Extracting color octet NRQCD matrix elements from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>J</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>?</mml:mi></mml:math> production at the EIC

Recently unpolarized and polarized $J/\ensuremath{\psi}(\mathrm{\ensuremath{\Upsilon}})$ 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: $?0|{\mathcal{O}}_{8}^{J/\ensuremath{\psi}}(^{1}{S}_{0})|0?$ $?0|{\mathcal{O}}_{8}^{J/\ensuremath{\psi}}(^{3}{P}_{0})|0?$. The method is based on comparison open heavy-quark pair ideally performed same kinematics. In this paper we analyze proposal in more detail provide predictions for EIC available determinations of elements. We also propose additional methods that do not require production.