Equation of State for physical quark masses (0911.2215v2)

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

Equation of State for Physical Quark Masses in Lattice QCD

This paper presents a detailed paper of the equation of state (EoS) in quantum chromodynamics (QCD) for temperatures corresponding to the transition region using the p4-action staggered fermion formulation on $N_{\tau}=8$ lattices. The research focuses on calculations with physical mass values for two light quark flavors and one strange quark. The authors investigate the thermodynamic properties by comparing their results with previous calculations done with larger quark masses and with predictions from the resonance gas model.

Methodology and Key Outcomes

• Improved Staggered Fermion Action: The calculations were performed using the p4-action, which optimizes flavor symmetry and quark dispersion relations. This ensures the thermodynamic observables have minimal cutoff dependence at high temperatures, which is crucial for obtaining accurate results in lattice QCD studies.
• Quark Mass Dependence: The paper explores how physical quark mass affects the EoS by comparing it with prior studies that used larger light quark masses ($m_l = 0.1 m_s$). It was observed that when the light quark mass halves, the transition temperature region shifts by about $5$ MeV towards lower temperatures.
• Equation of State: The trace anomaly, defined as $\epsilon - 3p$, was calculated and employed to derive the pressure $p$ and energy density $\epsilon$. The results indicate that, while the trace anomaly showed slight differences at low temperatures, the energy density and pressure in the transition region were significantly enhanced when using the physical quark masses.
• Comparisons with Resonance Gas Model: The results below the transition temperature were compared with the predictions from the resonance gas model. The lattice QCD data for the EoS were consistently lower than those predicted by the resonance gas model, though closer to the model compared to previous studies with larger quark masses.

Transition Behavior and Implications

• Polyakov Loop and Chiral Condensate: The renormalized Polyakov loop and subtracted chiral condensate $\Delta_{l,s}$ were analyzed to understand the deconfinement and chiral aspects of the QCD transition. Both quantities demonstrated pronounced changes in the temperature interval of 170-200 MeV, highlighting the region of rapid energy density increase associated with deconfinement.
• Strangeness Fluctuations: Indicative of deconfinement, strangeness fluctuations were examined. The paper confirmed that such fluctuations rose sharply in the transition region, consistent with the energy density behavior, and the adjusted temperature scales accounted well for the mass dependence observed.

Future Directions and Theoretical Implications

This research refines our understanding of QCD thermodynamics and provides essential insights into the QCD transition under physical quark masses. The observed shift in the transition region due to decreased quark mass highlights the sensitivity of thermodynamic observables to mass parameters. As lattice QCD calculations continue to improve with reduced discretization errors and better fermion actions, future studies might focus on even finer lattice spacings or explore further aspects of QCD phase transitions under varying parameters. The implications of these findings could extend to understanding heavy-ion collisions and the formation of quark-gluon plasma, central themes in high-energy physics.

In summary, this paper made significant contributions in analyzing the equation of state in QCD through precise lattice computations, showcasing the critical influence of quark masses on thermodynamic properties and the transition temperature. These findings serve as a foundation for subsequent advancements in theoretical modeling and experimental assessments in high-temperature QCD.