# Kinematic distributions of the $\eta_c$ photoproduction in $ep$ collisions within the nonrelativistic QCD framework

## TL;DR

This paper investigates the kinematic distributions of $ ext{eta}_c$ photoproduction in electron-proton collisions within the nonrelativistic QCD framework, highlighting the dominance of color-octet contributions and proposing the process as a testbed for the color-octet mechanism.

## Contribution

First calculation of the color-singlet contribution to $ ext{eta}_c$ photoproduction at leading order, analyzing its suppression relative to color-octet parts and exploring different long-distance matrix element sets.

## Key findings

- Color-singlet contribution is significantly suppressed compared to color-octet.
- The process can effectively test the color-octet mechanism in nonrelativistic QCD.
- Different matrix element sets lead to distinguishable predictions.

## Abstract

We study the $\eta_c$ photoproduction in $ep$ collisions in this paper. The short-distance coefficients for $c\bar{c}(^1S_0^{[1]})$, $c\bar{c}(^1S_0^{[8]})$, $c\bar{c}(^3S_1^{[8]})$, and $c\bar{c}(^1P_1^{[8]})$ photoproductions are evaluated at leading order in $\alpha_s$ expansion, where the color-singlet contribution is achieved for the first time. We have carefully analyzed different kinematic distributions of the cross sections and found that the color-singlet contribution is considerably suppressed comparing with the color-octet parts. This feature renders the $\eta_c$ photoproduction process an ideal laboratory to test the color-octet mechanism in nonrelativistic QCD. By taking different sets of long-distance matrix elements, we have observed some apparently distinguishable predictions, which can be utilized to scrutinize the validity of these matrix elements.