Medium-induced gluon radiation and jet quenching in heavy ion collisions

In this brief review, I summarize the new developments on the description of gluon radiation by energetic quarks traversing a medium as well as the observable consequences in high-energy heavy ion collisions. Information about the initial state is essential for a reliable interpretation of the experimental results and will also be reviewed. Comparison with experimental data from RHIC and expectation for the future LHC will be given.Comment: 16 pages, 9 postscript figures. Invited brief review for Modern Physics Letters

Calculating Quenching Weights

We calculate the probability (``quenching weight'') that a hard parton radiates an additional energy fraction due to scattering in spatially extended QCD matter. This study is based on an exact treatment of finite in-medium path length, it includes the case of a dynamically expanding medium, and it extends to the angular dependence of the medium-induced gluon radiation pattern. All calculations are done in the multiple soft scattering approximation (Baier-Dokshitzer-Mueller-Peign\'e-Schiff--Zakharov ``BDMPS-Z''-formalism) and in the single hard scattering approximation (N=1 opacity approximation). By comparison, we establish a simple relation between transport coefficient, Debye screening mass and opacity, for which both approximations lead to comparable results. Together with this paper, a CPU-inexpensive numerical subroutine for calculating quenching weights is provided electronically. To illustrate its applications, we discuss the suppression of hadronic transverse momentum spectra in nucleus-nucleus collisions. Remarkably, the kinematic constraint resulting from finite in-medium path length reduces significantly the transverse momentum dependence of the nuclear modification factor, thus leading to consistency with the data measured at the Relativistic Heavy Ion Collider (RHIC).Comment: 45 pages LaTeX, 20 eps-figure

Medium dependence of multiplicity distributions in MLLA

We study the modification of the multiplicity distributions in MLLA due to the presence of a QCD medium. The medium is introduced though a multiplicative constant ($f_{med}$) in the soft infrared parts of the kernels of QCD evolution equations. Using the asymptotic ansatz for quark and gluons mean multiplicities $=e^{\gamma y}$ and $=r^{-1}e^{\gamma y}$ respectively, we study two cases: fixed $\gamma$ as previously considered in the literature, and fixed $\alpha_s$. We find opposite behaviors of the dispersion of the multiplicity distributions with increasing $f_{med}$ in both cases. For fixed $\gamma$ the dispersion decreases, while for fixed $\alpha_s$ it increases.Comment: LaTeX, 9 pages, 4 eps figures; proceedings of the 3rd International Conference on Hard and Electromagnetic Probes in High-Energy Nuclear Collisions - Hard Probes 2008 (Illa de A Toxa, Spain, June 8th-14th 2008

Implementation of a medium-modified parton shower algorithm

We present a Monte Carlo implementation of medium-induced gluon radiation in the final-state branching process. Medium effects are introduced through an additive term in the splitting functions. We have implemented such modification within PYTHIA. We show the medium effects on the hump-backed plateau, and the transverse momentum and angular distributions with respect to the parent parton. As expected, with increasing medium densities there is an increase (decrease) of partons with small (large) momentum fraction, and angular broadening is observed. The effects on the transverse-momentum distributions are more involved, with an enhancement of low- and intermediate-$p_T$ partons and a decrease at large $p_T$, which is related to energy conservation, and to the lack of momentum exchange with the medium in our approach.Comment: LaTeX, 6 pages, 2 eps figures; proceedings of the 3rd International Conference on Hard and Electromagnetic Probes in High-Energy Nuclear Collisions - Hard Probes 2008 (Illa de A Toxa, Spain, June 8th-14th 2008

Angular-ordered parton showers with medium-modified splitting functions

Modified Altarelli-Parisi splitting functions were recenty proposed to model multi-parton radiation in a dense medium and describe jet quenching, one of most striking features of heavy-ion collisions. We implement medium-modified splitting functions in the HERWIG parton shower algorithm, which satisfies the angular ordering prescription, and present a few parton-level results, such as transverse momentum, angle and energy-fraction distributions, which exhibit remarkable medium-induced effects. We also comment on the comparison with respect to the results yielded by other implementations of medium-modified splitting functions in the framework of virtuality-ordered parton cascades.Comment: 19 pages, 8 figures, 1 table. Minor changes after referee repor

Medium-evolved fragmentation functions

Medium-induced gluon radiation is usually identified as the dominant dynamical mechanism underling the {\it jet quenching} phenomenon observed in heavy-ion collisions. In its actual implementation, multiple medium-induced gluon emissions are assumed to be independent, leading, in the eikonal approximation, to a Poisson distribution. Here, we introduce a medium term in the splitting probabilities so that both medium and vacuum contributions are included on the same footing in a DGLAP approach. The improvements include energy-momentum conservation at each individual splitting, medium-modified virtuality evolution and a coherent implementation of vacuum and medium splitting probabilities. Noticeably, the usual formalism is recovered when the virtuality and the energy of the parton are very large. This leads to a similar description of the suppression observed in heavy-ion collisions with values of the transport coefficient of the same order as those obtained using the {\it quenching weights}.Comment: LaTeX, 18 pages, 13 figures included using epsfig, uses JHEP3; v2: enlarged discussions, one figure replaced, some references added, final versio

Time singularities of correlators from Dirichlet conditions in AdS/CFT

Within AdS/CFT, we establish a general procedure for obtaining the leading singularity of two-point correlators involving operator insertions at different times. The procedure obtained is applied to operators dual to a scalar field which satisfies Dirichlet boundary conditions on an arbitrary time-like surface in the bulk. We determine how the Dirichlet boundary conditions influence the singularity structure of the field theory correlation functions. New singularities appear at boundary points connected by null geodesics bouncing between the Dirichlet surface and the boundary. We propose that their appearance can be interpreted as due to a non-local double trace deformation of the dual field theory, in which the two insertions of the operator are separated in time. The procedure developed in this paper provides a technical tool which may prove useful in view of describing holographic thermalization using gravitational collapse in AdS space.Comment: 30 pages, 3 figures. Version as in JHE