Solving the NLO BK equation in coordinate space

TL;DR

This paper numerically solves the NLO BK equation in coordinate space, revealing stability issues with typical initial conditions and identifying problematic terms related to large logarithms, which impact phenomenological applications.

Contribution

It provides the first numerical analysis of the NLO BK equation in coordinate space, highlighting stability problems and the influence of large logarithms on solutions.

Findings

Solution not stable for typical initial conditions

Problematic terms linked to large logarithms of dipole size

Rewriting in conformal dipole form does not resolve issues

Abstract

We present results from a numerical solution of the next-to-leading order (NLO) Balitsky-Kovchegov (BK) equation in coordinate space in the large Nc limit. We show that the solution is not stable for initial conditions that are close to those used in phenomenological applications of the leading order equation. We identify the problematic terms in the NLO kernel as being related to large logarithms of a small parent dipole size, and also show that rewriting the equation in terms of the "conformal dipole" does not remove the problem. Our results qualitatively agree with expectations based on the behavior of the linear NLO BFKL equation.