Subleading-N_c corrections in non-linear small-x evolution

TL;DR

This paper investigates the smallness of subleading-N_c corrections in small-x evolution equations, showing that saturation effects and group theory constraints suppress these corrections, resulting in minimal differences between BK and JIMWLK solutions.

Contribution

The study demonstrates that saturation effects and group theory constraints significantly suppress subleading-N_c corrections, explaining the near-equivalence of BK and JIMWLK solutions.

Findings

Subleading-N_c corrections are suppressed to about 0.1%.

Improved numerical solutions confirm small remaining corrections.

A Gaussian truncation captures some multi-reggeon exchange effects.

Abstract

We explore the subleading-N_c corrections to the large-N_c Balitsky-Kovchegov (BK) evolution equation by comparing its solution to that of the all-N_c Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) equation. In earlier simulations it was observed that the difference between the solutions of JIMWLK and BK is unusually small for a quark dipole scattering amplitude, of the order of 0.1%, which is two orders of magnitude smaller than the naively expected 1/N_c^2 or 11%. In this paper we argue that this smallness is not accidental. We show that saturation effects and correlator coincidence limits fixed by group theory constraints conspire with the particular structure of the dipole kernel to suppress subleading-N_c corrections reducing the difference between the solutions of JIMWLK and BK to 0.1%. We solve the JIMWLK equation with improved numerical accuracy and verify that the remaining 1/N_c corrections, while small, still manage to slow down the rapidity-dependence of JIMWLK evolution compared to that of BK. We demonstrate that a truncation of JIMWLK evolution in the form of a minimal Gaussian generalization of the BK equation captures some of the remaining 1/N_c contributions leading to an even better agreement with JIMWLK evolution. As the 1/N_c corrections to BK include multi-reggeon exchanges one may conclude that the net effect of multi-reggeon exchanges on the dipole amplitude is rather small.