Fragmentation functions of polarized heavy quarkonium

TL;DR

This paper calculates the polarized fragmentation functions of heavy quarkonium using NRQCD, enabling more accurate predictions of polarized heavy quarkonium production within a QCD factorization framework.

Contribution

It provides the first comprehensive calculation of polarized input fragmentation functions for heavy quarkonium based on NRQCD, including all relevant S-wave and P-wave states.

Findings

Derived polarized NRQCD long-distance matrix elements using symmetries.

Proposed a scheme to define matrix elements in arbitrary dimensions.

Calculated polarized input FFs from all S-wave and P-wave states.

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.