element, since they would not be present if one defined the matrix element nonperturbatively and evaluated it in terms of nonperturbative expressions. As we shall describe later in this paper, one can isolate the ambiguities that arise from the factorization scheme by computing the difference between an unambiguous definition of the operator matrix element (for example, a lattice definition) and an ambiguous definition (for example, one based on dimensional regularization). In the remainder of this paper, when we refer to ambiguities in operator matrix elements, we mean only those ambiguities that arise from the factorization scheme.

Because physical observables are unambiguous, the renormalon ambiguities in the short-distance coefficients must be cancelled by corresponding ambiguities in the operator matrix elements, to the level of accuracy of the factorization procedure. Factorization procedures that are based entirely on an underlying effective field theory, such as those in the light-cone expansion, OPE, HQET, and NRQCD, are, in principal, valid to all orders in an expansion in the inverse of the large scale in the process. In contrast, factorization procedures for hadron-hadron-induced hard-scattering processes, for example, the Drell-Yan process, are known to fail for contributions that are subleading in the inverse of the large scale 