TMD Evolution Study of the $\cos 2 \phi$ Azimuthal Asymmetry in Unpolarized $J/\psi$ Production at EIC

TL;DR

This study investigates the $ ext{cos} 2 ext{phi}$ azimuthal asymmetry in unpolarized $J/ ext{psi}$ production at the EIC, incorporating TMD evolution to improve understanding of gluon TMDs and their behavior at different kinematic regimes.

Contribution

The paper introduces TMD evolution into the analysis of azimuthal asymmetry in $J/ ext{psi}$ production, revealing growth patterns and validity constraints of TMD factorization at the EIC.

Findings

Asymmetry increases with $J/ ext{psi}$ transverse momentum in the TMD regime.

Predicted asymmetries can exceed positivity bounds at high $x$, $Q$, and transverse momenta.

TMD factorization validity is limited due to small $b$ region effects.

Abstract

Semi-inclusive $J/\psi$ production in electron-proton collisions is a promising process to study gluon transverse momentum distributions (TMDs) at the future Electron-Ion Collider. In this article, we improve on previous studies of the $\cos 2 \phi$ azimuthal asymmetry that arises from the linear polarization of gluons inside unpolarized protons by including TMD evolution. We find that in the TMD regime the asymmetry grows monotonically with increasing transverse momentum of the outgoing $J/\psi$, in contrast to tree level calculations with Gaussian TMDs. Our predictions for the asymmetry at EIC can become very large at larger $x$, $Q$, and transverse momenta, even larger than the positivity bound. This problem stems from the very small $b$ region and implies a range of validity of TMD factorization that is more restricted than usually expected. We also include an estimate of the nonperturbative uncertainty from the large $b$ region and we conclude that it is smaller than the largest source of uncertainty, which stems from the choice of Color Octet Long-Distance Matrix Elements.