Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 4, Pages -Publisher
SPRINGER
DOI: 10.1088/1126-6708/2007/04/094
Keywords
NLO computations; thermal field theory
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Inspired by the corresponding problem in QCD, we determine the pressure of massless O(N) scalar field theory up to order g(6) in the weak-coupling expansion, where g(2) denotes the quartic coupling constant. This necessitates the computation of all 4-loop vacuum graphs at a finite temperature: by making use of methods developed by Arnold and Zhai at 3-loop level, we demonstrate that this task is manageable at least if one restricts to computing the logarithmic terms analytically, while handling the constant 4-loop contributions numerically. We also inspect the numerical convergence of the weak-coupling expansion after the inclusion of the new terms. Finally, we point out that while the present computation introduces strategies that should be helpful for the full 4-loop computation on the QCD-side, it also highlights the need to develop novel computational techniques, in order to be able to complete this formidable task in a systematic fashion.
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