NLO JIMWLK evolution unabridged

TL;DR

This paper details the derivation of the NLO JIMWLK Hamiltonian for high energy QCD evolution, compares it with existing results, and extends the evolution equations to three-quark Wilson loops.

Contribution

It provides the full derivation of the NLO JIMWLK Hamiltonian, its form for various states, and establishes its equivalence with the NLO Balitsky hierarchy, including new evolution equations.

Findings

Derived the NLO JIMWLK Hamiltonian in detail.

Established equivalence with NLO Balitsky hierarchy.

Extended evolution equations to three-quark Wilson loops.

Abstract

In Ref. [1] we presented the JIMWLK Hamiltonian for high energy evolution of QCD amplitudes at the next-to-leading order accuracy in $\alpha_s$. 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].