  We analyze the renormalon ambiguities that appear in factorization formulas
in QCD. Our analysis contains a simple argument that the ambiguities in the
short-distance coefficients and operator matrix elements are artifacts of
dimensional-regularization factorization schemes and are absent in cutoff
schemes. We also present a method for computing the renormalon ambiguities in
operator matrix elements and apply it to a computation of the ambiguities in
the matrix elements that appear in the NRQCD factorization formulas for the
annihilation decays of S-wave quarkonia. Our results, combined with those of
Braaten and Chen for the short-distance coefficients, provide an explicit
demonstration that the ambiguities cancel in the physical decay rates. In
addition, we analyze the renormalon ambiguities in the Gremm-Kapustin relation
and in various definitions of the heavy-quark mass.
