The equation of state at high temperatures from lattice QCD

TL;DR

The paper tackles the QCD equation of state at high temperatures by extending lattice QCD methods to temperatures far above the conventional range. It introduces two strategies: a finite-temperature renormalization of the pressure using $p_{bar}(T)=p(T) - p(T/2)$ to form $p_{ren}(T)$, and a direct pressure measurement via an interpolating partition function, enabling pressure evaluation without T=0 data and with reduced computational cost. In pure SU(3) gauge theory (with extension to full QCD), the authors demonstrate consistency with standard renormalization results and perturbative predictions at high T, and they push the temperature reach toward the Stefan-Boltzmann limit. Overall, the work significantly broadens the temperature range accessible to lattice EOS studies, providing efficient, scalable methods and a robust reference for high-temperature QCD thermodynamics.

Abstract

We present results for the equation of state upto previously unreachable, high temperatures. Since the temperature range is quite large, a comparison with perturbation theory can be done directly.

Figures (7)

• Figure 1: The dimensionless pressure as a function of the temperature. By summing up the intermediate terms (indicated by solid blue lines, denoted by $p'$) we arrive at the total renormalized pressure (solid red line), which agrees completely with results obtained by the usual integral method.
• Figure 2: Asymptotic scaling seems to be realized, as the improved perturbation theory formula fits the lattice results of the Sommer parameter for larger values of $\beta$.
• Figure 3: We show the two, non-negligible terms (denoted by dotted lines) of the normalized pressure, and their sum (solid line). $P_{SB}$ denotes the pressure of the non-interacting gluon gas.
• Figure 4: Cancellation effect in calculating the pressure by our new method. These results were obtained on $N_t=4$ lattices at $\beta=50$ (which roughly corresponds to the Planck temperature).
• Figure 5: The pressure, normalized to its Stefan-Boltzmann value, as a function of the temperature obtained by our new techique. Results with smaller discretization errors ($N_t=8$, blue circles), seem to fit improved perturbation theory, and also reproduce results obtained by the standard method at lower temperatures. At the highest temperature, $3 \cdot 10^7 \cdot T_C$, the pressure (within its statistical uncertainty) is consistent with the Stefan-Boltzmann limit.