Helicity-dependent generalization of the JIMWLK evolution

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").

26 pages, 17 figures

References in corpus (10)

• NLO evolution of color dipoles
• Resumming double logarithms in the QCD evolution of color dipoles
• Next-to-eikonal corrections in the CGC: gluon production and spin asymmetries in pA collisions
• Non-linear evolution in QCD at high-energy beyond leading order
• Helicity Evolution at Small $x$: Flavor Singlet and Non-Singlet Observables
• The shape of the proton at high energies
• Small-$x$ asymptotics of the quark helicity distribution
• Orbital Angular Momentum at Small $x$
• Collinear Singularities and Running Coupling Corrections to Gluon Production in CGC
• The saturation scale and its x-dependence from Lambda polarization studies