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

Non-linear QCD evolution with improved triple-pomeron vertices

In a previous publication, we have constructed a set of non-linear evolution equations for dipole scattering amplitudes in QCD at high energy, which extends the Balitsky-JIMWLK hierarchy by including the effects of fluctuations in the gluon number in the target wavefunction. In doing so, we have relied on the color dipole picture, valid in the limit where the number of colors is large, and we have made some further approximations on the relation between scattering amplitudes and dipole densities, which amount to neglecting the non-locality of the two-gluon exchanges. In this Letter, we relax the latter approximations, and thus restore the correct structure of the `triple-pomeron vertex' which describes the splitting of one BFKL pomeron into two within the terms responsible for fluctuations. The ensuing triple-pomeron vertex coincides with the one previously derived by Braun and Vacca within perturbative QCD. The evolution equations can be recast in a Langevin form, but with a multivariable noise term with off-diagonal correlations. Our equations are shown to be equivalent with the modified version of the JIMWLK equation recently proposed by Mueller, Shoshi, and Wong.Comment: 15 page

Gluon Distributions and Color Charge Correlations in a Saturated Light-cone Wavefunction

We describe the light-cone wavefunction in the saturation regime in terms of the density of gluons per unit of transverse phase space, the occupation number, and in terms of the color charge correlator. The simple McLerran- Venugopalan model gives what are claimed to be general results for the phase space gluon density, but it does not well describe the general case for the charge correlator. We derive the general momentum dependence and rapidity dependence of the color charge correlator which exhibits strong color shielding. A simplel physical picture which leads to these general results is described.Comment: 17 pages, Latex, 7 figure

Di-jet asymmetry and wave turbulence

We describe a new physical picture for the fragmentation of an energetic jet propagating through a dense QCD medium, which emerges from perturbative QCD and has the potential to explain the di-jet asymmetry observed in Pb-Pb collisions at the LHC. The central ingredient in this picture is the phenomenon of wave turbulence, which provides a very efficient mechanism for the transport of energy towards the medium, via many soft particles which propagate at large angles with respect to the jet axis.Comment: 6 pages, 3 figures. Invited plenary talk at the 6th International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions (Hard Probes 2013), Stellenbosch, South Africa, Nov. 4-8, 201

The non-linear evolution of jet quenching

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 nucleus, or a slice of quark-gluon plasma). Different physical regimes refer to the ratio $L/\tau$ between the longitudinal size $L$ of the target and the lifetime $\tau$ of the gluon fluctuations. When $L/\tau \ll 1$, meaning that the target can be effectively treated as a shockwave, we recover the JIMWLK Hamiltonian, as expected. When $L/\tau \gg 1$, meaning that the fluctuations live inside the target, the new Hamiltonian governs phenomena like the transverse momentum broadening and the radiative energy loss, which accompany the propagation of an energetic parton through a dense QCD medium. Using this Hamiltonian, we derive a non-linear equation for the dipole amplitude (a generalization of the BK equation), which describes the high-energy evolution of jet quenching. As compared to the original BK-JIMWLK evolution, the new evolution is remarkably different: the plasma saturation momentum evolves much faster with increasing energy (or decreasing Bjorken's $x$) than the corresponding scale for a shockwave (nucleus). This widely opens the transverse phase-space for the evolution and implies the existence of large radiative corrections, enhanced by the double logarithm $\ln^2(LT)$, with $T$ the temperature of the medium. This confirms and explains from a physical perspective a recent result by Liou, Mueller, and Wu (arXiv:1304.7677). The dominant corrections are smooth enough to be absorbed into a renormalization of the jet quenching parameter $\hat q$. This renormalization is controlled by a linear equation supplemented with a saturation boundary, which emerges via controlled approximations from the generalized BK equation alluded to above.Comment: 54 pages plus 4 appendices, 6 figure