# JIMWLK evolution and small-x asymptotics of 2n-tuple Wilson line correlators

## TL;DR

This paper reformulates the JIMWLK evolution equation for 2n-tuple Wilson line correlators, analyzing their ultraviolet behavior and demonstrating geometric scaling in the saturation regime.

## Contribution

The paper presents a new integro-differential form of the JIMWLK equation for higher-order correlators with explicit real and virtual terms, and analyzes their ultraviolet properties and scaling behavior.

## Key findings

- Explicit form of the JIMWLK equation for 2n-tuple correlators.
- Identification of ultraviolet divergences in specific kernels.
- Demonstration of geometric scaling in the strong scattering regime.

## Abstract

JIMWLK equation tells how gauge invariant higher order Wilson line correlators would evolve at high energy. In this article we present a convenient integro-differential form of this equation, for 2n-tuple correlator, where all real and virtual terms are explicit. The `real' terms correspond to splitting (say at position z) of this 2n-tuple correlator to various pairs of 2m-tuple and (2n+2-2m)-tuple correlators whereas `virtual' terms correspond to splitting into pairs of 2m-tuple and (2n-2m)-tuple correlators. Kernels of virtual terms with m=0 (no splitting) and of real terms with m=1 (splitting with atleast one dipole) have poles and when integrated over z they do generate ultraviolet logarithmic divergences, separately for real and virtual terms. Except these two cases in all other terms the corresponding kernels, separately for real and virtual terms, have rather soften ultraviolet singularity and when integrated over z do not generate ultraviolet logarithmic divergences. We went on to study the solution of the JIMWLK equation for the 2n-tuple Wilson line correlator in the strong scattering regime where all transverse distances are much larger than inverse saturation momentum and shown that it also exhibits geometric scaling like color dipole deep inside saturation region.