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 (25)

• 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
• Helicity at Small $x$: Oscillations Generated by Bringing Back the 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
• Transverse momentum broadening from the lattice
• 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
• Rare fluctuations of the $S$-matrix at NLO in QCD
• Analytic solution of Balitsky-Kovchegov equation with running coupling constant using homogeneous balance method
• Statistical properties of partonic configurations and diffractive dissociation in high-energy electron-nucleus scattering
• Dipole model at Next-to-Leading Order meets HERA data
• Implementing consistent NLO factorization in single inclusive forward hadron production
• The High Energy Radiation Pattern from BFKLex
• Including resummation in the NLO BK equation
• Scattering off the Color Glass Condensate