Direct numerical solution of the coordinate space Balitsky-Kovchegov equation at next to leading order

TL;DR

This paper provides the first numerical solution to the next-to-leading order Balitsky-Kovchegov equation in coordinate space, revealing the impact of NLO corrections and initial conditions on the evolution of dipole operators.

Contribution

It introduces a numerical method for solving the NLO BK equation in coordinate space and analyzes the behavior of the conformal dipole and the effects of NLO corrections.

Findings

NLO corrections slow down the evolution.

Solution depends strongly on initial conditions.

Solution is not positive definite for relevant initial conditions.

Abstract

We present the first numerical solution to the next to leading order Balitsky-Kovchegov (BK) equation in coordinate space in the large-$N_\mathrm{c}$ limit. In addition to the dipole operator we also solve the evolution of the "conformal dipole" for which the conformal invariance breaking double logarithmic term is absent from the evolution equation. The NLO corrections are shown to slow down the evolution. We show that the solution depends strongly on the details of the initial condition, and that the solution to the equation is not positive definite with all initial conditions relevant for phenomenological applications.