Renormalon Ambiguities in NRQCD Operator Matrix Elements.pdf

a r X i v : h e p - p h / 9 8 0 7 4 9 2 v 2 3 J u n 1 9 9 9 ANL-HEP-PR-98-29 OHSTPY-HEP-T-98-008 June, 1999 Renormalon Ambiguities in NRQCD Operator Matrix Elements Geoffrey T. Bodwin High Energy Physics Division, Argonne National Laboratory, Argonne, IL 60439 Yu-Qi Chen Physics Department, Ohio State University, Columbus, Ohio 43210 Abstract We analyze the renormalon ambiguities that appear in factorization formu- las 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 ambigui- ties 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 [1], 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. Typeset using REVTEX 1 I. 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, a physical observable is written as a sum of products of short-distance coeffi- cients with long-distance operator matrix elements. The short-distance coefficients may be calculated as a perturbative series in the strong coupling constant αs, evaluated at the short- distance scale. The operator matrix elements contain all of the sensitivity of the physical observable to low-momentum (infrared) processes. Because of this infrared (IR) sensitivity, the operator matrix elements are generally not amenable to a perturbative calc