# Statistical analysis of the azimuthal asymmetry in the $J/\psi$ leptoproduction in unpolarized $ep$ collisions

## TL;DR

This paper analyzes azimuthal asymmetries in $J/$ leptoproduction in unpolarized $ep$ collisions to distinguish between different heavy quarkonium production models using specific modulations and kinematic regions.

## Contribution

It introduces a method to differentiate heavy quarkonium production models via azimuthal asymmetry modulations in $J/$ leptoproduction at future colliders.

## Key findings

- The $ ext{cos}()$ and $ ext{cos}(2)$ modulations can distinguish production mechanisms.
- Statistical analysis shows models can be separated with 1000 pb$^{-1}$ luminosity.
- Future $ep$ colliders can provide crucial insights into $J/$ production mechanisms.

## Abstract

In this paper, we study the azimuthal asymmetry in the $J/\psi$ leptoproduction in unpolarized $ep$ collisions. There are two independent azimuthal asymmetry modulations, namely $\mathrm{cos}(\psi)$ and $\mathrm{cos}(2\psi)$, where $\psi$ is the azimuthal angle of the lepton scattering plane with respect to the hadron-interacting plane. We calculate the two modulations as functions of four kinematic variables, and find that they provide a very good laboratory to distinguish several models describing the heavy quarkonium production, including the color-singlet (CS) model, the nonrelativistic QCD (NRQCD) associated with the $^1S_0^{[8]}$ dominance picture, and the NRQCD in which the values of all the three color-octet (CO) long-distance matrix elements are of the same order. In order to make definite conclusions, we restrict our calculation in a specific kinematic region, where the CS and CO mechanisms can be distinguished by scrutinizing the values of the $\mathrm{cos}(\psi)$ modulation, while the $^1S_0^{[8]}$ dominance picture can be tested by measuring the values of the $\mathrm{cos}(2\psi)$ modulation. Calculating their values and carrying out a meticulous statistical analysis, we find that at an integrated luminosity $\mathcal{L}=1000\mathrm{pb}^{-1}$, the statistical uncertainties of the two quantities are small enough to tell the three models apart. When this experiment is implemented at the future $ep$ colliders such as the EIC, crucial information for the $J/\psi$ production mechanism might be discovered.