First Saturation Correction in High Energy Proton-Nucleus Collisions: II. Single Inclusive Semi-Hard Gluon Production

TL;DR

This paper derives the first saturation correction to semi-hard gluon production in high energy proton-nucleus collisions using analytic solutions of classical Yang-Mills equations, advancing the understanding of gluon spectra.

Contribution

It provides a novel derivation of the first saturation correction employing a different approach from previous works, enabling more accurate predictions of gluon production.

Findings

Complete first saturation correction derived

Functional dependence of gluon spectrum on color charge densities obtained

Results applicable to double and multiple gluon production calculations

Abstract

Exploiting recently obtained analytic solutions of classical Yang-Mills equations for higher order perturbations in the field of the dilute object (proton), we derive the complete first saturation correction to the single inclusive semi-hard gluon production in high energy proton-nucleus collisions by applying the Lehmann-Symanzik-Zimmermann reduction formula. We thus finalize the program started by Balitsky (see Ref.~\cite{Balitsky:2004rr}) and independently by Chirilli, Kovchegov and Wertepny (see Ref.~\cite{Chirilli:2015tea}) albeit using a very different approach to carry out our calculations. We extracted the functional dependence of gluon spectrum on the color charge densities of the colliding objects; thus our results can be used to evaluate complete first saturation correction to the double/multiple inclusive gluon productions.