BFKL equation in the next-to-leading order: solution at large impact parameters

Abstract

In this paper, we show (i) that the NLO corrections do not change the power-like decrease of the scattering amplitude at large impact parameter ($b^2 \,>\,r^2 \exp\left( 2\bar(α}_S η(1 + 4 \barα_S)\right)$, where $r$ denotes the size of scattering dipole and $\eta =\ln (1/x_{Bj})$ for DIS), and, therefore, they do not resolve the inconsistency with unitarity; and (ii) they lead to an oscillating behaviour of the scattering amplitude atlarge $b$, in direct contradiction with the unitarity constraints. However, from the more practical point of view, the NLO estimates give a faster decrease of the scattering amplitude as a function of $b$, and could be very useful for description of the experimental data. It turns out, that in a limited range of $b$, the NLO corrections generates the fast decrease of the scattering amplitude with $b$, which can be parameterized as $N\propto \exp (-\mu b)$ with $\mu \propto 1/r$ in accord with the numerical estimates in Ref.[1].

14 pp, 21 figures in pdf files

References in corpus (3)

• Non-linear evolution in QCD at high-energy beyond leading order
• Collinearly improved kernel suppresses Coulomb tails in the impact-parameter dependent Balitsky-Kovchegov evolution
• Large $\mathbf{b}$ behaviour in the CGC/saturation approach: BFKL equation with pion loops

Cited by in corpus (7)

• Photonuclear $J/\psi$ production at the LHC: proton-based versus nuclear dipole scattering amplitudes
• Solutions to the Balitsky-Kovchegov equation including the dipole orientation
• Large impact parameter behaviour in the CGC/saturation approach: a new non-linear equation
• Non-linear evolution in the re-summed next-to-leading order of perturbative QCD:\confronting the experimental data
• Non-linear equation in the re-summed next-to-leading order of perturbative QCD: the leading twist approximation
• Impact-parameter-dependent solutions to the Balitsky-Kovchegov equation at next-to-leading order
• Contribution of the non-linear term in the Balitsky-Kovchegov equation to the nuclear structure functions