that go as powers of the ratio of scales.

In a well-defined theory, physical observables, in contrast with short-distance coefficients, are unambiguous. Of course, if one were to attempt to compute a physical observable entirely in perturbation theory, without making use of a factorization formalism, then one might encounter ambiguities, owing to the failure of the perturbation series to converge. However, such ambiguities are not intrinsic to the observable. They are artifacts of the method of computation and would be absent if one were to compute the observable in terms of nonperturbative expressions, such as lattice path integrals.

When one computes a physical observable by making use of a factorization scheme that is defined in perturbation theory, such as one that is based on dimensional regularization, then the short-distance coefficients and operator matrix elements can contain ambiguities that arise in consequence of the defining perturbation series. It is these ambiguities that arise from the factorization scheme that are the focus of this paper.

If one were to attempt to compute an operator matrix element entirely in perturbation theory, then additional ambiguities, which have nothing to do with the factorization scheme, might arise. Such ambiguities are not intrinsic to the matrix 