Renormalon Ambiguities in NRQCD Operator Matrix Elements

TL;DR

The paper analyzes renormalon ambiguities in QCD factorization, arguing these are artifacts of dimensional-regularization schemes and vanish in cutoff schemes. It develops a method to compute renormalon ambiguities in NRQCD operator matrix elements by comparing dim-reg and cutoff-regulated calculations and applies it to S-wave quarkonium decays, showing that the ambiguities cancel against those in the short-distance coefficients. The authors explicitly compute the leading u=1/2 renormalon in NRQCD matrix elements, confirm agreement with Braaten-Chen's results for short-distance coefficients, and discuss the Gremm-Kapustin relation and heavy-quark mass definitions. The work clarifies the scheme dependence of renormalons, provides a practical computational approach, and deepens understanding of heavy-quarkonium factorization and mass definitions in QCD.

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, 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.