Direct numerical solution of the coordinate space Balitsky-Kovchegov equation at next to leading order

Abstract

We present the first numerical solution to the next to leading order Balitsky-Kovchegov (BK) equation in coordinate space in the large-$N_{\mathrm{c}}$ limit. In addition to the dipole operator we also solve the evolution of the "conformal dipole" for which the conformal invariance breaking double logarithmic term is absent from the evolution equation. The NLO corrections are shown to slow down the evolution. We show that the solution depends strongly on the details of the initial condition, and that the solution to the equation is not positive definite with all initial conditions relevant for phenomenological applications.

8 pages, 10 figures. RevTeX. v2: references added, small clarifications to the text and Figs. 9 and 10, to be published in Phys. Rev. D

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Cited by in corpus (13)

• Resumming double logarithms in the QCD evolution of color dipoles
• 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
• Deep inelastic scattering in the dipole picture at next-to-leading order
• HERA data and collinearly-improved BK dynamics
• Saturation in inclusive production beyond leading logarithm accuracy
• Rare fluctuations of the $S$-matrix at NLO in QCD
• Statistical properties of partonic configurations and diffractive dissociation in high-energy electron-nucleus scattering
• Implementing consistent NLO factorization in single inclusive forward hadron production
• Including resummation in the NLO BK equation