Non Perturbative Renormalization Group, momentum dependence of nn-point functions and the transition temperature of the weakly interacting Bose gas

We propose a new approximation scheme to solve the Non Perturbative Renormalization Group equations and obtain the full momentum dependence of $n$-point functions. This scheme involves an iteration procedure built on an extension of the Local Potential Approximation commonly used within the Non Perturbative Renormalization Group. Perturbative and scaling regimes are accurately reproduced. The method is applied to the calculation of the shift $\Delta T_c$ in the transition temperature of the weakly repulsive Bose gas, a quantity which is very sensitive to all momenta intermediate between these two regions. The leading order result is in agreement with lattice calculations, albeit with a theoretical uncertainty of about 25%. The next-to-leading order differs by about 10% from the best accepted result

DCC: Attractive Idea Seeks Serious Confirmation

The theoretical ideas relevant for the physics of the disoriented chiral condensate (DCC) are reviewed.Comment: 18 pages LaTex, based on invited lecture given by A.Krzywicki at the workshop "Quark, plasma and beyond", Zif, Bielefeld, May 1996 ; a reference is correcte

Confinement, Turbulence and Diffraction Catastrophes

Many features of large N_c transition that occurs in the spectral density of Wilson loops as a function of loop area (observed recently in numerical simulations of Yang-Mills theory by Narayanan and Neuberger) can be captured by a simple Burgers equation used to model turbulence. Spectral shock waves that precede this asymptotic limit exhibit universal scaling with N_c, with indices that can be related to Berry indices for diffraction catastrophes.Comment: Presented at PANIC 200

Quark number susceptibilities from HTL-resummed thermodynamics

We compute analytically the diagonal quark number susceptibilities for a quark-gluon plasma at finite temperature and zero chemical potential, and compare with recent lattice results. The calculation uses the approximately self-consistent resummation of hard thermal and dense loops that we have developed previously. For temperatures between 1.5 to 5 $T_c$, our results follow the same trend as the lattice data, but exceed them in magnitude by about 5-10%. We also compute the lowest order contribution, of order $\alpha_s^3\log(1/\alpha_s)$, to the off-diagonal susceptibility. This contribution, which is not a part of our self-consistent calculation, is numerically small, but not small enough to be compatible with a recent lattice simulation.Comment: 13 pages, 5 figures, uses elsart.cls; v2: minor corrections; v3: sign in eq.(1) correcte

Comparing different hard-thermal-loop approaches to quark number susceptibilities

We compare our previously proposed hard-thermal-loop (HTL) resummed calculation of quark number susceptibilities using a self-consistent two-loop approximation to the quark density with a recent calculation of the same quantity at the one-loop level in a variant of HTL-screened perturbation theory. Besides pointing out conceptual problems with the latter approach, we show that it severely over-includes the leading-order interaction effects while including none of the plasmon term which after all is the reason to construct improved resummation schemes.Comment: 6 pages, 6 figures. Revised version to appear in Eur. J. Phys.

Proton-nucleus collisions in the color glass condensate framework

We discuss proton-nucleus collisions in the framework of the color glass condensate. By assuming that the proton can be described as a low density color source, we solve exactly the Yang-Mills equations corresponding to this type of collision, and then use this solution in order to calculate inclusive gluon production or quark-antiquark production. Our result shows that k_T-factorization, while valid for gluon production, is violated for quark pair production in proton-nucleus collisions.Comment: Talk given at SEWM2004, Helsinki, June 200

Non-Perturbative Renormalization Group calculation of the scalar self-energy

We present the first numerical application of a method that we have recently proposed to solve the Non Perturbative Renormalization Group equations and obtain the n-point functions for arbitrary external momenta. This method leads to flow equations for the n-point functions which are also differential equations with respect to a constant background field. This makes them, a priori, difficult to solve. However, we demonstrate in this paper that, within a simple approximation which turns out to be quite accurate, the solution of these flow equations is not more complicated than that of the flow equations obtained in the derivative expansion. Thus, with a numerical effort comparable to that involved in the derivative expansion, we can get the full momentum dependence of the n-point functions. The method is applied, in its leading order, to the calculation of the self-energy in a 3-dimensional scalar field theory, at criticality. Accurate results are obtained over the entire range of momenta.Comment: 29 page

The thermodynamics of the quark-gluon plasma: Self-consistent resummations vs. lattice data

We discuss a recent approach for overcoming the poor convergence of the perturbative expansion for the thermodynamic potential of QCD. This approach is based on self-consistent approximations which allow for a gauge-invariant and manifestly ultraviolet-finite resummation of the essential physics of the hard thermal/dense loops. The results thus obtained are in good agreement with available lattice data down to temperatures of about twice the critical temperature. Calculations for a plasma with finite quark density (i.e., with a non-zero chemical potential $\mu$) are no more difficult than at $\mu=0$.Comment: 4 pages LaTeX2e, contribution to the proceedings of the 15th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions (QM 2001), Long Island, New York, January 15 - 20, 200