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 study BFKL evolution and, in particular, the energy dependence of the saturation momentum in the presence of saturation boundaries limiting the region of linear BFKL evolution. In the case of fixed coupling evolution we confirm the previously found exponential term in Q s (Y ) and determine the prefactor Y and α dependences. In the running coupling case we find Y 1/6 corrections to the Y 1/2 exponential behavior previously known. Geometrical scaling of the scattering amplitude is valid in a wide range of momenta for fixed coupling evolution and in a more restricted region for running coupling evolution.

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.

The calculation of the radiative energy loss encountered by a fast charged particle which undergoes multiple scattering is being investigated. A detailed derivation of the Landau-Pomeranchuk-Migdal coherent effect in QED is given, focusing on the specific feature of the Coulomb interaction. As a result the radiation intensity per unit length in the coherent regime is shown to be proportional to $\sqrt \omega$ for a photon energy $\omega$ times a logarithmic enhancement which is determined exactly.Comment: 19 pages, LaTeX styl

This note is an addendum to [1,2]. In these papers we pointed out that charged-particle multiplicities measured in central heavy ion collisions at high energies may not directly be determined by the initial conditions as given by saturation models, but in addition by the way gluons are thermalized. This process may fill the gap between the multiplicities expected e.g. from saturation models with running coupling BK equation (rcBK) [3] and the ones measured by the ALICE Collaboration [4, 5] in central Pb-Pb collisions at √ s N N = 2.76TeV. We argue that this enhancement is evidence for a factor 1/α 2/5 s present in the weaklycoupled process of the "bottom-up" equilibration mechanism due to nonconservation of the number of gluons, i.e. due to entropy production.At RHIC and LHC energies in the central rapidity region of heavy ion collisions at high density energy is deposited mainly in the form of gluons. In saturation models (hereafter *