Helicity-dependent generalization of the JIMWLK evolution

TL;DR

This paper extends the JIMWLK evolution equation to include helicity effects at small x, providing a new functional framework for polarized Wilson line operators in high-energy QCD.

Contribution

The authors derive a generalized helicity-dependent JIMWLK evolution equation using Mueller's method, incorporating sub-eikonal effects into the functional evolution framework.

Findings

Derived a functional evolution equation with helicity dependence.

Introduced a kernel with sub-eikonal derivatives for polarized operators.

Provided a method to generate standard and polarized small-x evolution equations.

Abstract

We generalize the JIMWLK evolution equation to include the small-$x$ evolution of helicity distributions. To derive helicity JIMWLK, we use the method devised by A.H. Mueller for the usual unpolarized JIMWLK, and apply it to the helicity evolution equations derived earlier. We obtain a functional evolution equation for the generalized JIMWLK weight functional. The functional now is a sum of a helicity-independent term and a helicity-dependent term. The kernel of the new evolution equation consists of the standard eikonal leading-order JIMWLK kernel plus new terms containing derivatives with respect to the sub-eikonal quark and gluon fields. The new kernel we derive can be used to generate the standard JIMWLK evolution and to construct small-$x$ evolution equations for flavor-singlet operators made of any number of light-cone Wilson lines along with one Wilson line containing sub-eikonal helicity-dependent local operator insertions (a "polarized Wilson line").