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

Thermodynamics of the high-temperature quark-gluon plasma

We review the various methods which have been employed recently to describe the thermodynamics of the high temperature quark-gluon plasma using weak coupling techniques, and we compare their results with those of most recent lattice gauge calculations. Many of the difficulties encountered with perturbation theory at finite temperature are in fact not specific to QCD but are present in any field theory at finite temperature and will be discussed first in the simple example of the scalar field theory. We discuss the merits and limitations of various techniques which have been used to go beyond perturbation theory in the soft sector, such as dimensional reduction, screened perturbation theory or hard-thermal-loop perturbation theory, and Phi-derivable approximations. In the last part of the review, we focus on the later, which lead to a remarkably simple expression for the entropy of the quark-gluon plasma. When complemented with further, physically motivated, approximations, this approach reproduces accurately the entropy obtained from lattice gauge calculations at temperatures above 2.5 T_c, where T_c is the deconfinement temperature. This calculation thus provides also support to the physical picture of the quark-gluon plasma as a gas of weakly interacting quasiparticles.Comment: Review for "Quark-Gluon Plasma 3", eds. R.C. Hwa and X.-N. Wang, World Scientific, Singapore. 63 pages, 21 figures. v2: minor corrections and 2 references adde

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.

Next-to-leading order static gluon self-energy for anisotropic plasmas

In this paper the structure of the next-to-leading (NLO) static gluon self energy for an anisotropic plasma is investigated in the limit of a small momentum space anisotropy. Using the Ward identities for the static hard-loop (HL) gluon polarization tensor and the (nontrivial) static HL vertices, we derive a comparatively compact form for the complete NLO correction to the structure function containing the space-like pole associated with magnetic instabilities. On the basis of a calculation without HL vertices, it has been conjectured that the imaginary part of this structure function is nonzero, rendering the space-like poles integrable. We show that there are both positive and negative contributions when HL vertices are included, highlighting the necessity of a complete numerical evaluation, for which the present work provides the basis.Comment: 9 pages, 2 figure

The dynamics of cosmological perturbations in thermal λϕ4\lambda\phi^4 theory

Using a recent thermal-field-theory approach to cosmological perturbations, the exact solutions that were found for collisionless ultrarelativistic matter are generalized to include the effects from weak self-interactions in a $\lambda\phi^4$ model through order $\lambda^{3/2}$. This includes the effects of a resummation of thermal masses and associated nonlocal gravitational vertices, thus going far beyond classical kinetic theory. Explicit solutions for all the scalar, vector, and tensor modes are obtained for a radiation-dominated Einstein-de Sitter model containing a weakly interacting scalar plasma with or without the admixture of an independent component of perfect radiation fluid.Comment: 32 pages, REVTEX, 13 postscript figures included by epsf.st