Collinearly improved JIMWLK evolution in Langevin form

Abstract

The high-energy evolution of Wilson line operators, which at leading order is described by the Balitsky-JIMWLK equations, receives large radiative corrections enhanced by single and double collinear logarithms at next-to-leading order and beyond. We propose a method for resumming such logarithmic corrections to all orders, at the level of the Langevin formulation of the JIMWLK equation. The ensuing, collinearly-improved Langevin equation features generalized Wilson line operators, which depend not only upon rapidity (the logarithm of the longitudinal momentum), but also upon the transverse size of the color neutral projectile to which the Wilson lines belong. This additional scale dependence is built up during the evolution, via the condition that the successive emissions of soft gluons be ordered in time. The presence of this transverse scale in the Langevin equation furthermore allows for the resummation of the one-loop running coupling corrections.

24 pages, 1 figure

References in corpus (13)

• The Color Glass Condensate
• Universality of Unintegrated Gluon Distributions at small x
• NLO evolution of color dipoles
• Quark contribution to the small-$x$ evolution of color dipole
• Triumvirate of Running Couplings in Small-x Evolution
• Resumming double logarithms in the QCD evolution of color dipoles
• Direct numerical solution of the coordinate space Balitsky-Kovchegov equation at next to leading order
• Quark loop contribution to BFKL evolution: Running coupling and leading-N_f NLO intercept
• 3-D Glasma initial state for relativistic heavy ion collisions
• The shape of the proton at high energies
• On the running coupling in the JIMWLK equation
• High energy pA collisions in the Color Glass Condensate approach
• JIMWLK evolution of the odderon

Cited by in corpus (20)

• Mining for Gluon Saturation at Colliders
• Transverse-momentum-dependent gluon distributions from JIMWLK evolution
• CGC factorization for forward particle production in proton-nucleus collisions at next-to-leading order
• Helicity-dependent generalization of the JIMWLK evolution
• Back-to-back inclusive dijets in DIS at small $x$: Sudakov suppression and gluon saturation at NLO
• Low $x$ physics as an infinite twist (G)TMD framework: unravelling the origins of saturation
• Wigner, Husimi and GTMD distributions in the Color Glass Condensate
• On the use of a running coupling in the NLO calculation of forward hadron production
• Forward dijets in proton-nucleus collisions at next-to-leading order: the real corrections
• Forward trijet production in proton-nucleus collisions
• Selected topics in diffraction with protons and nuclei: past, present, and future
• Dihadron production in DIS at NLO: the real corrections
• Threshold Resummation for Hadron Production in the Small-$x$ Region
• Gluon-mediated inclusive Deep Inelastic Scattering from Regge to Bjorken kinematics
• Finite-size effects on small-$x$ evolution and saturation in proton and nuclear targets
• On systematic effects in the numerical solutions of the JIMWLK equation
• On the different forms of the kinematical constraint in BFKL
• Complete calculation of exclusive heavy vector meson production at next-to-leading order in the dipole picture
• Finite volume effects in the McLerran-Venugopalan initial condition for the JIMWLK equation
• Dijet photoproduction at low $x$ at next-to-leading order and its back-to-back limit