Three-loop free energy for pure gauge QCD

Journal Article · Thu Dec 15 04:00:00 EST 1994 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.50.7603· OSTI ID:6785275

Arnold, P; Zhai, C ^[1]

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1. Department of Physics, FM-15, University of Washington, Seattle, Washington 98195 (United States)

We compute the free energy density for pure non-Abelian gauge theory at high temperature and zero chemical potential. The three-loop result to [ital O]([ital g][sup 4]) is [ital F]=[ital d][sub [ital A]][ital T][sup 4][pi][sup 2]/9[l brace][minus]1/5+([ital g][sub [ital A]]/4[pi])[sup 2][minus]16/[radical]3([ital g][sub [ital A]]/4[pi])[sup 3] [minus]48([ital g][sub [ital A]]/4[pi])[sup 4]ln([ital g][sub [ital A]]/2[pi][radical]3) +([ital g][sub [ital A]]/4[pi])[sup 4][22/3ln[bar [mu]]/4[pi][ital T]+38/3[zeta][prime]([minus]3)/[zeta]([minus]3) [minus]148/3[zeta][prime]([minus]1)/[zeta]([minus]1)[minus]4[gamma][sub [ital E]]+64/5]+[ital O]([ital g][sub [ital A]][sup 5])[r brace], where [ital T] is the temperature, [zeta] is the Riemann zeta function, [ital g][sub [ital A]]==[ital g]([bar [mu]])[ital C][sub [ital A]][sup 1/2], [bar [mu]] is the M[bar S] renormalization scale, [ital g]([bar [mu]]) is the corresponding coupling constant, and [ital d][sub [ital A]] and [ital C][sub [ital A]] are the dimension and Casimir number of the adjoint representation. We examine the sensitivity of this result to the choice of renormalization scale [bar [mu]]. We also give a result for the free energy of scalar [phi][sup 4] theory, correcting a result previously given in the literature.

• DOE Contract Number: FG06-91ER40614
• OSTI ID: 6785275
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 50:12; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
662230 -- Quantum Chromodynamics-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CASIMIR OPERATORS
COUPLING CONSTANTS
ENERGY
ENERGY DENSITY
FIELD THEORIES
FREE ENERGY
MATHEMATICAL OPERATORS
PHI4-FIELD THEORY
PHYSICAL PROPERTIES
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
RENORMALIZATION
SENSITIVITY
THERMODYNAMIC PROPERTIES