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.

arXiv comment16 pages, 5 figures

References in corpus (28)

• Operator expansion for high-energy scattering
• Small-x F_2 Structure Function of a Nucleus Including Multiple Pomeron Exchanges
• 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
• The Renormalization Group Equation for the Color Glass Condensate
• JaxoDraw: A graphical user interface for drawing Feynman diagrams
• 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
• A resummation of large sub-leading corrections at small x
• Renormalization Group Improved Small-x Equation
• A unified BFKL and GLAP description of $F_2$ data
• The Energy Dependence of the Saturation Momentum from RG Improved BFKL Evolution
• Renormalisation group improved small-x Green's function
• Improving the kinematics for low-x QCD evolution equations in coordinate space
• Rapidity evolution of Wilson lines at the next-to-leading order
• Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner evolution at next to leading order
• Direct numerical solution of the coordinate space Balitsky-Kovchegov equation at next to leading order
• Irreducible part of the next-to-leading BFKL kernel
• An "all-poles" approximation to collinear resummations in the Regge limit of perturbative QCD
• Non Abelian $q\bar{q}$ contributions to small-$x$ anomalous dimensions
• Constraints on gluon evolution at small x
• Exact kinematics in the small x evolution of the color dipole and gluon cascade
• Next-to-leading and resummed BFKL evolution with saturation boundary
• Testing the Gaussian Approximation to the JIMWLK Equation

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