Fragmentation functions of polarized heavy quarkonium

TL;DR

This paper develops a polarization-aware QCD factorization framework for heavy quarkonium production and provides a complete calculation of polarized input fragmentation functions at the NRQCD input scale. It defines polarized NRQCD LDMEs in arbitrary $d$ dimensions, derives the necessary selection rules and power-counting to identify relevant $Qar{Q}$ channels (including $S$- and $P$-wave states), and computes the perturbative short-distance coefficients to NLO for both single-parton and heavy quark-pair fragmentation. Through careful handling of divergences and matching, the work establishes the ingredients needed to predict polarized quarkonium yields and angular distributions at high transverse momentum, with particular relevance to $J//spsi$ polarization. The results enable resummation of large logs via FF evolution and provide a practical path to confronting collider polarization data within a convergent, systematic framework.

Abstract

Study of the polarized heavy quarkonium production in recently proposed QCD factorization formalism requires knowledge of a large number of input fragmentation functions (FFs) from a single parton or a heavy quark-antiquark pair to a polarized heavy quarkonium. In this paper, we calculate these FFs at the input scale in terms of nonrelativistic QCD (NRQCD) factorization. We derive all relevant polarized NRQCD long-distance matrix elements based symmetries and propose a self-consistent scheme to define them in arbitrary $d$ dimensions. We then calculate polarized input FFs contributed from all $S$-wave and $P$-wave NRQCD intermediate states. With our calculation of the polarized input FFs, and the partonic hard part available in literatures, the QCD factorization formalism is ready to be applied to polarized heavy quarkonium production.

Figures (1)

• Figure 1: Schematic picture of angular momentum coupling in the hadronization from $Q\bar{Q}$-pair to heavy quarkonium $H$.