Factorized power expansion for high-$p_T$ heavy quarkonium production

TL;DR

It is shown that when the factorized cross section for heavy quarksonium production includes next-to-leading power contributions associated with the production of the heavy quark pair at short distances, it naturally reproduces all high p(T) results calculated in nonrelativistic QCD (NRQCD) factorization.

Abstract

We show that when the factorized cross section for heavy quarkonium production includes next-to-leading power (NLP) contributions associated with the production of the heavy quark pair at short distances, it naturally reproduces all high $p_T$ results calculated in non-relativistic QCD (NRQCD) factorization. This extended formalism requires fragmentation functions for heavy quark pairs, as well as for light partons. When these fragmentation functions are themselves calculated using NRQCD, we find that two of the four leading NRQCD production channels, ${^3\hspace{-0.6mm}S_{1}^{[1]}}$ and ${^1\hspace{-0.6mm}S_{0}^{[8]}}$, are dominated by the NLP contributions for a very wide $p_T$ range. The large next-to-leading order corrections of NRQCD are absorbed into the leading order of the first power correction. The impact of this finding on the heavy quarkonium production and its polarization is discussed.

Figures (3)

• Figure 1: Ratio of ${J/\psi}$ production rate from LO QCD factorization over that of NLO NRQCD calculation for four leading NRQCD channels. See the text for details.
• Figure 2: Ratio of NLP contributions to total contribution in LO QCD for each channel. $d\tilde{\sigma}$ means we have a special choice for PDFs. See text for details.
• Figure 3: First few moments of ${\cal D}^{[n_1,n_2]}_{[c\bar{c}(v^{[8]})]\to {^3\space S_{1}^{[1]}}}(z)$ with an arbitrary normalization.