Paper
Heavy quarkonium fragmentation functions from a heavy quark pair. I. $S$ wave
Authors
Abstract
A QCD factorization formalism was recently proposed for evaluating heavy quarkonium production at large at collider energies. With systematically calculated short-distance partonic hard parts and evolution kernels of fragmentation functions (FFs), the predictive power of this factorization approach relies on our knowledge of a large number of universal FFs at an input factorization scale with heavy quark mass . With the large heavy quark mass, the relative motion of the heavy quark pair inside a heavy quarkonium is effectively non-relativistic. We evaluate these universal input FFs using non-relativistic QCD (NRQCD) factorization, and express the large number of FFs in terms of a few universal NRQCD long-distance matrix elements (LDMEs) with perturbatively calculated coefficients. We derive complete contributions to the single-parton FFs at both and , and the heavy quark pair FFs at . We present detailed derivation for all contributions involving LDMEs of -wave NRQCD -states (-wave contributions in a companion paper). Our results bridge the gap between the QCD factorization formalism and its phenomenological applications.