Related papers: Solution to the evolution equation at NLL for high…
We solve the Balitsky-Kovchegov evolution equation at next-to-leading order accuracy including a resummation of large single and double transverse momentum logarithms to all orders. We numerically determine an optimal value for the constant…
We derive two coupled non-linear evolution equations corresponding to the truncation of the Balitsky infinite hierarchy of saturation equations after inclusion of dipole-dipole correlations, i.e. one step beyond the Balitsky-Kovchegov (BK)…
We include resummation of large transverse logarithms into the next-to-leading order Balitsky-Kovchegov equation. The resummed NLO evolution equation is shown to be stable, the evolution speed being significantly reduced by higher order…
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…
Nonlinear QCD evolution equations are essential tools in understanding the saturation of partons at small Bjorken $x_{\rm B}$, as they are supposed to restore an upper bound of unitarity for the cross section of high energy scattering. In…
In this paper we revisit the problem of the solution to Balitsky-Kovchegov equation deeply in the saturation domain. We find that solution has the form of Levin-Tuchin solution but it depends on variable $\bar{z} = \ln(r^2 Q^2_s) +…
We propose a general method to study the solutions to nonlinear QCD evolution equations, based on a deep analogy with the physics of traveling waves. In particular, we show that the transition to the saturation regime of high energy QCD is…
The Balitsky-Kovchegov equation describes the high-energy growth of gauge theory scattering amplitudes as well as nonlinear saturation effects which stop it. We obtain the three-loop corrections to this equation in planar $\mathcal{N}=4$…
We present results from analytic solutions to the running coupling, full next-to-leading order, and collinearly improved next-to-leading order Balitsky-Kovchegov equations in the saturation region with the smallest dipole size QCD running…
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…
In this talk the results of the analytical and numerical analysis of the nonlinear Balitsky-Kovchegov equation are presented. The characteristic BFKL diffusion into infrared regime is suppressed by the generation of the saturation scale. We…
The next-to-leading order (NLO) Balitsky-Kovchegov (BK) equation describing the high-energy evolution of the scattering between a dilute projectile and a dense target suffers from instabilities unless it is supplemented by a proper…
When computed to next-to-leading order in perturbative QCD, the non-linear Balitsky-Kovchegov (BK) equation for the high-energy evolution of the dipole-hadron scattering appears to be unstable. We show that this instability can be avoided…
High parton density effects with energy obey non-linear QCD evolution equations for which exact solutions are not known. The mathematical class to which the non-linear Balitsky-Kovchegov equation belongs is identified, proving the existence…
The Balitsky-Kovchegov QCD equation for rapidity evolution describing saturation effects at high energy admits universal asymptotic traveling-wave solutions when the nonlinear damping becomes effective. The asymptotic solutions fall in…
An extended collinearly-improved Balitsky-Kovchegov evolution equation in the target rapidity representation is derived by including the running coupling corrections during the expansion of the "real" $S$-matrix. We find that the running…
We propose a modified version of the Balitsky-Kovchegov (B-K) evolution equation, which includes the main NLO corrections. We use the result that the main NLO corrections to the BFKL kernel are the LO DGLAP corrections. We present a…
We analytically solve the Sudakov suppressed Balitsky-Kovchegov evolution equation with the fixed and running coupling constants in the saturation region. The analytic solution of the $S$-matrix shows the $\exp(\mathcal{O}(\eta^2))$…
We revisited solution of a linearized form of leading order Balitsky-Kovchegov equation (linear in S-matrix for dipole-nucleus scattering). Here we adopted dipole transverse width dependent cutoff in order to regulate the dipole integral.…
The high-energy evolution in perturbative QCD suffers from a severe lack-of-convergence problem, due to higher order corrections enhanced by double and single transverse logarithms. We resum double logarithms to all orders within the…