integral.[^7] However, we wish to emphasize the insensitivity of the renormalon ambiguities to the low-energy physics by working with the right side of Eq. (\[matrix-diff\]), which contains no low-momentum contribution. With this computational procedure, the dimensionally-regulated matrix elements contain only UV renormalons.

Dimensional-regularization prescription {#sec:dim-reg-prescrip}
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Let us now explain more precisely what we mean by dimensional regularization of operator matrix elements. It is well-known that dimensionally-regulated expressions can sometimes be ambiguous when the integrand involves a limiting procedure. For example, the result for a dimensionally-regulated integral can be changed by carrying out formal manipulations involving power series in the integration variable. Consequently, it is necessary to specify how the integrand is to be arranged before the dimensional regularization is imposed.

In computing the short-distance coefficients in the dimensional-regularization scheme, it is conventional to integrate IR-finite terms down to zero loop momentum. As we have discussed in Sec. \[sec:factorization\], such an approach corresponds to setting to zero the UV power divergences in the operator matrix elements. Therefore, for consistency with conventional calculations of the short-distance coefficients, we wish to follow a procedure for the dimensional regularization of the operator matrix elements in which UV power divergences are set to zero. 