The small-x evolution equations for the quark and gluon helicity distribution have recently been constructed by finding sub-eikonal corrections to the eikonal shock wave formalism. Those equations are written for correlators of infinite light-cone Wilson lines along with the so-called polarized Wilson lines. Those equations close in the large Nc-limit (Nc is the number of quark colors), but also in the large Nc & Nf-limit (Nf is the number of quark flavors). However, in the shock wave formalism, no closed form can be obtained for arbitrary value of Nc and Nf.
For the unpolarized case, the generalization of the Balitsky-Kovchegov equation is done by the Jalilian-Marian—Iancu—McLerran—Weigert—Leonidov—Kovner (JIMWLK) functional evolution equation. Such an approach for the small-x evolution of the helicity is beneficial for numerical evaluation at finite Nc and Nf (beyond previously used limit), and for the evaluation of helicity-dependent operator with an arbitrary number of Wilson lines. We derive an analogue of the JIMWLK evolution equation for the small-x evolution of flavor-singlet helicity distributions and obtain an evolution equation for the target weight functional.
