QCD Phase Transition with Chiral Quarks and Physical Quark Masses

We report on the first lattice calculation of the QCD phase transition using chiral fermions with physical quark masses. This calculation uses $2+1$ quark flavors, spatial volumes between $(4\mathrm{fm}{)}^3$ and $(11\mathrm{fm}{)}^3$ and temperatures between 139 and 196 MeV. Each temperature is calculated at a single lattice spacing corresponding to a temporal Euclidean extent of $N_t=8$. The disconnected chiral susceptibility, ${\chi }_{\text{disc}}$ shows a pronounced peak whose position and height depend sensitively on the quark mass. We find no metastability near 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 crossover for $m_{\pi }=135\mathrm{MeV}$. The peak location determines a pseudocritical temperature $T_c=155(1)(8)\mathrm{MeV}$, in agreement with earlier staggered fermion results. However, the peak height is 50% greater than that suggested by previous staggered results. Chiral $SU(2{)}_L\times SU(2{)}_R$ symmetry is fully restored above 164 MeV, but anomalous $U(1{)}_A$ symmetry breaking is nonzero above $T_c$ and vanishes as $T$ is increased to 196 MeV.

Figure 1

The dependence of the disconnected chiral susceptibility on $T$ for $m_{\pi }=135$ and 200 MeV. The $m_{\pi }=135\mathrm{MeV}$ data show a near $2\times$ increase over that for $m_{\pi }=200\mathrm{MeV}$. HISQ results for $m_{\pi }=161\mathrm{MeV}$ [7, 13] are also plotted. The errors in the conversion of ${\chi }_{l,\text{disc}}$ from bare to $\overline{\mathrm{MS}}$ values, common to all of the DWF results, are not shown.

Figure 2

The time histories of $⟨{\overline{q}}_l{q}_l⟩$ for four streams at $T=154\mathrm{MeV}$. Streams beginning with an ordered or disordered configuration are labeled ord or dis. Each point averages results from 10 random sources on 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 $T>164\mathrm{MeV}$ we see accurate chiral symmetry. Here and in Fig. 4 only $32^3$ data is shown. Little volume dependence is seen for these differences [7] for $16^3$, $24^3$, and $32^3$ volumes and $m_{\pi }=200\mathrm{MeV}$.

Figure 4

The $T$ dependence of the anomalous $U(1{)}_A$-breaking difference ${\chi }_{\pi }-{\chi }_{\delta }$, which remains nonzero and becomes mass independent for $T>168\mathrm{MeV}$.