In the discussions in the remainder of this paper, we have in mind the factorization procedures that are based entirely on underlying effective field theories. However, our results may also apply to other factorization procedures at the level of leading orders in the inverse of the large scale.

If one determines operator matrix elements by comparing factorized expressions for physical observables with results from experiment, then the cancellation of renormalon ambiguities holds by construction, for those observables. On the other hand, if one determines operator matrix elements through a calculation in the underlying effective field theory, as we do in this paper, then the cancellation of renormalon ambiguities is a nontrivial confirmation of the accuracy of the effective field theory in reproducing the low-momentum behavior of the full theory and of the consistency of the definitions of the short-distance coefficients and operator matrix elements.

In this paper, we investigate the relations between the renormalon ambiguities in the short-distance coefficients and the renormalon ambiguities in the operator matrix elements. In our analysis, it is clear that the short-distance coefficients and the operator matrix elements display no ambiguities in a factorization scheme in which ultraviolet (UV) divergences in the operator matrix 