of NRQCD). Then, each term in the series is homogeneous in $l$. Now, any terms that are IR finite (that is, UV power divergent) require no IR regulator. Hence, such terms are scale invariant, and their integrals over all $l$ vanish in dimensional regularization. We note that this formal procedure is equivalent to absorbing the UV-power divergences into a renormalization of the operator matrix elements.

In light of these general considerations, we see that the application of Eq. (\[matrix-diff\]) requires some care. To obtain a result that is consistent with conventional calculations of the short-distance coefficients in the dimensional-regularization scheme, it is essential to use a procedure for computing the dimensionally-regulated matrix elements, such as the one that we have specified, in which the UV power divergences vanish.

NRQCD factorization formalism {#sec:nrqcd}
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In order to establish our notation and conventions, we now give a brief review of the NRQCD factorization formalism for heavy-quarkonium decays.

In the nonrelativistic limit, in which the heavy-quark (or antiquark) velocity $v$ is much less than unity, full QCD is described accurately by the effective theory NRQCD. In particular, NRQCD is convenient for describing heavy-quarkonium bound states. In such systems, there are three important energy 