On the inclusive gluon jet production from the triple pomeron vertex in the perturbative QCD

Single and double inclusive cross-sections for gluon jet production from within the triple pomeron vertex are studied in the reggeized gluon technique. It is shown that to satisfy the AGK rules the vertex has to be fully symmetric in all four reggeized gluons which form the two final pomerons. The single inclusive cross-sections are found for different cuttings of the triple pomeron vertex. They sum into the expression obtained by Yu.Kovchegov and K.Tuchin in the colour dipole picture. The found double inclusive cross-sections satisfy the AGK rules.Comment: 17 pages in LaTex, 6 figures, revised version with partially changed rsult

Saturation and parton level Cronin effect: enhancement vs suppression of gluon production in p-A and A-A collisions

We note that the phenomenon of perturbative saturation leads to transverse momentum broadening in the spectrum of partons produced in hadronic collisions. This broadening has a simple interpretation as parton level Cronin effect for systems in which saturation is generated by the "tree level" Glauber-Mueller mechanism. For systems where the broadening results form the nonlinear QCD evolution to high energy, the presence or absence of Cronin effect depends crucially on the quantitative behavior of the gluon distribution functions at transverse momenta kt outside the so called scaling window. We discuss the relation of this phenomenon to the recent analysis by Kharzeev-Levin-McLerran of the momentum and centrality dependence of particle production in nucleus-nucleus collisions at RHIC.Comment: 22 pages LaTex, 7 eps-figures, discussion of evolved gluon distribution revised significantl

Cronin Effect and High-p_T Suppression in pA Collisions

We review the predictions of the theory of Color Glass Condensate for gluon production cross section in p(d)A collisions. We demonstrate that at moderate energies, when the gluon production cross section can be calculated in the framework of McLerran-Venugopalan model, it has only partonic level Cronin effect in it. At higher energies/rapidities corresponding to smaller values of Bjorken x quantum evolution becomes important. The effect of quantum evolution at higher energies/rapidities is to introduce suppression of high-p_T gluons slightly decreasing the Cronin enhancement. At still higher energies/rapidities quantum evolution leads to suppression of produced gluons at all values of p_T.Comment: 32 pages, 8 figures, v2: extended and improved discussion, references adde

The Reggeon →\to 2 Reggeons ++ Particle vertex in the Lipatov effective action formalism

The vertex for gluon emission during the splitting of a reggeized gluon into two is constructed in the framework of Lipatov effective action formalism. Its reduction to a pure transverse form for the diffractive amplitude gives the standard Bartels vertex plus an additional contribution corresponding to the emission from a pointlike splitting vertex. This additional contribution turns out to be given by a longitudinal integral divergent both in the ultraviolet and infrared. A certain specific recipe for this part, including the principal value prescription for the integration, allows to eliminate this unwanted contribution.Comment: 4 figures; misprints corrected; to be published in Eur.Phys.J.

Traveling wave fronts and the transition to saturation

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 identical to the formation of the front of a traveling wave. Within this physical picture, we provide the expressions for the saturation scale and the gluon density profile as a function of the total rapidity and the transverse momentum. The application to the Balitsky-Kovchegov equation for both fixed and running coupling constants confirms the effectiveness of this method.Comment: 9 pages, 3 figures, references adde

Saturation Physics in Ultra High Energy Cosmic Rays: Heavy Quark Production

In this work we estimate the heavy quark production in the interaction of ultra high energy cosmic rays in the atmosphere, considering that the primary cosmic ray is a proton or a photon. At these energies the saturation momentum Q_{sat}^2 stays above the hard scale \mu_c^2=4m_c^2, implying charm production probing the saturation regime. In particular, we show that the ep HERA data presents a scaling on \tau_c = (Q^2+\mu_c^2)/Q_{sat}^2. We derive our results considering the dipole picture and the Color Glass Condensate formalism, which one shows to be able to describe the heavy quark production in photon-proton and proton-proton collisions. Nuclear effects are considered in computation of cross sections for scattering on air nuclei. Implications on the flux of prompt leptons at the earth are analyzed and a large suppression is predicted.Comment: 18 pages, 10 figures, 2 tables. Version to be published in JHE

The gluon field of a fast moving nucleus and the effective langrangian for QCD at high energy

Starting from the effective lagrangian for QCD at high energy we calculate the lowest perturbative contributions to the potential of a relativistic nucleus and compare our results to those derived by Kovchegov (see Y.V. Kovchegov, Phys. Rev. {\bf D55}, 5445 (1997)). The results differ already at order g^3 which can be traced to the fact that the meaning of the underlying gluon fields is different. (The effective gluon field we use is a gauge invariant object.) Both approaches should therefore be seen as alternatives, the relative merits of which have to be judged by their phenomenological success.Comment: 13 pages, 4 figures. v2: eq. 18 corrected, modified discussion of the relation between the standard and the effective lagrangian approac

Wilson line correlator in the MV model: relating the glasma to deep inelastic scattering

In the color glass condensate framework the saturation scale measured in deep inelastic scattering of high energy hadrons and nuclei can be determined from the correlator of Wilson lines in the hadron wavefunction. These same Wilson lines give the initial condition of the classical field computation of the initial gluon multiplicity and energy density in a heavy ion collision. In this paper the Wilson line correlator in both adjoint and fundamental representations is computed using exactly the same numerical procedure that has been used to calculate gluon production in a heavy ion collision. In particular the discretization of the longitudinal coordinate has a large numerical effect on the relation between the color charge density parameter g^2 mu and the saturation scale Qs. Our result for this relation is Qs = 0.6 g^2 mu, which results in the classical Yang-Mills value for the "gluon liberation coefficient" c = 1.1.Comment: 8 pages, 10 figures, RevTEX4, V2: typo corrections, V3: small clarifications, to be published in EPJ

Non-linear QCD dynamics and exclusive production in epep collisions

The exclusive processes in electron-proton ($ep$) interactions are an important tool to investigate the QCD dynamics at high energies as they are in general driven by the gluon content of proton which is strongly subject to parton saturation effects. In this paper we compute the cross sections for the exclusive vector meson production as well as the deeply virtual Compton scattering (DVCS) relying on the color dipole approach and considering the numerical solution of the Balitsky-Kovchegov equation including running coupling corrections. We show that the small-$x$ evolution given by this evolution equation is able to describe the DESY-HERA data and is relevant for the physics of the exclusive observables in future electron-proton colliders and in photoproduction processes to be measured in coherent interactions at the LHC.Comment: 6 pages, 4 figure

Dynamics of Quark-Gluon-Plasma Instabilities in Discretized Hard-Loop Approximation

Non-Abelian plasma instabilities have been proposed as a possible explanation for fast isotropization of the quark-gluon plasma produced in relativistic heavy-ion collisions. We study the real-time evolution of these instabilities in non-Abelian plasmas with a momentum-space anisotropy using a hard-loop effective theory that is discretized in the velocities of hard particles. We extend our previous results on the evolution of the most unstable modes, which are constant in directions transverse to the direction of anisotropy, from gauge group SU(2) to SU(3). We also present first full 3+1-dimensional simulation results based on velocity-discretized hard loops. In contrast to the effectively 1+1-dimensional transversely constant modes we find subexponential behaviour at late times.Comment: 30 pages, 16 figures. v3 typos fixe