Three-loop free energy for pure gauge QCD

We compute the free energy density for pure non-Abelian gauge theory at high temperature and zero chemical potential. The three-loop result to O(g⁴) is F=dA{T}⁴π²/9{-1/5+(gA/4{π})²-16/{}3(gA/4{π})³ -48(gA/4{π})⁴ln(gA/2{π}{}3) +(gA/4{π})⁴[22/3ln{μ}{}/4{π}T+38/3{ζ}'(-3)/{ζ}(-3) -148/3{ζ}'(-1)/{ζ}(-1)-4γE+64/5]+O(gA⁵)}, where T is the temperature, {ζ} is the Riemann zeta function, gA==g({μ}{})CA1/2, {μ}{} is the MS{} renormalization scale, g({μ}{}) is the corresponding coupling constant, and dA and CA are the dimension and Casimir number of the adjoint representation. We examine the sensitivity of this result to the choice of renormalization scale {μ}{}. We also give a result for the free energy of scalar φ⁴ theory, correcting a result previously given in the literature.