The pressure of hot QCD up to g^6 ln(1/g)

Abstract

The free energy density, or pressure, of QCD has at high temperatures an expansion in the coupling constant g, known so far up to order g^5. We compute here the last contribution which can be determined perturbatively, g^6 ln(1/g), by summing together results for the 4-loop vacuum energy densities of two different three-dimensional effective field theories. We also demonstrate that the inclusion of the new perturbative g^6 ln(1/g) terms, once they are summed together with the so far unknown perturbative and non-perturbative g^6 terms, could potentially extend the applicability of the coupling constant series down to surprisingly low temperatures.

Figures (2)

• Figure 1: Left: perturbative results at various orders (the precise meanings thereof are explained in Sec. \ref{['se:numerics']}), including ${\cal O}(g^6)$ for an optimal constant, normalised to the non-interacting Stefan-Boltzmann value $p_{\hbox{\scriptsize SB}}$. Right: the dependence of the ${\cal O}(g^6)$ result on the (not yet computed) constant, which contains both perturbative and non-perturbative contributions. The 4d lattice results are from boyd.
• Figure 2: The absolute values of the various terms of the slowly convergent expansion for $p_{\hbox{\scriptsize M}}(T)+p_{\hbox{\scriptsize G}}(T)$, normalised by $T g_{\hbox{\scriptsize E}}^6$.