The medium-induced p ⊥ -broadening and induced gluon radiation spectrum of a high energy quark or gluon traversing a large nucleus is studied. Multiple scattering of the high energy parton in the nucleus is treated in the Glauber approximation. We show that −dE/dz, the radiative energy loss of the parton per unit length, grows as L, the length of the nuclear matter, as does the characteristic transverse momentum squared of the parton p 2 ⊥W . We find −dE/dz = 1 8 α s N c p 2 ⊥W holds independent of the details of the parton-nucleon scatterings so long as L is large. Numerical estimates suggest that p ⊥ -broadening and energy loss may be significantly enhanced in hot matter as compared to cold matter, thus making the study of such quantities a possible signal for quark-gluon plasma formation.

The medium induced energy loss spectrum of a high energy quark or gluon traversing a hot QCD medium of finite volume is studied. We model the interaction by a simple picture of static scattering centres. The total induced energy loss is found to grow as L 2 , where L is the extent of the medium. The solution of the energy loss problem is reduced to the solution of a Schrödingerlike equation whose "potential" is given by the single-scattering cross section of the high energy parton in the medium. These results should be directly applicable to a quark-gluon plasma.

We describe how thermalization occurs in heavy ion collisions in the framework of perturbative QCD. When the saturation scale Q s is large compared to Λ QCD , thermalization takes place during a time of order α −13/5 Q −1 s and the maximal temperature achieved is α 2/5 Q s .

We review the properties of energetic parton propagation in hot or cold QCD matter, as obtained in recent works. Advances in understanding the energy loss -collisional and radiative -are summarized, with emphasis on the latter: it features very interesting properties which may help to detect the quark-gluon plasma produced in heavy ion collisions. We describe * preprint BI-TP 2000/08, LPT-Orsay 00-22 submitted to Annual Review of Nuclear and Particle Science two different theoretical approaches, which lead to the same radiated gluon energy spectrum.

Soft gluon radiation induced by multiple scattering of a fast quark or gluon propagating through QCD matter is discussed. After revisiting the Landau-Pomeranchuk-Migdal effect in QED we show that large formation times of bremsstrahlung quanta determine the QCD radiation intensity (in analogy to QED) and derive the gluon energy spectrum. Coherent suppression takes place as compared to the Bethe-Heitler situation of independent emissions. As a result the energy loss of fast partons in a QCD medium depends on the incident energy E similarly to QED, −dE/dz ∝ √ E. † Permanent address: Petersburg Nuclear Physics Institute,

We determine how the yield of large transverse momentum hadrons is modified due to induced gluon radiation off a hard parton traversing a QCD medium. The quenching factor is formally a collinear-and infrared-safe quantity and can be treated perturbatively. In spite of that, in the p ⊥ region of practical interest, its value turns out to be extremely sensitive to large distances and can be used to unravel the properties of dense quark-gluon final states produced in heavy ion collisions. We also find that the standard modelling of quenching by shifting p ⊥ in the hard parton cross section by the mean energy loss is inadequate.

We extend the BDMPS formalism for calculating radiative energy loss to the case when the radiated gluon carries a finite fraction of the quark momentum. Some virtual terms, previously overlooked, are now included. The equivalence between the formalism of BDMPS and that of B. Zakharov is explicitly demonstrated.

We study analytically the medium-induced energy loss of a high energy parton passing through a finite size QCD plasma, which is expanding longitudinally according to Bjorken's model. We extend the BDMPS formalism already applied to static media to the case of a quark which hits successive layers of matter of decreasing temperature, and we show that the resulting radiative * Permanent address: Petersburg Nuclear Physics Institute, Gatchina 188350, St. Petersburg, Russia † Supported in part by the U.S. Department of Energy under Grant DE-FG02-94ER-40819 ‡ Laboratoire associé du Centre National de la Recherche Scientifique 1 energy loss can be as large as 6 times the corresponding one in a static plasma at the reference temperature T = T (L), which is reached after the quark propagates a distance L.