2003/03/31 by Jean-Paul Blaizot, J. -P. Blaizot, Edmond Iancu +3 · 5 citations
Mathematics · Physics and Astronomy · #Combinatorics #Coupling constant #High-Energy Particle Collisions Research #Inverse #Lattice (music) #Lattice QCD #Logarithm #Loop (graph theory) #Mathematical analysis #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Perturbation theory (quantum mechanics) #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum electrodynamics #Quantum mechanics #Rate of convergence #Renormalization #Renormalization group #Statistical physics #hep-ph
paper · pdf · doi:10.1103/physrevd.68.025011
published as Phys.Rev. D68 (2003) 025011 · v2: 18 pages, 8 figures, REVTEX4, 2 additional subsections discussing the effect of 4-loop logarithms; v3: references updated, minor additions and a new paragraph in sect. IIIC
arxiv created 2003/05/13 · openalex publication_date 2003/07/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The successive perturbative estimates of the pressure of QCD at high temperature T show no sign of convergence, unless the coupling constant g is unrealistically small. Exploiting known results of an effective field theory which separates hard (order 2\ensuremathπT) and soft (order gT) contributions, we explore the accuracy of simple resummations which at a given loop order systematically treat hard contributions strictly perturbatively, but soft contributions without truncations. This turns out to improve significantly the two-loop and the three-loop results in that both remain below the ideal-gas value, and the degree of renormalization scale dependence decreases as one goes from two to three loop order, whereas it increases in the conventional perturbative results. Including the four-loop logarithms recently obtained by Kajantie et al., we find that this trend continues and that with a particular sublogarithmic constant the untruncated four-loop result is close to the three-loop result, which itself agrees well with available lattice results down to temperatures of about 2.5Tc. We also investigate the possibility of optimization by using a variational (``screened'') perturbation theory in the effective theory. At two loops, this gives a result below the ideal gas value and also closer to lattice results than the recent two-loop hard-thermal-loop-screened result of Andersen et al. While at three-loop order the gap equation of dimensionally reduced screened perturbation theory does not have a solution in QCD, this is remedied upon inclusion of the four-loop logarithms.