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 ${\alpha }_s$. 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].

39 pages

References in corpus (36)

• Operator expansion for high-energy scattering
• Nonlinear Gluon Evolution in the Color Glass Condensate: I
• The Wilson renormalization group for low x physics: towards the high density regime
• The BFKL Equation from the Wilson Renormalization Group
• BFKL pomeron in the next-to-leading approximation
• Nonlinear Gluon Evolution in the Color Glass Condensate: II
• Unitarization of the BFKL Pomeron on a Nucleus
• The Renormalization Group Equation for the Color Glass Condensate
• The Wilson renormalization group for low x physics: Gluon evolution at finite parton density
• Unitarity at small Bjorken x
• Energy Scale(s) and Next-to-leading BFKL Equation
• Relating different approaches to nonlinear QCD evolution at finite gluon density
• NLO evolution of color dipoles
• Factorization and high-energy effective action
• Quark contribution to the small-$x$ evolution of color dipole
• Factorization for high-energy scattering
• Vector potential versus colour charge density in low-x evolution
• Odderon in the Color Glass Condensate
• Rapidity evolution of Wilson lines at the next-to-leading order
• Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner evolution at next to leading order
• In pursuit of Pomeron loops: the JIMWLK equation and the Wess-Zumino term
• Nonlinear evolution in high-density QCD
• From target to projectile and back again: selfduality of high energy evolution
• NLO evolution of color dipoles in N=4 SYM
• Odderon and seven Pomerons: QCD Reggeon field theory from JIMWLK evolution
• One gluon, two gluon: multigluon production via high energy evolution
• Remarks on High Energy Evolution
• JIMWLK evolution in the Gaussian approximation
• Treading on the cut: Semi inclusive observables at high energy
• Reggeon Field Theory for Large Pomeron Loops
• NLO Corrections to the kernel of the BKP-equations
• The initial state of heavy-ion collisions
• Connected contribution to the kernel of the evolution equation for 3-quark Wilson loop operator
• The dipole form of the BFKL kernel in supersymmetric Yang--Mills theories
• Conformal symmetry of JIMWLK Evolution at NLO
• Evolution equation for 3-quark Wilson loop operator

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• Dipole factorization for DIS at NLO I: Loop correction to the photon to quark-antiquark light-front wave-functions
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• HERA data and collinearly-improved BK dynamics
• High Energy QCD at NLO: from light-cone wave function to JIMWLK evolution
• Heavy quarks in proton-nucleus collisions - the hybrid formalism
• Rapidity loss, spin and angular asymmetries in scattering of a quark from color field of a proton (nucleus)
• Hard scale dependent gluon density, saturation and forward-forward dijet production at the LHC
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• Forward dijets in proton-nucleus collisions at next-to-leading order: the real corrections
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• Selected topics in diffraction with protons and nuclei: past, present, and future
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• Initial State Quantum Fluctuations in the Little Bang
• NLO evolution of 3-quark Wilson loop operator
• Dipole evolution: perspectives for collectivity and ${\gamma }^{\ast }$A collisions
• High energy asymptotic behavior of the $S$-matrix in the saturation region with the smallest dipole running coupling prescription
• Extended collinearly-improved Balitsky-Kovchegov evolution equation in target rapidity
• Reggeon Field Theory and Self Duality: Making Ends Meet
• Initial state in relativistic nuclear collisions and Color Glass Condensate
• Small-$x$ QCD evolution of $2n$ Wilson line correlator: the weak field limit
• Non-linear evolution in the re-summed next-to-leading order of perturbative QCD:\confronting the experimental data
• Off-shell amplitudes as boundary integrals of analytically continued Wilson line slope
• Solution to the Sudakov suppressed Balitsky-Kovchegov equation and its application to the HERA data
• Structure functions from renormalization group improved small $x$ evolution
• Non-linear equation in the re-summed next-to-leading order of perturbative QCD: the leading twist approximation
• Taming of preasymptotic small x evolution within resummation framework
• CGC and saturation approach: Impact-parameter dependent model of perturbative QCD and combined HERA data
• Dijet impact factor in DIS at next-to-leading order in the Color Glass Condensate
• Perturbative Corrections to Quark TMDPDFs in the Background-Field Method: Gauge Invariance, Equations of Motion, and Multiple Interactions
• On the low-x NLO evolution of 4 point colorless operators
• Exploring the DGLAP resummation in the JIMWLK Hamiltonian
• Collinear resummations for the non-linear evolution in QCD at high energy
• Dijet photoproduction at low $x$ at next-to-leading order and its back-to-back limit