$Cos(2\phi_h)$ asymmetry in $J/\psi$ production in unpolarized $ep$ collision

TL;DR

This paper calculates the $cos(2 heta_h)$ asymmetry in $J/$ production during unpolarized electron-proton collisions at the future EIC, aiming to probe gluon transverse momentum distributions and their polarization states.

Contribution

It provides a next-to-leading order calculation of the asymmetry within the NRQCD framework, incorporating both color singlet and octet contributions, and explores different gluon TMD parameterizations.

Findings

The asymmetry can be sizable in the small-$x$ region.

The asymmetry depends on gluon TMD parameterizations and LDMEs.

Results suggest the asymmetry is a useful probe for gluon polarization.

Abstract

We present a calculation of the $cos (2 \phi_h)$ asymmetry in $J/\psi$ production in electron-proton collision at the future electron-ion collider (EIC), a useful channel to probe the gluon TMDs. We calculate the asymmetry at next-to-leading order (NLO) in $\alpha_s$ in the framework of generalized factorization. The dominating sub-process is $\gamma^* +g \rightarrow J/\psi+g$. The production of $J/\psi$ is calculated in the non-relativistic QCD(NRQCD) framework with the inclusion of both color singlet and color octet contributions. Numerical estimates of the $cos(2\phi_h)$ asymmetry are given in the kinematical region to be accessed by the future EIC. The asymmetry depends on the parameterization of the gluon TMDs, as well as on the long distance matrix elements (LDMEs). We use both Gaussian-type parameterization and McLerran-Venugopalan model for the TMDs in the kinematical region of small-$x$, where the gluons play a dominant role. We obtain sizable asymmetry, which may be useful to probe the ratio of the linearly polarized and the unpolarized gluon distribution in the proton.