Heavy quarkonium fragmentation functions from a heavy quark pair. I. $S$ wave

Understand

A QCD factorization formalism was recently proposed for evaluating heavy quarkonium production at large $p_T$ 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 $\mu_0\gtrsim 2m_Q$ with heavy quark mass $m_Q$.
• 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.