The chiral and deconfinement aspects of the QCD transition

TL;DR

This work analyzes the finite-temperature QCD transition by separating chiral and deconfinement aspects using 2+1 flavors with three improved staggered actions (p4, asqtad, HISQ/tree) on N_{ au}=6,8,12 lattices. It combines universal O(N) scaling analyses with controlled continuum extrapolations to extract a continuum chiral transition temperature T_c ≈ 154 MeV, and cross-validates chiral observables with deconfinement probes such as quark number susceptibilities and the renormalized Polyakov loop. The study demonstrates that taste violations are markedly reduced by the HISQ/tree action, enabling closer agreement with continuum stout results and providing a robust, multi-action consensus on Tc and the interplay between chiral restoration and deconfinement. The results have implications for the QCD phase diagram, heavy-ion phenomenology, and the interpretation of lattice thermodynamics in the continuum limit.

Abstract

We present results on the chiral and deconfinement properties of the QCD transition at finite temperature. Calculations are performed with 2+1 flavors of quarks using the p4, asqtad and HISQ/tree actions. Lattices with temporal extent N_tau=6, 8 and 12 are used to understand and control discretization errors and to reliably extrapolate estimates obtained at finite lattice spacings to the continuum limit. The chiral transition temperature is defined in terms of the phase transition in a theory with two massless flavors and analyzed using O(N) scaling fits to the chiral condensate and susceptibility. We find consistent estimates from the HISQ/tree and asqtad actions and our main result is T_c=154 +/- 9 MeV.

Figures (32)

• Figure 1: The free energy density of an ideal quark gas calculated for different values of the temporal extent $N_{\tau}$ divided by the corresponding value for $N_\tau = \infty$.
• Figure 2: The static potential calculated for the HISQ/tree action with $m_l=0.2m_s$ (left) and $m_l=0.05m_s$ (right) in units of $r_0$. In the plot on the left, we compare the HISQ/tree and p4 results obtained at a similar value of the lattice spacing. The dashed line in the plot on the right is the string potential $V_{string}(r)=-\pi/(12 r)+\sigma r$ matched to the data at $r/r_0=1.5$.
• Figure 3: The ratio $r_0/r_1$ for the HISQ/tree action. Fitting all the data at $\beta \geq 6.423$ by a constant gives $r_0/r_1 = 1.508(5)$ as our best estimate of the continuum extrapolated value.
• Figure 4: The splitting $M_\pi^2 -M_G^2$ of pseudoscalar meson multiplets calculated with the HISQ/tree and stout actions as a function of $\alpha_V^2 a^2$ (left). The right panel shows the RMS pion mass with $M_G=140$ MeV as a function of the lattice spacing for the asqtad, stout and HISQ/tree actions. The band for the asqtad and stout actions shows the variation due to removing the fourth point at the largest $a$ in the fit. These fits become unreliable for $a \hbox{$>$$\sim$} 0.16$ fm and are, therefore, truncated at $a=0.16$ fm. The vertical arrows indicate the lattice spacing corresponding to $T \approx 160$ MeV for $N_{\tau}=6$, $8$ and $12$.
• Figure 5: The decay constants of $\eta_{s\bar{s}}$, K and $\pi$ mesons with the HISQ/tree action at $m_l = 0.05 m_s$ measured in units of $r_0$ (left) and $r_1$ (right) are shown as a function of the lattice spacings. The black points along the y-axis are the result of a linear extrapolation to the continuum limit. The experimental results are shown as horizontal bands along the y-axis with the width corresponding to the error in the determination of $r_0$ and $r_1$, respectively. We use the HPQCD estimate for $f_{\eta_{s \bar{s}}}$Davies:2009tsa as the continuum value.