x-Evolution of Phenomenological Dipole Cross Sections

TL;DR

This paper compares saturation-inspired dipole models with numerical solutions of the BK equation, revealing differences in geometric scaling and anomalous dimensions at small x in deep inelastic scattering.

Contribution

It demonstrates that the BK equation's solutions differ from phenomenological models, especially in geometric scaling and the anomalous dimension at saturation.

Findings

BK equation results differ from phenomenological models

Geometric scaling appears only at high rapidities

Anomalous dimension approaches 0.44 at saturation

Abstract

Deep inelastic scattering at small x can be described very effectively using saturation inspired dipole models. We investigate whether such models are compatible with the numerical solutions of the Balitsky-Kovchegov (BK) equation which is expected to describe the nonlinear evolution in x of the dipole cross section. We find that the BK equation yields results that are qualitatively different from those of phenomenological studies. Geometric scaling is recovered only towards asymptotic rapidities. In this limit the value of the anomalous dimension gamma(r,x) at the saturation scale approaches approximately 0.44, in contrast to the value 0.63 commonly used in the models.