The pressure of deconfined QCD for all temperatures and quark chemical potentials

We present a new method for the evaluation of the perturbative expansion of the QCD pressure which is valid at all values of the temperature and quark chemical potentials in the deconfined phase and which we work out up to and including order g^4 accuracy. Our calculation is manifestly four-dimensional and purely diagrammatic -- and thus independent of any effective theory descriptions of high temperature or high density QCD. In various limits, we recover the known results of dimensional reduction and the HDL and HTL resummation schemes, as well as the equation of state of zero-temperature quark matter, thereby verifying their respective validity. To demonstrate the overlap of the various regimes, we furthermore show how the predictions of dimensional reduction and HDL resummed perturbation theory agree in the regime T~\sqrt{g}*mu. At parametrically smaller temperatures T~g*mu, we find that the dimensional reduction result agrees well with those of the nonstatic resummations down to the remarkably low value T~0.2 m_D, where m_D is the Debye mass at T=0. Beyond this, we see that only the latter methods connect smoothly to the T=0 result of Freedman and McLerran, to which the leading small-T corrections are given by the so-called non-Fermi-liquid terms, first obtained through HDL resummations. Finally, we outline the extension of our method to the next order, where it would include terms for the low-temperature entropy and specific heats that are unknown at present.Comment: 45 pages, 21 figures; v2: minor corrections and clarifications, references added; v3: Fig 16 added, version accepted for publication in PR

How Much do Heavy Quarks Thermalize in a Heavy Ion Collision?

We investigate the thermalization of charm quarks in high energy heavy ion collisions. To this end, we calculate the diffusion coefficient in the perturbative Quark Gluon Plasma and relate it to collisional energy loss and momentum broadening. We then use these transport properties to formulate a Langevin model for the evolution of the heavy quark spectrum in the hot medium. The model is strictly valid in the non-relativistic limit and for all velocities \gamma v < \alphas^{-1/2} to leading logarithm in $T/m_D$. The corresponding Fokker-Planck equation can be solved analytically for a Bjorken expansion and the solution gives a simple estimate for the medium modifications of the heavy quark spectrum as a function of the diffusion coefficient. Finally we solve the Langevin equations numerically in a hydrodynamic simulation of the heavy ion reaction. The results of this simulation are the medium modifications of the charm spectrum $R_{AA}$ and the expected elliptic flow $v_2(p_T)$ as a function of the diffusion coefficient.Comment: 34 pages, 9 figures. Inculdes a detailed comparison with Boltzmann simulation

Fermi spectra and their gauge invariance in hot and dense Abelian and non-Abelian theories

The one-loop Fermi spectra (one-particle and collective ones) are found for all momenta in the $T^2$-approximation and their gauge invariance in hot and dense Abelian and non-Abelian theories is studied. It is shown that the one-particle spectrum, if the calculation accuracy is kept strictly, is gauge invariant for all momenta and has two branches as the bare one. The collective spectrum always has four branches which are gauge dependent including also their |\q|=0 limit. The exception is the case $m,\mu=0$ for which this spectrum is gauge invariant for all momenta as well.Comment: 16 pages, latex, no figure

SELF-ENERGY PECULIARITIES OF THE HOT GAUGE THEORY AFTER SYMMETRY BREAKING

A tensor representation of the gluon propagator is found within covariant gauges for a non-Abelian theory after symmetry breaking due to $\ne 0$ and the exact equations which determine the dispersion laws of plasma excitations are explicitly obtained. In the high temperature region and fixing the Feynman gauge we solved these equations and found the damping of the plasma oscillations and the shifting of their frequency. The phase transition of a gauge symmetry restoration is estimated to be $\alpha_c(T) \approx{4/3}$.Comment: 13 pages, LaTex, No figure

Infrared Properties of the Hot Gauge Theory after Symmetry Breaking

It is shown that the fictitious infrared pole is eliminated from the hot gauge theory which acquires a new vacuum after the global gauge symmetry spontaneously breaking. The nonzero W-condensate is generated and leads to the screening of the chromomagnetic forces through the scenario with the standard magnetic mass.Comment: 12 pages, LaTeX, Yukawa Institute Preprint YITP/K-1071 (April 1994