Reconciling the kinematical constraint with the JIMWLK evolution equation: correlation functions non-local in rapidity

TL;DR

This paper investigates the evolution of two-point correlation functions of Wilson line operators at different rapidities within the JIMWLK framework, addressing infrared divergences and their impact on the kinematical constraint in high-energy QCD.

Contribution

It introduces a new class of correlation functions with different rapidities and analyzes their behavior and divergences within the Langevin formulation of JIMWLK evolution.

Findings

Correlation functions are affected by infrared divergence.

Regularization methods impact the implementation of the kinematical constraint.

Insights into the evolution of non-local correlation functions in high-energy QCD.

Abstract

In the high-energy limit of DIS experiments the effective degrees of freedom of QCD are Wilson line operators. Their evolution in the rapidity variable is predicted by the set of Balitsky-JIMWLK evolution equations. We analyze a new class of two-point correlation functions of Wilson line operators where the Wilson lines are taken at different values of the rapidity variable. Such correlation functions can appear in the discussion of the kinematical constraint. We find that in the Langevin formulation of the JIMWLK equation, such correlation functions are affected by an infrared divergence. We discuss a possible regularization of this divergence and its consequences for the implementation of the kinematical constraint for the JIMWLK equation.