Related papers: Infrared instability from nonlinear QCD evolution
The perturbative QCD predicts that the growth of the gluon density at small-$x$ (high energies) should saturate, forming a Color Glass Condensate (CGC), which is described in mean field approximation by the Balitsky-Kovchegov (BK) equation.…
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…
The Balitsky-Fadin-Kuraev-Lipatov (BFKL) evolution equation is known to be ``unstable'' with respect to fluctuations in gluon virtuality, transverse momentum and energy requiring to go beyond the leading order BFKL. Still, these…
The BFKL pomeron in perturbative QCD is plagued by the lack of unitarity and diffusion into the infra-red region of gluon virtualities. These two problems are intimately related. We perform numerical studies of the evolution equation…
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…
Considering the Balitsky-Kovchegov QCD evolution equation in full momentum space, we derive the travelling wave solutions expressing the nonlinear saturation constraints on the dipole scattering amplitude at non-zero momentum transfer. A…
After a brief introduction to Deep Inelastic Scattering in the Bjorken limit and in the Regge Limit we discuss the operator product expansion in terms of non local string operator and in terms of Wilson lines. We will show how the…
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…
We investigate Kolmogorov wave turbulence in QCD or, in other words, we calculate the spectrum of gluons as a function of time, f_k(t), in the presence of a source which feeds in energy density in the infrared region at a constant rate. 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…
The number of gluons in the hadron wave function is discrete, and their formation in the chain of small $x$ evolution occurs over discrete rapidity intervals of $\Delta y \simeq 1/\as$. We therefore consider the evolution as a discrete…
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…
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…
We derive the asymptotic traveling-wave solutions of the nonlinear 1-dimensional Balitsky-Kovchegov QCD equation for rapidity evolution in momentum-space, with 1-loop running coupling constant and equipped with the…
Using consistent truncations of the BFKL kernel, we derive analytical traveling-wave solutions of the Balitsky-Kovchegov saturation equation for both fixed and running coupling. A universal parametrization of the ``interior'' of the wave…
We consider the perturbative description of saturation based on the nonlinear QCD evolution equation of Balitsky and Kovchegov (BK). Although the nonlinear corrections lead to saturation of the scattering amplitude locally in impact…
The dynamics of the modulation instability induced by cross phase modulation is studied by considering the influence of the walk-off and noninstantaneous response effects for two copropagating optical fields travelling in the anomalous…
We establish exactly and uniquely the infrared structure of the full gluon propagator in QCD, not solving explicitly the corresponding dynamical equation of motion. By construction, this structure is an infinite sum over all possible severe…
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…
The perturbative non-linear (NL) effects in the small-$x$ evolution of the gluon densities depend crucially on the infrared (IR) regularization. The IR regulator, $R_c$, is determined by the scale of the non-perturbative fluctuations of QCD…