---
abstract: '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 [@braaten-chen], 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.'
address:
- 'High Energy Physics Division, Argonne National Laboratory, Argonne, IL 60439'
- 'Physics Department, Ohio State University, Columbus, Ohio 43210'
author:
- 'Geoffrey T. Bodwin'
- 'Yu-Qi Chen'
title: Renormalon Ambiguities in NRQCD Operator Matrix Elements
---

Introduction {#sec:introduction}
============

In Quantum Chromodynamics (QCD), it is often useful to describe physical processes involving more than one distance scale by making use of a factorization formalism. In such a formalism, 