Recent lattice results on finite temerature and density QCD, part II

TL;DR

The paper addresses the finite-temperature QCD transition in (2+1)-flavor QCD with near-physical light masses and a physical strange mass, focusing on the relationship between deconfinement and chiral symmetry restoration. It relies on lattice QCD calculations with $O(a^2)$-improved staggered fermions and multiple discretizations to determine the transition temperature and analyze observables sensitive to confinement and chiral dynamics. The main result is that deconfinement and chiral restoration occur in a common crossover window, with a transition region around $T_c \\approx 185$–$195$ MeV for $N_ au=8$, and that quartic fluctuations provide robust signals of the transition. These findings support a unified crossover picture in the physical regime and guide continuum extrapolations and scale-setting strategies.

Abstract

We discuss recent progress in studies of QCD thermodynamics with almost physical light quark masses and a physical value of the strange quark mass. We summarize results on the transition temperature in QCD and analyze the relation between deconfinement and chiral symmetry restoration.

Figures (5)

• Figure 1: Left: Quark mass and cut-off dependence of the transition temperature calculated with the p4fat3 staggered fermion action on lattices with temporal extent $N_\tau=4$ and $6$p4_Tc. Right: Transition temperatures determined in several recent studies of QCD thermodynamics. From top to bottom the first two data points show results obtained in simulations of 2-flavor QCD using clover improved Wilson fermions on lattices with temporal extent $N_\tau =8,\; 10$ and $12$Bornyakov1Bornyakov2 and $N_\tau =4$ and $6$Maezawa, respectively. The remaining data points have been obtained in simulations of QCD with 2 light quark masses and a physical strange quark mass. They are based on calculations with staggered fermions using the asqtad action on $N_\tau =4$, $6$ and $8$ lattices milc_Tc, the p4fat3 action on $N_\tau =4$, $6$p4_Tc and 1-link, stout smeared action on $N_\tau =4$, $6$, $8$ and $10$ lattices aoki_Tc. Circles indicate that the determination of the transition temperature is based on observables sensitive to chiral symmetry restoration, i.e. the chiral condensate and susceptibilities deduced from it. Squares indicate that observables sensitive to deconfinement have been used to determine the transition temperature, e.g.the Polyakov loop, its susceptibility and/or light and strange quark number susceptibilities. The diamond indicates that both sets of observables have been analyzed. With the exception of results presented in Maezawa all calculations aimed at an extrapolation to the continuum limit ($N_\tau \rightarrow \infty$) for physical values of the quark masses. All results have been rescaled to a common physical scale using $r_0=0.469$ fm Gray.
• Figure 2: Disconnected part of the light quark chiral susceptibility and the Polyakov loop susceptibility (left) p4_Tc and the quartic fluctuations of the light quark number (right) Schmidt calculated on lattices with temporal extent $N_\tau =4$ in simulations with the p4fat3 action.
• Figure 3: Preliminary results of the hotQCD collaboration lat07 for the strange quark number susceptibility calculated on lattices of size $32^3 8$ using two different ${\@fontswitch\mathcal{O}}(a^2)$ improved staggered fermion actions, asqtad and p4fat3 (left). The vertical lines indicate a band of temperatures, $185{\rm MeV} \le T \le 195{\rm MeV}$, which characterizes the transition region in the $N_\tau =8$ calculations lat07 (see also Figs. $4$ and $5$). The right hand figure shows a comparison of calculations performed with the p4fat3 action on lattices of temporal extent $N_\tau =4$, $6$Schmidt and $8$lat07 and with the 1-link, stout smeared action for $N_\tau =4$, $6$, $8$ and $10$aoki_Tc. Note that different conventions have been used to define the temperature scale (see text)
• Figure 4: The difference of light and strange quark chiral condensates normalized to its zero temperature value as defined in Eq. \ref{['delta']} (left) and the renormalized Polyakov loop expectation value (right). Shown are results from simulations on $N_\tau=4$ and $6$ lattice obtained with the p4fat3 p4_eos action as well as preliminary results for $N_\tau =8$ obtained by the hotQCD Collaboration lat07. The upper axis shows the temperature in units of the distance $r_0$ extracted from the heavy quark potential. The lower temperature scale in units of MeV has been obtained from this using $r_0 = 0.469$ fm Gray. The vertical lines indicate a band of temperatures, $185{\rm MeV} \le T \le 195{\rm MeV}$, which characterizes the transition region in the $N_\tau =8$ calculations.
• Figure 5: Subtracted finite temperature chiral condensates normalized by the corresponding zero temperature quantity evaluated at the same value of the cut-off (top), the disconnected part of the light quark chiral susceptibility (middle) and the total light quark chiral susceptibility (bottom). All figures show preliminary results of the hotQCD Collaboration obtained with two different ${\@fontswitch\mathcal{O}}(a^2)$ improved staggered fermion actions on lattices of size $32^3\, 8$lat07.