Finite-size effects on small-$x$ evolution and saturation in proton and nuclear targets

TL;DR

This paper investigates how finite target size influences small-x evolution and saturation phenomena in protons and nuclei within the Color Glass Condensate framework, highlighting the importance of impact-parameter dependence.

Contribution

It demonstrates the significance of including impact-parameter dependence in BK evolution for accurate saturation predictions, especially for protons, and shows robustness of predictions for heavy nuclei.

Findings

Neglecting impact-parameter dependence overestimates proton saturation effects.

Impact-parameter dependence has minimal effect on heavy nuclei at current energies.

Predictions for lead targets are insensitive to various theoretical scheme choices.

Abstract

Within the Color Glass Condensate effective field theory, we assess the importance of including a finite size for the target on observables sensitive to small-$x$ evolution. To this end, we study the Balitsky-Kovchegov (BK) equation with impact-parameter dependence in the initial condition. We demonstrate that neglecting the dependence on the impact parameter can result in overestimated saturation effects for protons, while it has little effect for heavy nuclei at the energies available at current experiments. When fixing the nonperturbative parameters to the energy dependence of the exclusive $J/\psi$ photoproduction cross section with proton targets, predictions for lead targets are not sensitive to the applied running-coupling prescription, the scheme chosen to resum large transverse logarithms in the BK equation, or the infrared regulator in the evolution.