Full result for the QCD equation of state with 2+1 flavors

Abstract

We present a full result for the 2+1 flavor QCD equation of state. All the systematics are controlled, the quark masses are set to their physical values, and the continuum extrapolation is carried out. This extends our previous studies [JHEP 0601:089 (2006); 1011:077 (2010)] to even finer lattices and now includes ensembles with Nt = 6,8,10,12 up to Nt = 16. We use a Symanzik improved gauge and a stout-link improved staggered fermion action. Our findings confirm our earlier results. In order to facilitate the direct use of our equation of state we make our tabulated results available for download.

Figures (6)

• Figure 1: The lattice spacing $a$ for the $\beta$ range used in this paper. Down to $a=0.047$ fm two quantities were used to determine the scale, $f_K$ and $w_0$. For higher couplings a step-scaling approach was applied.
• Figure 2: The $T=0$ lattices and the collected statistics at various lattice spacings.
• Figure 3: Left: the trace anomaly as a function of the temperature for $N_t=8, 10, 12$ and $16$ lattices. The continuum extrapolated result including all systematic uncertainties is shown by the shaded band. Using a different action (see text), we performed a continuum extrapolation at the fixed temperature value of $214$ MeV, indicated here with a smaller filled red point. This independent result serves as a crosscheck on the peak's hight (also on r.h.s.). Right: comparison of the result with the parallel effort using the HISQ action by the hotQCD collaboration (as it was presented at the Lattice 2012 conference Petreczky:2012gi, with $f_K$ scale setting) and the related parametrization 's95p-v1' of Huovinen:2009yb. A comparison to the Hadron Resonance Gas model's prediction and our result Borsanyi:2010cj from 2010 ("WB 2010") is also shown.
• Figure 4: Continuum extrapolation of the trace anomaly at $T\approx 214$ MeV with (blue points) and without (orange points) tree level improvement. The left panel shows our results with $2+1+1$ flavors of 4-step stout improved staggered quarks extrapolating from $N_t=6,8,10$ and $12$, whereas on the right panel $N_f=2+1$ 2-step stout improved quarks are used on $N_t=8,10,12$ and $16$.
• Figure 5: Left: contributions of the light (magenta) and strange quarks (turquoise) to the the pressure at $T=214$ MeV at our two finest lattice spacings. The curves represent a scan though various theories with different masses. The sum of the area under the curves gives $p/T^4$. Right: continuum extrapolation of the pressure at $T\approx 214$ MeV with (blue) and without (orange) tree level improvement. Only statistical errors are shown.