Asymptotics of QCD traveling waves with fluctuations and running coupling effects

TL;DR

This paper analyzes the combined effects of running coupling and fluctuations on the asymptotic behavior of solutions to the Balitsky-Kovchegov (BK) equation, revealing how these factors influence the saturation scale in QCD.

Contribution

It extends the analysis of the BK equation to include both running coupling and fluctuation effects simultaneously, deriving the exact asymptotic distribution of the saturation scale.

Findings

Qualitative changes in traveling-wave solutions due to combined effects.

Exact asymptotic distribution of the saturation scale derived.

Insights into QCD saturation phenomena with realistic effects.

Abstract

Extending independently the Balitsky-Kovchegov (BK) equation to running coupling or to fluctuation effects due to Pomeron loops is known to lead in both cases to qualitative changes of the traveling-wave asymptotic solutions. In this paper we study the extension of the forward BK equation, including both running coupling and fluctuations effects, using the method developed for the fixed coupling case. We derive the exact asymptotic behavior of the probabilistic distribution of the saturation scale.