The Jalilian-Marian,Iancu, McLerran, Weigert, Leonidov, Kovner (JIMWLK) Hamiltonian for high energy evolution of QCD amplitudes is presented at the next-to-leading order accuracy in αs. The form of the Hamiltonian is deduced from the symmetries and the structure of the hadronic light cone wavefunction and by comparing the rapidity evolution of the quark dipole and the three-quark singlet states with results available in the literature. The next-to-leading corrections should allow for more robust phenomenological applications of perturbative saturation approach.It is believed that at high energy gluons saturate in perturbative regime. The idea of perturbative gluon saturation was first suggested and discussed in detail in [1]. To date there exist numerous phenomenological applications of this idea to DIS, heavy ion collisions and proton-proton collisions at the LHC [2]. These applications are based on the Balitsky-Kovchegov (BK) non-linear evolution equation [3,4], which at large N c describes the growth of the gluon density with energy and the gluon saturation. The more general approach to the calculation of high energy hadronic amplitudes is known as the Jalilian-Marian,Iancu, McLerran, Weigert, Leonidov, Kovner (JIMWLK) evolution. The JIMWLK Hamiltonian [5] is the limit of the QCD Reggeon Field Theory (RFT), applicable for computations of high energy scattering amplitudes of dilute (small parton number) projectiles on dense (nuclei) targets. In general it predicts the rapidity evolution of any hadronic observable O via the functional equation of the formIn ref.[5], the JIMWLK Hamiltonian was derived in the leading order in α s in pQCD. It contains a wealth of information about high energy evolution equations. In the dilute-dilute limit it generates the linear BFKL equation [6] and its BKP extension [7]. Beyond the dilute limit, the Hamiltonian incorporates non-linear effects responsible for unitarization of scattering amplitudes. The BK equation arises as the mean field approximation to JIMWLK evolution at large N c . Successful BK phenomenology mandates inclusion of next to leading order corrections, since at leading order the evolution predicted by the BK equation is too rapid to describe experimental data. Currently only the running coupling corrections are included in applications, although it is clearly desirable to include all next to leading corrections. The complete set of such corrections to the evolution of a fundamental dipole was calculated in a remarkable paper by Balitsky and Chirilli [8]. The complete functional JIMWLK equation however, at the moment is only known at leading order. The next to leading order extension of the JIMWLK framework is imperative for calculation of more general amplitudes, beyond the dipole, which determine interesting experimental observables like single-and double inclusive particle production [9].Beyond phenomenological interest, deriving and exploring RFT at NLO is a fundamental theoretical question and it is the focus of this paper.The NLO BFKL equation was derived ...

Soft components of the light cone wave-function of a fast moving projectile hadron is computed in perturbation theory to the third order in QCD coupling constant. At this order, the Fock space of the soft modes consists of one-gluon, two-gluon, and a quark-antiquark states. The hard component of the wave-function acts as a non-Abelian background field for the soft modes and is represented by a valence charge distribution that accounts for non-linear density effects in the projectile. When scattered off a dense target, the diagonal element of the S-matrix reveals the Hamiltonian of high energy evolution, the JIMWLK Hamiltonian. This way we provide a new direct derivation of the JIMWLK Hamiltonian at the Next-to-Leading Order.

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].

Using the formalism of the light-cone wave function in perturbative QCD together with the hybrid factorization, we compute the cross-section for three particle production at forward rapidities in proton-nucleus collisions. We focus on the quark channel, in which the three produced partonsa quark accompanied by a gluon pair, or two quarks plus one antiquark -are all generated via two successive splittings starting with a quark that was originally collinear with the proton. The three partons are put on-shell by their scattering off the nuclear target, described as a Lorentz-contracted "shockwave". The three-parton component of the quark light-cone wave function that we compute on this occasion is also an ingredient for other interesting calculations, like the next-to-leading order correction to the cross-section for the production of a pair of jets.

Abstract:We construct the Next to Leading Order JIMWLK Hamiltonian for high energy evolution in N = 4 SUSY theory, and show that it possesses conformal invariance, even though it is derived using sharp cutoff on rapidity variable. The conformal transformation properties of Wilson lines are not quite the naive ones, but at NLO acquire an additional anomalous piece. We construct explicitly the inversion symmetry generator. We also show how to construct for every operator O, including the Hamiltonian itself, its "conformal extension" O, such that it transforms under the inversion in the naive way.