Equation of state and QCD transition at finite temperature

TL;DR

This study computes the QCD equation of state for (2+1) flavors with near-physical light masses and a physical strange mass on Nt=8 lattices, comparing two ${\cal O}(a^2)$-improved staggered actions (asqtad and p4) to quantify discretization errors. By evaluating the trace anomaly $\Theta^{\mu\mu}/T^4$ and deriving $p$, $\epsilon$, and $s$, the authors demonstrate consistent thermodynamics across actions, identify cutoff effects primarily near the peak of the trace anomaly, and show that deconfinement and chiral restoration occur in the same narrow temperature window around 180–200 MeV. They decompose the trace anomaly into gluonic and fermionic parts, analyze the high-temperature behavior with perturbative-like fits, and provide a renormalized Polyakov loop treatment. A parametrization of the EoS is offered for hydrodynamic modeling, and preliminary Nt=12 results suggest reduced discretization errors, supporting a reliable continuum extrapolation in the high-temperature regime.

Abstract

We calculate the equation of state in 2+1 flavor QCD at finite temperature with physical strange quark mass and almost physical light quark masses using lattices with temporal extent Nt=8. Calculations have been performed with two different improved staggered fermion actions, the asqtad and p4 actions. Overall, we find good agreement between results obtained with these two O(a^2) improved staggered fermion discretization schemes. A comparison with earlier calculations on coarser lattices is performed to quantify systematic errors in current studies of the equation of state. We also present results for observables that are sensitive to deconfining and chiral aspects of the QCD transition on Nt=6 and 8 lattices. We find that deconfinement and chiral symmetry restoration happen in the same narrow temperature interval. In an Appendix we present a simple parametrization of the equation of state that can easily be used in hydrodynamic model calculations. In this parametrization we also incorporated an estimate of current uncertainties in the lattice calculations which arise from cutoff and quark mass effects. We estimate these systematic effects to be about 10 MeV

Figures (17)

• Figure 1: (color online) The trace anomaly $(\epsilon -3p)/T^4$ calculated on lattices with temporal extent $N_\tau =6,~8$. The upper x-axis shows the temperature scale in units of the scale parameter $r_0$ which has been determined in studies of the static quark potential. The lower x-axis gives the temperature in units of MeV, which has been obtained using for $r_0$ the value determined from the level splitting of bottomonium states, $r_0 = 0.469$ fm gray. The right hand figure shows the region around the maximum of $(\epsilon -3p)/T^4$, which also is the temperature region where results obtained with the two different discretization schemes show the largest differences. Open symbols for the $N_\tau=6$, asqtad data set denote data obtained with the R algorithm. All other data have been obtained with an RHMC algorithm.
• Figure 2: (color online) The trace anomaly calculated with the p4 (left) and asqtad (right) actions. Shown is a comparison of results obtained on lattices with temporal extent $N_\tau=6$ and $8$. The curves show interpolations discussed in the text. Open symbols for the $N_\tau=6$, asqtad data set denote data obtained with the R algorithm. All other data have been obtained with an RHMC algorithm.
• Figure 3: (color online) The trace anomaly at low temperatures calculated with the asqtad and p4 actions on lattices with temporal extent $N_\tau=6$ and $8$. Open symbols for the $N_\tau=6$, asqtad data set denote data obtained with the R algorithm. All other data have been obtained with an RHMC algorithm. Solid lines show interpolation curves for the p4 action discussed in the text. The dashed and dashed-dotted curves give the trace anomaly calculated in a hadron resonance gas model with two different cuts for the maximal mass, $m_{max}=1.5$ GeV (dashed-dotted) and $2.5$ GeV (dashed).
• Figure 4: (color online) The trace anomaly at high temperatures calculated with the asqtad and p4 actions on lattices with temporal extent $N_\tau=6$ and $8$. For the p4 action we also show results obtained on lattices with temporal extent $N_\tau=4$rbcBIeos. Open symbols for the $N_\tau=6$, asqtad data set denote data obtained with the R algorithm. All other data have been obtained with an RHMC algorithm. Solid curves show fits to the data based on Eq. (\ref{['e3phigh']}). Fit parameters are given in Table \ref{['tab:bc_fit']}.
• Figure 5: (color online) Gluon condensate and quark condensate contributions to the trace anomaly. Shown are results for the asqtad and p4 actions obtained on lattices of size $N_\tau =4,~6$ and $8$. Some results shown for the asqtad and p4 actions on lattices of size $N_\tau =4,~6$ have been taken from earlier calculations rbcBIeosmilc_eos. Open symbols for the $N_\tau=4$ and $6$ asqtad data sets denote data obtained with the R algorithm. All other data have been obtained with an RHMC algorithm.