An influence functional for ultrasoft QCD

A real-time path integral for ultrasoft QCD is formulated. It exhibits a Feynman's influence functional. The statistical properties of the theory and the gauge symmetry are explicit. The correspondence is established with the alternative version, where a noise term enters a transport equation.Comment: 6 pages, no figure Strong Electroweak Matter (SEWM 2002), Heidelberg, 2-5 october 200

Anomalous Gluon Production and Condensation in Glasma

The collinear color electric and magnetic fields have been discussed to be produced immediately after high energy heavy ion collisions. We discuss anomalous gluon production under the background gauge fields. The gluons are Nielsen-Olesen unstable modes. The production rate of the modes by Schwinger mechanism has recently been found to be anomalously larger than the rate of quarks or other stable gluons. Analyzing classical evolutions of the modes with initial conditions given by vacuum fluctuations, we find that their production makes the color electric field decay very rapidly. The life time of the field is approximately given by the inverse of saturation momentum in the collisions. We also show that the mode with zero momentum form a Bose condensate and its gluon number density grows up to be of the order of $1/\alpha_g$. After the saturation of the gluon number density, the condensate melts into quark gluon plasma owing to nonlinear interactions in QCD.Comment: 9 pages, 2figures To be published in Phys. Rev.

JIMWLK evolution for multi-particle production with rapidity correlations

We study multi-particle production with rapidity correlations in proton-nucleus collisions at high energy in the Color Glass Condensate framework. The high-energy evolution responsible for such correlations is governed by a generalization of the JIMWLK equation describing the simultaneous evolution of the strong nuclear color fields in the direct amplitude and the complex conjugate amplitude. This functional equation can be used to derive ordinary evolution equations for the cross-sections for particle production, but the ensuing equations appear to be too complicated to be useful in practice, including in the limit of a large number of colors Nc. We propose an alternative formulation based on a Langevin process, which is valid for generic Nc and is better suited for numerical implementations. For illustration, we present the stochastic equations which govern two gluon production with arbitrary rapidity separation.Comment: 8 pages, 6 figures, based on talk given at IS 2013, 8 - 14 Sep 2013, Illa da Toxa, Spai

A zero-dimensional model for high-energy scattering in QCD

We investigate a zero-dimensional toy model originally introduced by Mueller and Salam which mimics high-energy scattering in QCD in the presence of both gluon saturation and gluon number fluctuations, and hence of Pomeron loops. Unlike other toy models of the reaction-diffusion type, the model studied in this paper is consistent with boost invariance and, related to that, it exhibits a mechanism for particle saturation close to that of the JIMWLK equation in QCD, namely the saturation of the emission rate due to high-density effects. Within this model, we establish the dominant high-energy behaviour of the S-matrix element for the scattering between a target obtained by evolving one particle and a projectile made with exactly n particles. Remarkably, we find that all such matrix elements approach the black disk limit S=0 at high rapidity Y, with the same exponential law: ~ exp(-Y) for all values of n. This is so because the S-matrix is dominated by rare target configurations which involve only few particles. We also find that the bulk distribution for a saturated system is of the Poisson type.Comment: 34 pages, 9 figures. Some explanations added on the frame-dependence of the relevant configurations (new section 3.3

Universality of the saturation scale and the initial eccentricity in heavy ion collisions

Recent estimates that Color Glass Condensate initial conditions may generate a larger initial eccentricity for noncentral relativistic heavy ion collisions (relative to the initial eccentricity assumed in earlier hydrodynamic calculations) have raised the possibility of a higher bound on the viscosity of the Quark Gluon Plasma. We show that this large initial eccentricity results in part from a definition of the saturation scale as proportional to the number of nucleons participating in the collision. A saturation scale proportional to the nuclear thickness function (and therefore independent of the probe) leads to a smaller eccentricity, albeit still larger than the value used in hydrodynamic models. Our results suggest that the early elliptic flow in heavy ion collisions (unlike multiplicity distributions) is sensitive to the universality of the saturation scale in high energy QCD.Comment: 5 pages, 3 figures, RevTE

From target to projectile and back again: selfduality of high energy evolution

We prove that the complete kernel for the high energy evolution in QCD must be selfdual. The relevant duality transformation is formulated in precise mathematical terms and is shown to transform the charge density into the functional derivative with respect to the single-gluon scattering matrix. This transformation interchanges the high and the low density regimes. We demostrate that the original JIMWLK kernel, valid at large density is indeed dual to the low denisity limit of the complete kernel derived recently in hep-ph/0501198.Comment: 4 pages. References and comments added. To appear in PR

Interference Phenomena in Medium Induced Radiation

We consider the interference pattern for the medium-induced gluon radiation produced by a color singlet quark-antiquark antenna embedded in a QCD medium with size $L$ and `jet quenching' parameter $\hat q$. Within the BDMPS-Z regime, we demonstrate that, for a dipole opening angle $\theta_{q\bar q} \gg\theta_c\equiv {2}/{\sqrt{\hat q L^3}}$, the interference between the medium--induced gluon emissions by the quark and the antiquark is suppressed with respect to the direct emissions. This is so since direct emissions are delocalized throughout the medium and thus yield contributions proportional to $L$ while interference occurs only between emissions at early times, when both sources remain coherent. Thus, for \tqq \gg\theta_c, the medium-induced radiation is the sum of the two spectra individually produced by the quark and the antiquark, without coherence effects like angular ordering. For \tqq \ll\theta_c, the medium--induced radiation vanishes.Comment: 4 pages, 2 figures; Proceedings of the "Quark Matter 2011" conferenc