NLO JIMWLK evolution unabridged

TL;DR

The paper provides a detailed derivation of the next-to-leading order JIMWLK Hamiltonian for high-energy QCD evolution and demonstrates its compatibility with Balitsky’s hierarchy and with results for color nonsinglet Wilson lines. By expressing the Hamiltonian in a kernel-based form and fixing kernels through Balitsky-Chirilli and Grabovsky benchmarks, it extends JIMWLK to general Wilson-line operators, including the three-quark (baryon) Wilson loop $B$. It also constructs a conformal extension ${\cal B}$ in ${\cal N}=4$ SYM and shows that the NLO dynamics can be made exactly conformal with the appropriate kernel redefinitions, highlighting the theoretical consistency and potential applications to multi-particle production and baryon-like correlators at high energy. Overall, the work provides a unified, operator-centric framework for computing full NLO high-energy evolution beyond the dipole, with explicit results for singlet and nonsinglet sectors and for baryon-like observables.

Abstract

In Ref. [1] we presented the JIMWLK Hamiltonian for high energy evolution of QCD amplitudes at the next-to-leading order accuracy in $α_s$. In the present paper we provide details of our original derivation, which was not reported in [1], and provide the Hamiltonian in the form appropriate for action on color singlet as well as color nonsinglet states. The rapidity evolution of the quark dipole generated by this Hamiltonian is computed and compared with the corresponding result of Balitsky and Chirilli [2]. We then establish the equivalence between the NLO JIMWLK Hamiltonian and the NLO version of the Balitsky's hierarchy [3], which includes action on nonsinglet combinations of Wilson lines. Finally, we present complete evolution equation for three-quark Wilson loop operator, thus extending the results of Grabovsky [4].