The QCD Equation of State with almost Physical Quark Masses (0710.0354v2)

Abstract: We present results on the equation of state in QCD with two light quark flavors and a heavier strange quark. Calculations with improved staggered fermions have been performed on lattices with temporal extent Nt =4 and 6 on a line of constant physics with almost physical quark mass values; the pion mass is about 220 MeV, and the strange quark mass is adjusted to its physical value. High statistics results on large lattices are obtained for bulk thermodynamic observables, i.e. pressure, energy and entropy density, at vanishing quark chemical potential for a wide range of temperatures, 140 MeV < T < 800 MeV. We present a detailed discussion of finite cut-off effects which become particularly significant for temperatures larger than about twice the transition temperature. At these high temperatures we also performed calculations of the trace anomaly on lattices with temporal extent Nt=8. Furthermore, we have performed an extensive analysis of zero temperature observables including the light and strange quark condensates and the static quark potential at zero temperature. These are used to set the temperature scale for thermodynamic observables and to calculate renormalized observables that are sensitive to deconfinement and chiral symmetry restoration and become order parameters in the infinite and zero quark mass limits, respectively.

• The paper employs improved lattice QCD methods with near-physical quark masses to accurately capture the QCD equation of state and finite cut-off effects across a broad temperature range.
• Analyses on lattices with Nτ = 4, 6, and 8 reveal that high-temperature bulk properties approach Stefan–Boltzmann limits while non-perturbative effects persist.
• Renormalized observables are used to delineate deconfinement and chiral symmetry restoration transitions, offering insights relevant to heavy ion collision experiments.

Insights into the QCD Equation of State with Physical Quark Masses

This paper presents a detailed exploration of the Quantum Chromodynamics (QCD) equation of state (EoS), focusing on configurations with two light quark flavors and a heavier strange quark at near physical mass values. The research is rooted in the non-perturbative lattice QCD studies and particularly explores the complexities of the QCD EoS with attention to the transition from hadronic matter to quark-gluon plasma.

Methodology and Scope

The paper employs improved staggered fermions on lattices with varying temporal extents ($N_\tau = 4, 6, 8$), ensuring calculations are performed along a line of constant physics at nearly physical quark masses. Notably, the pion and strange quark masses are about 220 MeV and akin to the physical strange quark mass, respectively. These calculations span a temperature range from roughly 140 MeV to 800 MeV, addressing both the hadronic phase and the high-temperature quark-gluon plasma phase. The paper also rigorously examines finite cut-off effects, especially vital for characterizing high-temperature behavior.

Key Findings

1. Finite Cut-off Effects: The research highlights the significant impact of finite cut-off effects beyond double the transition temperature. For temperatures exceeding 350 MeV, $N_\tau=8$ lattices were employed to refine the trace anomaly computations.
2. High-Temperature Regime: With broader temperature coverage, the results reveal that the bulk thermodynamic quantities such as pressure and energy density approach their Stefan-Boltzmann limits but retain deviations attributable to non-perturbative effects.
3. Low-Temperature Regime: At lower temperatures, where hadronic models like the resonance gas model are applicable, the paper notes consistency with such models, albeit recognizing the nuances introduced by lattice spacing and finite quark mass adjustments.
4. Chiral and Deconfinement Transitions: Utilization of renormalized observables aids in analyzing deconfinement and chiral symmetry restoration, positioning these transitions as sensitive indicators within the lattice QCD landscape.

Implications for QCD and Lattice Calculations

1. Non-Perturbative Insights: The paper offers insights into the non-perturbative nature of QCD thermodynamics, emphasizing the lattice QCD's critical role in bridging the gap where perturbative approaches begin to falter.
2. Model Comparisons: The use of realistic quark masses bolsters the comparison between lattice results and phenomenological models, pushing towards more accurate descriptions of QCD matter properties.
3. Impacts on Heavy Ion Collisions: Broad implications for interpreting heavy ion collision data at RHIC and prospective LHC experiments are underscored. A precise understanding of the EoS and properties like the speed of sound are crucial for hydrodynamic models used in these studies.

Future Prospects

The paper suggests several avenues for further work, notably refining the lattice calculations through enhanced computational resources and extending investigations to smaller lattice spacings and full physical quark mass ratios. Such advances will likely improve the precision of the QCD EoS, critical for theoretical predictions and experimental analyses in high-energy physics.

In summary, this paper represents a significant step in understanding the QCD EoS with near-physical quark masses. It underscores the necessity of sophisticated lattice techniques to probe the behaviors of strongly interacting matter, laying foundations for future theoretical and experimental exploration in QCD thermodynamics.