Precision SU(3) lattice thermodynamics for a large temperature range (1204.6184v2)

Abstract: We present the equation of state (pressure, trace anomaly, energy density and entropy density) of the SU(3) gauge theory from lattice field theory in an unprecedented precision and temperature range. We control both finite size and cut-off effects. The studied temperature window (0.7...1000 T_c) stretches from the glueball dominated system into the perturbative regime, which allows us to discuss the range of validity of these approaches. We also determine the preferred renormalization scale of the Hard Thermal Loop scheme and we fit the unknown g^6 order perturbative coefficient at extreme high temperatures T>100 T_c. We furthermore quantify the nonperturbative contribution to the trace anomaly using a simple functional form. Our high precision data allows one to have a complete theoretical description of the equation of state from T=0 all the way to the phase transition, through the transition region into the perturbative regime up to the Stefan-Boltzmann limit. We will discuss this description, too.

• The paper presents a high-precision lattice approach to derive the SU(3) gauge theory equation of state over a wide temperature range.
• It quantifies non-perturbative effects in the transition region using a parameterized quadratic term that bridges standard perturbative methods.
• The findings offer practical simulation tools and refined models for extreme temperature regimes in QCD thermodynamics.

Precision SU(3) Lattice Thermodynamics for Large Temperature Range

The paper presents an extensive paper on the thermodynamic equation of state for the SU(3) gauge theory using lattice field theory at high precision across a temperature range of $0.7 \, T_c$ to $1000 \, T_c$. This research is notable for controlling both finite size and cut-off effects, making it a significant contribution to understanding the non-perturbative aspects and the transition into the perturbative regime.

Equation of State

The authors derive the equation of state, including pressure, trace anomaly, energy density, and entropy density, through lattice simulations with a Symanzik improved gauge action. Key features involve the calculation of the trace anomaly $\epsilon - 3p$, which allows reconstruction of other observables via thermodynamic identities. The paper spans temperatures from the glueball-dominated non-perturbative regime to the perturbative high-temperature zone.

Non-Perturbative and Perturbative Contributions

In the transition region $T_c < T < 5\, T_c$, the trace anomaly's behavior suggested non-perturbative contributions inadequately depicted by standard perturbative expansions. The authors quantify these contributions using a parameterized functional form, indicating dominance of a quadratic component over the logarithmic corrections traditionally expected from perturbation theory.

Furthermore, at temperatures $T > 10\, T_c$, perturbative methods regain predictive power. The paper successfully fits the coefficient for the $g^6$ order term and determines the appropriate renormalization scale for the Hard Thermal Loop (HTL) scheme precisely. This allows for accurate matching of non-perturbative lattice results with perturbative expectations, effectively bridging these two regimes.

Practical and Theoretical Implications

The findings offer practical tools for future simulations and theoretical studies in QCD thermodynamics, shedding light on the range where perturbative and non-perturbative methods are valid. The fitted perturbative parameters can guide simulations at extreme temperature conditions, beneficial for experiments and models considering high energy physics.

Conclusion and Future Prospects

The paper's high-precision data enlighten the behavior of SU(3) gauge theory from confinement to perturbative limits, paving the way for more refined models that incorporate both lattice results and perturbative corrections. Future research could expand upon these findings by exploring full QCD scenarios or extending similar methodologies to other gauge theories, enhancing our understanding of thermal phenomena in strong interactions. This work serves as a benchmark for the paper of thermodynamics in lattice gauge theories, offering detailed insights into critical phenomena across diverse temperature ranges.