Travelling waves and impact-parameter correlations

TL;DR

This paper investigates whether high-energy QCD evolution remains local in impact-parameter space, finding that while some differences exist, the assumption of locality holds approximately with minor rescaling effects.

Contribution

The study provides a numerical comparison confirming that impact-parameter evolution in high-energy QCD is approximately local, with differences reducible to a simple coupling rescaling.

Findings

Quantitative differences between toy and exact models.

Differences amount to a rescaling of the strong coupling constant.

Locality in impact-parameter evolution is well verified up to subleading terms.

Abstract

It is usually assumed that the high-energy evolution of partons in QCD remains local in coordinate space. In particular, fixed impact-parameter scattering is thought to be in the universality class of one-dimensional reaction-diffusion processes as if the evolutions at different points in the transverse plane became uncorrelated through rapidity evolution. We check this assumption by numerically comparing a toy model with QCD-like impact-parameter dependence to its exact counterpart with uniform evolution in impact-parameter space. We find quantitative differences, but which seem to amount to a mere rescaling of the strong coupling constant. Since the rescaling factor does not show any strong alpha_s-dependence, we conclude that locality is well verified, up to subleading terms at small alpha_s.