Resumming double logarithms in the QCD evolution of color dipoles

Abstract

The higher-order perturbative corrections, beyond leading logarithmic accuracy, to the BFKL evolution in QCD at high energy are well known to suffer from a severe lack-of-convergence problem, due to radiative corrections enhanced by double collinear logarithms. Via an explicit calculation of Feynman graphs in light cone (time-ordered) perturbation theory, we show that the corrections enhanced by double logarithms (either energy-collinear, or double collinear) are associated with soft gluon emissions which are strictly ordered in lifetime. These corrections can be resummed to all orders by solving an evolution equation which is non-local in rapidity. This equation can be equivalently rewritten in local form, but with modified kernel and initial conditions, which resum double collinear logs to all orders. We extend this resummation to the next-to-leading order BFKL and BK equations. The first numerical studies of the collinearly-improved BK equation demonstrate the essential role of the resummation in both stabilizing and slowing down the evolution.

16 pages, 5 figures

References in corpus (3)

• NLO evolution of color dipoles
• Direct numerical solution of the coordinate space Balitsky-Kovchegov equation at next to leading order
• Testing the Gaussian Approximation to the JIMWLK Equation

Cited by in corpus (51)

• Mining for Gluon Saturation at Colliders
• Non-linear evolution in QCD at high-energy beyond leading order
• CGC factorization for forward particle production in proton-nucleus collisions at next-to-leading order
• Dipole factorization for DIS at NLO: Combining the $q\bar{q}$ and $q\bar{q}g$ contributions
• High Gluon Densities in Heavy Ions Collisions
• Helicity-dependent generalization of the JIMWLK evolution
• Back-to-back inclusive dijets in DIS at small $x$: Sudakov suppression and gluon saturation at NLO
• Deep inelastic scattering in the dipole picture at next-to-leading order
• HERA data and collinearly-improved BK dynamics
• Wigner, Husimi and GTMD distributions in the Color Glass Condensate
• The Analytic Structure of Non-Global Logarithms: Convergence of the Dressed Gluon Expansion
• Massive quarks in NLO dipole factorization for DIS: Transverse photon
• Helicity at Small $x$: Oscillations Generated by Bringing Back the Quarks
• Proton structure functions at NLO in the dipole picture with massive quarks
• Diffractive deep inelastic scattering at NLO in the dipole picture: the $q\bar{q}g$ contribution
• The Asymptotic Form of Non-Global Logarithms, Black Disc Saturation, and Gluonic Deserts
• Energy dependent nuclear suppression from gluon saturation in exclusive vector meson production
• Selected topics in diffraction with protons and nuclei: past, present, and future
• Dihadron production in DIS at NLO: the real corrections
• Cascades of high-energy SM particles in the primordial thermal plasma
• Transverse momentum broadening from the lattice
• Gluon-mediated inclusive Deep Inelastic Scattering from Regge to Bjorken kinematics
• Inferring the initial condition for the Balitsky-Kovchegov equation
• CGC/saturation approach: a new impact-parameter dependent model in the next-to-leading order of perturbative QCD
• Saturation in inclusive production beyond leading logarithm accuracy
• High-energy dipole scattering amplitude from evolution of low-energy proton light-cone wave functions
• Finite-size effects on small-$x$ evolution and saturation in proton and nuclear targets
• Incoherent diffractive dijet production in electron DIS off nuclei at high energy
• Gluon Saturation Effects in Exclusive Heavy Vector Meson Photoproduction
• Solutions to the Balitsky-Kovchegov equation including the dipole orientation
• Complete Next-to-Leading Order Calculation of Single Inclusive ${\pi }^0$ Production in Forward Proton-Nucleus Collisions
• Rare fluctuations of the $S$-matrix at NLO in QCD
• NLO JIMWLK evolution with massive quarks
• Initial condition for the Balitsky-Kovchegov equation at next-to-leading order
• Analytic solution of Balitsky-Kovchegov equation with running coupling constant using homogeneous balance method
• A parton shower generator based on the GLR equation
• Complete calculation of exclusive heavy vector meson production at next-to-leading order in the dipole picture
• Impact-parameter-dependent solutions to the Balitsky-Kovchegov equation at next-to-leading order
• Determination of the initial condition for the Balitsky-Kovchegov equation with transformers
• Perturbative Corrections to Quark TMDPDFs in the Background-Field Method: Gauge Invariance, Equations of Motion, and Multiple Interactions
• A numerical implementation of the NLO DIS structure functions in the dipole picture
• Statistical properties of partonic configurations and diffractive dissociation in high-energy electron-nucleus scattering
• Exploring the DGLAP resummation in the JIMWLK Hamiltonian
• Implementing consistent NLO factorization in single inclusive forward hadron production
• Dijet photoproduction at low $x$ at next-to-leading order and its back-to-back limit
• Finite volume effects in the McLerran-Venugopalan initial condition for the JIMWLK equation
• The High Energy Radiation Pattern from BFKLex
• Exclusive production of light vector mesons at next-to-leading order in the dipole picture
• Dipole model at Next-to-Leading Order meets HERA data
• Including resummation in the NLO BK equation
• Scattering off the Color Glass Condensate