The QCD equation of state with dynamical quarks (1007.2580v2)

Abstract: The present paper concludes our investigation on the QCD equation of state with 2+1 staggered flavors and one-link stout improvement. We extend our previous study [JHEP 0601:089 (2006)] by choosing even finer lattices. Lattices with $N_t=6,8$ and 10 are used, and the continuum limit is approached by checking the results at $N_t=12$. A Symanzik improved gauge and a stout-link improved staggered fermion action is utilized. We use physical quark masses, that is, for the lightest staggered pions and kaons we fix the $m_\pi/f_K$ and $m_K/f_K$ ratios to their experimental values. The pressure, the interaction measure, the energy and entropy density and the speed of sound are presented as functions of the temperature in the range $100 ...1000 \textmd{MeV}$. We give estimates for the pion mass dependence and for the contribution of the charm quark. We compare our data to the equation of state obtained by the "hotQCD" collaboration.

• The paper computes the QCD equation of state using 2+1 staggered fermion simulations, yielding precise thermodynamic quantities between 100 and 1000 MeV.
• It employs advanced lattice techniques, including Symanzik improved gauge and stout-link improved staggered fermion actions, to maintain accurate physical quark mass ratios.
• The results, benchmarked against hotQCD collaboration data, provide valuable insights into the thermodynamic impact of both light and charm quarks in high-temperature QCD.

The QCD Equation of State with Dynamical Quarks

This paper presents a comprehensive paper of the equation of state (EoS) in Quantum Chromodynamics (QCD) with a focus on dynamical quarks, utilizing $2+1$ staggered flavors and one-link stout improvement. Building on previous research, this paper employs finer lattice discretizations, specifically with $N_t=6, 8,$ and $10$, while extending the continuum limit by evaluating results at $N_t=12$. The use of the Symanzik improved gauge and a stout-link improved staggered fermion action underscores the methodological rigor in achieving precision in lattice QCD thermodynamics.

Methodology

In this paper, physical quark masses are deployed, ensuring that the ratios $m_\pi/f_K$ and $m_K/f_K$ align with the experimental values, therefore maintaining the physical realism of the simulation. Various thermodynamic quantities such as pressure, interaction measure, energy density, entropy density, and the speed of sound are computed as functions of temperature. These computations span a wide temperature range of $100 \ldots 1000 \textmd{MeV}$.

This work makes significant use of methodological innovations such as the integral technique and the Hadron Resonance Gas (HRG) model, which aid in the accurate determination of thermodynamic quantities on the lattice. Additionally, the paper presents a detailed analysis of pion mass-dependence and includes preliminary insights into the contributions of the charm quark, adding depth to the exploration of QCD EoS.

Results and Comparison

The results are benchmarked against those from the "hotQCD" collaboration, allowing a comparative analysis that highlights consistencies and discrepancies across different lattice QCD approaches. This comparative evaluation is crucial for validating the accuracy and reliability of results obtained in this complex domain of high-temperature QCD.

The EoS results for both light quarks and the impact of charm quarks are thoroughly discussed, laying the groundwork for future enhancements, such as further refinement of lattice parameters or inclusion of additional flavor effects. Such precise evaluation is instrumental in understanding phenomena such as quark-gluon plasma, which are pivotal for both theoretical implications and experimental predictions in high-energy physics.

Implications and Future Directions

This research has implications for furthering knowledge in thermal field theories and the paper of lattice QCD thermodynamics. By expanding the range of dependable data on QCD EoS, it provides a solid basis for future explorations of phase transitions and critical phenomena in QCD. The methodologies and results could influence improved computational strategies in lattice QCD studies.

Future research could investigate the role of different fermion discretization schemes or explore alternative stout-link improvements for potentially greater accuracy or computational efficiency. Additionally, the approach used here can be expanded to investigate other dynamical properties of QCD, providing an insightful avenue for future theoretical and computational investigations in the domain.