Impact-parameter-dependent solutions to the Balitsky-Kovchegov equation at next-to-leading order

TL;DR

This paper presents the first stable numerical solutions to the impact-parameter-dependent next-to-leading order Balitsky-Kovchegov equation, analyzing dipole amplitude evolution and comparing it to leading-order results, highlighting suppression of Coulomb tails.

Contribution

It provides the first stable numerical solutions to the impact-parameter-dependent NLO BK equation and compares their properties to LO solutions with collinear improvements.

Findings

NLO solutions are stable and suppress Coulomb tails.

Dipole amplitude evolution is detailed as a function of impact parameter.

NLO evolution differs significantly from LO in amplitude behavior.

Abstract

A stable numerical solution of the impact-parameter-dependent next-to-leading order Balitsky-Kovchegov equation is presented for the first time. The rapidity evolution of the dipole amplitude is discussed in detail. Dipole amplitude properties, such as the evolution speed or anomalous dimension behaviour, are studied as a function of the impact parameter and the dipole size and compared to solutions of the impact-parameter-dependent leading-order Balitsky-Kovchegov equation with the collinearly improved kernel. The next-to-leading evolution also strongly suppresses the Coulomb tails compared to the collinearly improved and leading order solutions.