The QCD phase transition with physical-mass, chiral quarks

TL;DR

The paper addresses whether the finite-temperature QCD transition at physical quark masses is a first-order phase transition or a cross-over. It employs a lattice QCD approach with chirally symmetric Möbius domain-wall fermions, 2+1 flavors, and physical light-quark mass on Nt=8 lattices with large volumes. The main findings include a cross-over with a pseudo-critical temperature near 155 MeV, restoration of chiral SU(2)L×SU(2)R above about 164 MeV, and persistent U(1)A breaking up to around 196 MeV; the disconnected chiral susceptibility shows strong mass dependence consistent with critical scaling, while discretization errors are modest. These results, consistent with but extending staggered-quark studies, provide a robust, symmetry-respecting benchmark for QCD thermodynamics at physical masses.

Abstract

We report on the first lattice calculation of the QCD phase transition using chiral fermions at physical values of the quark masses. This calculation uses 2+1 quark flavors, spatial volumes between (4 fm$)^3$ and (11 fm$)^3$ and temperatures between 139 and 196 MeV . Each temperature was calculated using a single lattice spacing corresponding to a temporal Euclidean extent of $N_t=8$. The disconnected chiral susceptibility, $χ_{\rm disc}$ shows a pronounced peak whose position and height depend sensitively on the quark mass. We find no metastability in the region of the peak and a peak height which does not change when a 5 fm spatial extent is increased to 10 fm. Each result is strong evidence that the QCD ``phase transition'' is not first order but a continuous cross-over for $m_π=135$ MeV. The peak location determines a pseudo-critical temperature $T_c = 155(1)(8)$ MeV. Chiral $SU(2)_L\times SU(2)_R$ symmetry is fully restored above 164 MeV, but anomalous $U(1)_A$ symmetry breaking is non-zero above $T_c$ and vanishes as $T$ is increased to 196 MeV.

Figures (4)

• Figure 1: The dependence of the disconnected chiral susceptibility on temperature for $m_\pi=135$ and 200 MeV. The $m_\pi=135$ MeV data shows a near $2\times$ increase over that for $m_\pi=200$ MeV. HISQ results for $m_\pi=161$ MeV Bazavov:2011nkBuchoff:2013nra are also plotted.
• Figure 2: The time histories of $\langle\overline{q}_lq_l\rangle$ for four streams with $T=154$ MeV . Streams beginning with an ordered or disordered configuration are labeled "ord" and "dis". Each point is the average of measurements made with 10 random sources on each of 20 configurations, separated by one time unit.
• Figure 3: Two susceptibility differences are shown that reflect the $SU(2)_L\times SU(2)_R$ symmetry of QCD and our chiral fermion formulation. Below $T_c$ this symmetry is spontaneously broken. For $T > 164$ MeV we see accurate chiral symmetry.
• Figure 4: The $T$-dependence of the anomalous $U(1)_A$-breaking difference $\chi_\pi-\chi_\delta$, which remains non-zero and becomes mass independent for $T > 168$ MeV.