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

Abstract

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.

45 pages, 21 figures; v2: minor corrections and clarifications, references added; v3: Fig 16 added, version accepted for publication in PRD

References in corpus (1)

• The pressure of QCD at finite temperature and quark number density

Cited by in corpus (21)

• Color superconductivity in dense quark matter
• Soft interactions in cold quark matter
• The strongly interacting Quark Gluon Plasma, and the critical behaviour of QCD at imaginary chemical potential
• Cold quark matter at N3LO: soft contributions
• The leading non-perturbative coefficient in the weak-coupling expansion of hot QCD pressure
• Pion and Kaon Condensation at Finite Temperature and Density
• Quark magnetar in three-flavor Nambu--Jona-Lasinio model with vector interaction and magnetized gluon potential
• Equation of State of Cold Quark Matter to $O({\alpha }_s^3\ln {\alpha }_s)$
• Quark number susceptibilities from resummed perturbation theory
• Hard Thermal Loop -- theory and applications
• Soft gluon self-energy at finite temperature and density: hard NLO corrections in general covariant gauge
• QCD mesonic screening masses using Gribov quantization
• Three loop HTL perturbation theory at finite temperature and chemical potential
• The pressure of deconfined QCD for all temperatures and quark chemical potentials
• Fermi-liquid theory of imbalanced quark matter
• High temperature phase of QCD
• Cold Quark Matter: Renormalization Group Improvement at next-to-next-to leading order
• Method for comparing finite temperature field theory results with lattice data
• Phase diagram at finite temperature and quark density in the strong coupling region of lattice QCD for color SU(3)
• High order quark number susceptibilities in hot QCD from lattice EQCD
• A massive high density effective theory