Equation of state and QCD transition at finite temperature (0903.4379v1)

Abstract: We calculate the equation of state in 2+1 flavor QCD at finite temperature with physical strange quark mass and almost physical light quark masses using lattices with temporal extent Nt=8. Calculations have been performed with two different improved staggered fermion actions, the asqtad and p4 actions. Overall, we find good agreement between results obtained with these two O(a^2) improved staggered fermion discretization schemes. A comparison with earlier calculations on coarser lattices is performed to quantify systematic errors in current studies of the equation of state. We also present results for observables that are sensitive to deconfining and chiral aspects of the QCD transition on Nt=6 and 8 lattices. We find that deconfinement and chiral symmetry restoration happen in the same narrow temperature interval. In an Appendix we present a simple parametrization of the equation of state that can easily be used in hydrodynamic model calculations. In this parametrization we also incorporated an estimate of current uncertainties in the lattice calculations which arise from cutoff and quark mass effects. We estimate these systematic effects to be about 10 MeV

• The paper demonstrates how improved staggered fermion actions reduce O(a²) discretization errors for precise QCD EoS calculations.
• The paper finds that deconfinement and chiral symmetry restoration occur synchronously, supported by trace anomaly and quark susceptibility analyses.
• The paper confirms consistency between asqtad and p4 actions, underpinning reliable lattice QCD methods for heavy-ion collision simulations.

An Evaluation of the QCD Equation of State at Finite Temperature with Improved Actions

The paper offers an analytical paper of the equation of state (EoS) in quantum chromodynamics (QCD) at finite temperature, specifically leveraging the lattice framework with (2+1) flavors. The focus is on lattices with a temporal extent of $N_\tau=8$, using physical strange quark masses and nearly physical light quark masses. The paper leverages two distinct improved staggered fermion actions, namely the asqtad and p4 actions, to discern thermodynamic phenomena. The authors report a satisfactory agreement between the two approaches, as well as comparison with prior calculations on coarser lattices to assess systematic errors inherent in contemporary EoS studies.

Major Contributions and Technical Approach

The main pursuit of the research is to calculate the QCD EoS, a critical aspect of understanding finite temperature QCD, which serves as a pivotal input for hydrodynamic modeling of dense matter dynamics in heavy-ion collisions. With experiments being conducted at the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC), accurate EoS determination is essential for explaining phenomena such as jet quenching and hydrodynamic flow.

Lattice QCD calculations allow for the EoS to be determined using realistic quark mass spectrums. Within this paper, the authors demonstrate how improved staggered fermion actions can address these needs by reducing $\mathcal{O}(a^2)$ discretization errors. Calculations employ simulations on $N_\tau=8$ lattices with zero-temperature results adjusted accordingly, enabling accurate thermodynamic predictions. A line of constant physics is maintained by tuning bare quark masses, ensuring observables remain constant as the temperature changes.

Key Findings

1. Trace Anomaly: Central to the work is the calculation of the trace anomaly $(\epsilon - 3p)/T^4$, a measure of the deviation from conformal symmetry. The results exhibit a high degree of consistency between the asqtad and p4 actions, with minimal discrepancies arising largely around the anomaly peak temperature.
2. Deconfinement and Chiral Symmetry Restoration: Empirical evidence suggests that the deconfinement of quarks coincides with the restoration of chiral symmetry within a narrow temperature range around the transition. Observables such as quark number susceptibilities and renormalized Polyakov loop measurements support this assertion, indicating that both phenomena occur synchronously.
3. Quark Number Susceptibilities: The paper demonstrates a strong correlation between energy density and light quark number susceptibility within the transition region, essential for delineating deconfinement aspects.
4. Equation of State: From the trace anomaly, other thermodynamic variables such as pressure, energy, and entropy densities were derived. The paper confirms that cutoff dependencies are manageable at high temperatures ($T > 200$ MeV) and speculates that lattice spacings corresponding to $N_\tau=12$ could further minimize discretization errors.

Implications and Future Directions

The EoS results obtained not only aid in precisely modeling QCD matter dynamics in collider environments but also provide insights into the fundamental understanding of strong interactions at the quantum level. The implication of consistent observations using both improved actions affirms the viability of these lattice approaches as reliable tools for theoretical physics.

Moving forward, the paper suggests that investigations into cutoff effects and the extension of the framework to even finer lattices would enhance predictive accuracy in both computational and experimental collaboration settings. Additionally, exploring lower quark masses will provide a more rigorous test of chiral symmetry breaking and restoration mechanisms.

Overall, the research offers a comprehensive lattice computation perspective on QCD thermodynamics, bolstering the theoretical underpinnings essential for contemporary and future high-energy physics inquiries.