it is of the same nominal size as power corrections in the factorization formulas.

We have seen that IR renormalons can arise from the region of integration near zero loop momentum. In an analogous fashion, UV renormalons can arise from the region of integration near infinite loop momentum. The loop integration extends to infinity in unregulated, UV-finite integrals and in UV-divergent integrals in dimensional regularization. In a renormalizable theory, the loop integration in a short-distance coefficient is, at worst, logarithmically divergent in the UV region when $u=0$. (The integrand that we have displayed in the expression (\[bubble-integral\]) is an approximate form that is valid only in the IR region.) In the case of a logarithmic UV divergence, the pole at $u=0$ is identical to the dimensional-regularization pole in $\epsilon=(4-D)/2$, where $D$ is the number of space-time dimensions, and it is removed in the standard minimal-subtraction renormalization procedure. The remaining pieces of the integrand, which have a convergent power count in the large-momentum region when $u=0$, may contribute additional renormalons. However, by virtue of their convergent power count, these pieces yield renormalons only on the negative real $u$ axis. Renormalons on the negative real $u$ axis do not introduce ambiguities into 