Equation of State for physical quark masses

TL;DR

The paper addresses the QCD equation of state near the crossover for physical (2+1)-flavor quark masses. It employs the improved $p4$ staggered fermion action on lattices with $N_{ au}=8$, performing zero-temperature scale setting to define a line of constant physics, and computes the trace anomaly $rac{ heta_{}}{T^4}$ to derive $p/T^4$ and $ extepsilon/T^4$, comparing with results at heavier quark masses and with the Hadron Resonance Gas model. A key finding is that lowering the light-quark mass to $m_l=0.05m_s$ shifts the transition region by about $5$ MeV toward smaller $T$, while for $T\gtrsim200$ MeV there is no significant quark-mass dependence, with the renormalized Polyakov loop, subtracted chiral condensate and strangeness fluctuations supporting a simultaneous deconfinement and chiral restoration. The results provide physically ground-truth EoS data and deconfinement/chiral observables for QCD thermodynamics, while caveats about lattice spacing and taste violations indicate the need for finer lattices and higher statistics for full control of systematic errors.

Abstract

We calculate the QCD equation of state for temperatures corresponding to the transition region with physical mass values for two degenerate light quark flavors and a strange quark using an improved staggered fermion action (p4-action) on lattices with temporal extent N_tau=8. We compare our results with previous calculations performed at twice larger values of the light quark masses as well as with results obtained from a resonance gas model calculation. We also discuss the deconfining and chiral aspects of the QCD transition in terms of renormalized Polyakov loop, strangeness fluctuations and subtracted chiral condensate. We show that compared to the calculations performed at twice larger value of the light quark mass the transition region shifts by about 5 MeV toward smaller temperatures

Figures (4)

• Figure 1: The trace anomaly $(\epsilon-3p)/T^4$ calculated for the physical quark mass and compared with previous calculations at larger light quark masses $m_l=0.1m_s$ as well as with the HRG model which includes all the resonances up to $2.5$GeV. Also shown are the interpolations of the lattice data.
• Figure 2: Energy density and three times the pressure at the physical value of the light quark mass and compared with previous calculations performed at $m_l=0.1m_s$. The horizontal band shows the expected uncertainty in the energy density due to the choice of the lower integration limit (see text).
• Figure 3: The renormalized Polyakov loop (top) and the subtracted chiral condensate (bottom) as function of the temperature calculated at $m_l=0.05m_s$ and at $0.1m_s$.
• Figure 4: Strangeness fluctuations as function of the temperature calculated at $m_l=0.05m_s$ and at $0.1m_s$. In the bottom figure the numerical data for $m_l=0.1m_s$ have been shifted by $5$ MeV.