# Azimuthal asymmetries in semi-inclusive $J/\psi\,+\,\mathrm{jet}$ production at an EIC

## TL;DR

This paper explores how azimuthal asymmetries in $J/eta$ production at an Electron-Ion Collider can reveal details about gluon distributions inside protons, emphasizing the dominance of gluon-induced processes and the potential for experimental measurement.

## Contribution

It provides a model-independent analysis of azimuthal asymmetries related to gluon distributions, including estimates of their maximal values and behavior in the small-$x$ limit using the McLerran-Venugopalan model.

## Key findings

- Quark contributions are suppressed in the considered kinematic regions.
- Maximal asymmetries are within measurable ranges according to positivity bounds.
- Small-$x$ behavior of $ ext{cos}2 heta$ asymmetries studied with the McLerran-Venugopalan model.

## Abstract

We consider transverse momentum dependent gluon distributions inside both unpolarized and transversely polarized protons and show how they can be probed by looking at azimuthal modulations in $e \, p \to e \, J/\psi \, \mathrm{jet} \, X$. We find that the contribution due to quark induced subprocesses is always suppressed in the considered kinematic regions, accessible in principle at a future Electron-Ion Collider. Our model-independent estimates of the maximal values of these asymmetries allowed by positivity bounds suggest the feasibility of their measurement. In addition, by adopting the McLerran-Venugopalan model for the unpolarized and linearly polarized gluon densities, we study the behavior of the $\cos2\phi$ asymmetries in the small-$x$ limit.