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

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• First analysis of world polarized DIS data with small-$x$ helicity evolution
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• Small $x$ Physics Beyond Eikonal Approximation: an Effective Hamiltonian Approach
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• Multiparticle production in proton-nucleus collisions beyond eikonal accuracy
• Helicity Evolution at Small $x$: Revised Asymptotic Results at Large $N_c\&N_f$
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• Multiplicity dependence of ${\chi }_c$ and ${\chi }_b$ meson production
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• JAM small-$x$ helicity phenomenology
• Exclusive photoproduction of $B_c^{\pm }$ and bottomonia pairs
• Electroproduction of $D$- and $B$-mesons in high-multiplicity $ep$ collisions
• Parton model contributions as next-to-eikonal corrections to the dipole factorization of DIS and SIDIS at low $x_{Bj}$
• Exclusive photoproduction of heavy quarkonia pairs