Progress in implementing the kinematical constraint into the small-x JIMWLK evolution equation

TL;DR

This paper advances the implementation of the kinematical constraint into the JIMWLK evolution equation by deriving and numerically solving new correlation functions, enhancing the understanding of high-energy Wilson line evolution.

Contribution

It introduces a set of nonlocal correlation functions in rapidity, derives their large-N evolution equations, and explores their numerical behavior for improved kinematical constraint implementation.

Findings

Derived evolution equations for new correlation functions.

Numerically solved the correlation functions.

Discussed implications for the full kinematical constraint.

Abstract

The most complete high-energy evolution of Wilson line operators is described by the set of equations called Balitsky-JIMWLK evolution equations. It is known from the studies of the linear - the BFKL - evolution equation that the leading corrections come from the kinematically enhanced double collinear logarithms. A method for resumming such logarithmic corrections to all orders for the Balitsky-Kovchegov equation is known under the name of kinematical constraint. In this work, we discuss the progress in implementing these corrections into the Langevin formulation of the JIMWLK equation. In particular, we introduce a set of correlation functions which are nonlocal in the rapidity variable. They appear in the construction of the kinematical constraint, however, their behavior with rapidity has not been investigated numerically so far. We derive their large-$N$ evolution equations, solve them numerically, and comment on their implications for the implementation of the full kinematical constraint.