# Non-linear evolution in QCD at high-energy beyond leading order

## TL;DR

This paper addresses the instabilities in the NLO BK equation for high-energy QCD evolution by proposing resummation methods directly in the target rapidity, reducing scheme dependence and extending to full NLO accuracy.

## Contribution

It introduces a new approach to resumming collinear logarithms directly in the target rapidity, improving stability and scheme independence of the NLO BK evolution equations.

## Key findings

- Resummation in target rapidity reduces scheme dependence.
- Proposed prescriptions effectively tame collinear instabilities.
- Equations can be extended to full NLO accuracy.

## Abstract

The next-to-leading order (NLO) Balitsky-Kovchegov (BK) equation describing the high-energy evolution of the scattering between a dilute projectile and a dense target suffers from instabilities unless it is supplemented by a proper resummation of the radiative corrections enhanced by (anti-)collinear logarithms. Earlier studies have shown that if one expresses the evolution in terms of the rapidity of the dilute projectile, the dominant anti-collinear contributions can be resummed to all orders. However, in applications to physics, the results must be re-expressed in terms of the rapidity of the dense target. We show that although they lead to stable evolution equations, resummations expressed in the rapidity of the dilute projectile show a strong, unwanted, scheme dependence when their results are translated in terms of the target rapidity. Instead, in this paper, we work directly in the rapidity of the dense target where anti-collinear contributions are absent but where new, collinear, instabilities arise. These are milder since disfavoured by the typical BK evolution. We propose several prescriptions for resumming these new double logarithms and find only little scheme dependence. The resummed equations are non-local in rapidity and can be extended to full NLO accuracy.