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

TL;DR

This paper extends the factorized cross section formalism for heavy quarkonium production to include next-to-leading power contributions, aligning with NRQCD results and revealing dominance of certain channels at high transverse momentum.

Contribution

It introduces an extended factorization approach incorporating NLP contributions and calculates relevant fragmentation functions using NRQCD, clarifying dominant production channels.

Findings

NLP contributions reproduce high-$p_T$ NRQCD results.

Two NRQCD channels are NLP-dominated over wide $p_T$ range.

Large NLO corrections are absorbed into leading order of power corrections.

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.