Extracting color octet NRQCD matrix elements from $J/\psi$ production at the EIC

TL;DR

This paper explores methods to extract poorly known color-octet NRQCD matrix elements from $J/eta$ production at the EIC, providing detailed analysis, predictions, and alternative approaches that do not rely on open heavy-quark pair comparisons.

Contribution

It offers a detailed analysis of a new method and proposes two additional approaches for extracting color-octet NRQCD matrix elements at the EIC.

Findings

Predictions for matrix elements based on existing determinations.

Analysis of the proposed comparison method's effectiveness.

Introduction of two alternative extraction methods.

Abstract

Recently unpolarized and polarized $J/\psi \,(\Upsilon)$ production at the Electron-Ion Collider (EIC) has been proposed as a new way to extract two poorly known color-octet NRQCD long-distance matrix elements: $\langle0\vert{\cal O}_{8}^{J/\psi}(^{1}S_{0})\vert0\rangle$ and $\langle0\vert{\cal O}_{8}^{J/\psi}(^{3}P_{0})\vert0\rangle$. The proposed method is based on a comparison to open heavy-quark pair production ideally performed at the same kinematics. In this paper we analyze this proposal in more detail and provide predictions for the EIC based on the available determinations of the color-octet matrix elements. We also propose two additional methods that do not require comparison to open heavy-quark pair production.