First saturation correction in high energy proton-nucleus collisions: Part III. Ensemble averaging

TL;DR

This paper investigates the effects of gluon saturation in high energy proton-nucleus collisions, focusing on ensemble averaging and the role of initial and final state interactions in shaping the gluon spectrum.

Contribution

It provides the first ensemble-averaged expression for saturation corrections in proton-nucleus collisions within the Color Glass Condensate framework.

Findings

Final state interactions dominate the saturation correction.

Gluon spectrum scales approximately as 1/k_perp^4 at small k_perp.

Higher order saturation corrections are needed to regulate the infrared behavior.

Abstract

In high energy proton-nucleus collisions, the gluon saturation effects from the nucleus are fully incorporated into the light-like Wilson lines. The gluon saturation effects from the proton, which are anticipated to be important either in the extreme high energy limit or towards the dense-dense (nucleus-nucleus) collision regimes, have been studied perturbatively within the Color Glass Condensate effective theory in previous papers of this series. A configuration-by-configuration expression for the single inclusive semi-hard gluon production including the first saturation correction was obtained. In this paper, we perform ensemble averaging in the McLerran-Venugopalan model and the Dipole Approximation. We find that, in the saturation correction, the effects of the initial state interactions are negligible while the final state interactions play most important role and give a positive-valued contribution to the semi-hard gluon spectrum. Furthermore, we show that the single gluon spectrum scales approximately $1/k_{\perp}^{4}$ at small $k_{\perp}$, suggesting that a resummation of higher order saturation corrections is required to regulate the infrared region of the gluon spectrum.