[en] This talk is a brief overview of the present status of our understanding of nucleus-nucleus collisions at high energy and the search for signals of the quark-gluon plasma

[en] In this talk I discuss collective excitations that carry fermion quantum numbers. Such excitations occur in the quark–gluon plasma and can also be produced in cold atom systems under special conditions

[en] We study the radiative processes that affect the propagation of a high energy gluon in a dense medium, such as a quark–gluon plasma. In particular, we investigate the role of the large double logarithmic corrections, ∼α_sln²L/τ₀, that were recently identified in the study of p_⊥-broadening by Liou, Mueller and Wu. We show that these large corrections can be reabsorbed in a renormalization of the jet quenching parameter controlling both momentum broadening and energy loss. We argue that the probabilistic description of these phenomena remains valid, in spite of the large non-locality in time of the radiative corrections. The renormalized jet-quenching parameter is enhanced compared to its standard perturbative estimate. As a particular consequence, the radiative energy loss scales with medium size L as L^2+γ, with γ=2√(α_sN_c/π), as compared to the standard scaling in L²

[en] In this paper, we study the thermalization of gluons and N_f flavors of massless quarks and antiquarks in a spatially homogeneous system. First, two coupled transport equations for gluons and quarks (and antiquarks) are derived within the diffusion approximation of the Boltzmann equation, with only 2↔2 processes included in the collision term. Then, these transport equations are solved numerically in order to study the thermalization of the quark–gluon plasma. At initial time, we assume that only gluons are present and we choose the gluon distribution of a form inspired by the color glass picture, namely f=f₀θ(1−p/(Q_s) ) with Q_s the saturation momentum and f₀ a constant. The subsequent evolution of the system may, or may not, lead to the formation of a (transient) Bose condensate (BEC) of gluons, depending on the value of f₀. In fact, we observe, depending on the value of f₀, three different patterns: (a) thermalization without BEC for f₀≤f_0t, (b) thermalization with transient BEC for f_0t< f₀≤f_0c, and (c) thermalization with BEC for f_0c< f₀. The values of f_0t and f_0c depend on N_f. When f₀≳1>f_0c, the onset of BEC occurs at a finite time t_c∼1/((α_sf₀)²) 1/(Q_s) . We also find that quark production slows down the thermalization process: the equilibration time for N_f=3 is typically about 5 to 6 times longer than that for N_f=0 at the same Q_s and f₀

[en] We discuss the renormalizability of PHI-derivable approximations in scalar φ⁴ theory in four dimensions. The formalism leads to self-consistent equations for the 2-point and the 4-point functions which are plagued by ultraviolet divergences. Through a detailed analysis of the one and two-loop self-energy skeletons, we show that both equations can be renormalized simultaneously and determine the corresponding counterterms. These insure the elimination of ultraviolet divergences both at zero and finite temperature

[en] We explore and clarify the connections between two different forms of the renormalization group equations describing the quantum evolution of hadronic structure functions at small x. This connection is established via a Langevin formulation and associated path integral solutions that highlight the statistical nature of the quantum evolution, pictured here as a random walk in the space of Wilson lines. The results confirm known approximations, form the basis for numerical simulations and widen the scope for further analytical studies

[en] In the context of the recently derived probabilistic picture of in-medium jet evolution, we study radiative corrections which yield potentially large double logarithms, α_sln²⁡L, for large enough medium length L. We show that these large corrections are universal and can be reabsorbed in a renormalization of the jet quenching parameter controlling both momentum broadening and energy loss. We argue that the probabilistic description of these phenomena remains valid, in spite of the large non-locality in time of the radiative corrections. The renormalized jet-quenching parameter is enhanced compared to its standard perturbative estimate. As a particular consequence, the radiative energy loss scales with medium size L as L^2+γ, with γ=2√(α_sN_c/π), as compared to the standard scaling in L²

[en] I recall the difficulties of QCD thermal perturbation theory and how weak coupling techniques, which appropriate resummations, can nevertheless be used to obtain a good description of the thermodynamics of the quark-gluon plasma for temperature T≥3T_c. I also argue that for such temperatures, hot QCD does not look too close to the strong coupling regime of strongly coupled N=4 supersymmetric Yang-Mills theories. (author)

[en] We present a derivation of a Boltzmann equation for the QCD plasma, starting from the quantum field equations. The derivation is based on a gauge-covariant gradient expansion which takes consistently into account all possible dependences on the gauge coupling assumed to be small. We point out a limitation of the gradient expansion arising when the range of the interactions becomes comparable with that of the space-time inhomogeneities of the system. The method is first applied to the case of scalar electrodynamics, and then to the description of long wavelength colour fluctuations in the QCD plasma. In the latter case, we recover Boedecker's effective theory and its recent reformulation by Arnold, Son and Yaffe. We discuss interesting cancellations among various collision terms, which occur in the calculation of most transport coefficients, but not in that of the quasiparticle lifetime, or in that of the relaxation time of colour excitations

[en] I give a brief overview of recent theoretical developments concerning the high temperature phase of QCD and the structure of hadronic wavefunctions at high energy