NLO JIMWLK evolution unabridged

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].

Rapidity evolution of gluon TMD from low to moderate x

“…The NLO corrections to the BFKL [44,45] and BK [17][18][19][20][46][47][48][49] equation are available but they suffer from the well-known problem that they lead to negative cross sections. This difficulty can be overcome by the "collinear resummation" of double-logarithmic contributions for the BFKL [50][51][52][53] and BK [54][55][56] equations and we hope that our eq.…”

On the low-x NLO evolution of 4 point colorless operators

“…These results were also obtained in the Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov and Kovner (JIMWLK) formalism [15][16][17][18][19][20][21]. The hamiltonian equivalent to the NLO hierarchy was obtained in [22] and the evolution equation for the 3QWL in [23]. The NLO kernel for the evolution Wilson line operators was also constructed in [24].…”

“…Although such treatment gave the equations satisfying all the checks, it is important to have the initial expressions with the regularization of the IR singularities and to check the results of this paper. Such checks may be performed starting from the evolution equations found in [23] and [24].…”

“…The evolution equations for the quadrupole and double dipole operators can be obtained from the NLO JIMWLK hamiltonian [23] and the general evolution equations from [24]. In this paper the following two checks were done.…”

Rapidity evolution of gluon TMD from low to moderate x

“…If we consider now the intermediate case As an outlook, it would be very interesting to obtain the NLO correction to the evolution equation (5.5). The NLO corrections to the BFKL [29] and BK [14,30,31] equation are available but they suffer from the well-known problem that they lead to negative cross sections. This difficulty can be overcome by the "collinear resummation" of double-logarithmic contributions for the BFKL [32] and BK [33] equations and we hope that our Eq.…”