Helicity-dependent generalization of the JIMWLK evolution

We generalize the Jalilian-Marian--Iancu--McLerran--Weigert--Leonidov--Kovner (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 in Phys. Lett. B 523, 243 (2001) for the usual unpolarized JIMWLK and apply it to the helicity evolution equations derived by Y. V. Kovchegov et al. J. High Energy Phys. 01 (2016) 072; Phys. Rev. D 95, 014033 (2017) ; J. High Energy Phys. 10 (2017) 198; Phys. Rev. D 99, 054032 (2019). 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 subeikonal 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 subeikonal helicity-dependent local operator insertions (a ``polarized Wilson line'').