Related papers: Saturation at low x and nonlinear evolution
The small-$x_B$ deep inelastic scattering in the saturation region is governed by the non-linear evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the BK equation for the evolution of color dipoles.…
We propose a modified Balitsky-Fadin-Kuraev-Lipatov equation from the viewpoint of the resummation technique, which contains an intrinsic dependence on momentum transfer Q, and satisfies the unitarity bound. The idea is to relax the strong…
We construct a generalization of the JIMWLK Hamiltonian, going beyond the eikonal approximation, which governs the high-energy evolution of the scattering between a dilute projectile and a dense target with an arbitrary longitudinal extent…
A variant of the abstract Cauchy-Kovalevskaya theorem is considered. We prove existence and uniqueness of classical solutions to the nonlinear, non-autonomous initial value problem \[ \frac{du(t)}{dt} = A(t)u(t) + B(u(t),t), \ \ u(0) = x \]…
The Balitskii-Fadin-Kuraev-Lipatov (BFKL) and the Gribov-Lipatov- Dokshitzer-Altarelli-Parisi (GLDAP) evolution equations for the diffractive deep inelastic scattering at ${1\over x} \gg 1$ are shown to have a common solution in the weak…
We propose a modified Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation for the summation of large $\ln(1/x)$, $x$ being the Bjorken variable, which contains an extra dependence on momentum transfer $Q$ compared to the conventional BFKL…
A computer study is performed to estimate the influence of the small-$k_T$ region in the BFKL evolution equation. We consider the small-x region of the deep inelastic structure function $F_2$ and show that the magnitude of the small-$k_T$…
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 find approximate solutions to the renormalization group equation which governs the quantum evolution of the effective theory for the Color Glass Condensate. This is a functional Fokker-Planck equation which generates in particular the…
We study the energy dependence of the total and diffractive neutrino-nucleon and neutrino-nucleus cross sections at very high energies. The calculation employs the QCD dipole model and the small-$x$ nonlinear Balitsky-Kovchegov evolution.…
We establish H\"older regularity for the weak solution to a degenerate diffusion equation in the presence of a local (drift) potential and nonlocal (interaction) term, posed in a bounded domain with no-flux boundary conditions. The…
Extending independently the Balitsky-Kovchegov (BK) equation to running coupling or to fluctuation effects due to Pomeron loops is known to lead in both cases to qualitative changes of the traveling-wave asymptotic solutions. In this paper…
Density perturbations and their dynamic evolution from early to late times can be used for an improved understanding of interesting physical phenomena both in cosmology and in the context of heavy-ion collisions. We discuss the spectrum and…
The ultrahigh energy neutrino-nucleon cross sections are computed taking into account different phenomenological implementations of the non-linear QCD dynamic s. Based on the color dipole framework, the results for the saturation model…
A main feature of high-energy scattering in QCD is saturation in the number density of gluons. This phenomenon is described by non-linear evolution equations, JIMWLK and BK, which have been derived at leading logarithmic accuracy. In this…
Saturation and geometrical scaling (GS) of gluon distributions are a consequence of the non-linear evolution equations of QCD. We argue that in pp GS holds for the inelastic cross-section rather than for the multiplicity distributions. We…
A new type of approximate scaling compatible with the Balitsky-Kovchegov equation with running coupling is found, which is different from the previously known running coupling geometric scaling. The corresponding asymptotic traveling wave…
In this paper we solve the equations that describe nucleus nucleus scattering, in high density QCD,in the framework of the BFKL Pomeron calculus. We found that (i) the contribution of short distances to the opacity for nucleus-nucleus…
We show that the GBW saturation model provides an exact solution to the one dimensional linear transport equation. We also show that it is motivated by the BK equation considered in the saturated regime when the diffusion and the splitting…
We present a model based on the concept of saturation for small $Q^2$ and small $x$. With only three parameters we achieve a good description of all Deep Inelastic Scattering data below $x=0.01$. This includes a consistent treatment of…