[Paper Review] Static quark anti-quark interactions at zero and finite temperature QCD. II.Quark anti-quark internal energy and entropy

Olaf Kaczmarek, F. Zantow|arXiv (Cornell University)|Jun 17, 2005

High-Energy Particle Collisions Research22 citations

TL;DR

This paper computes the static quark-antiquark internal energy and entropy in 2-flavor QCD at finite temperature using lattice QCD simulations. It shows that both observables exhibit a sharp peak at the deconfinement transition temperature, signaling a crossover rather than a first-order phase transition, and that internal energies suggest quarkonium states may remain bound near T_c, with dissociation occurring at higher temperatures than predicted by free energy models.

ABSTRACT

We analyze the change in free energy, internal energy and entropy due to the presence of a heavy quark anti-quark pair in a QCD heat bath. The internal energies and entropies are introduced as intensive observables calculated through thermal derivatives of the QCD partition function containing additional static color sources. The quark anti-quark internal energy and, in particular, the entropy clearly signal the phase change from quark confinement below and deconfinement above the transition and both observables are introduced such that they survive the continuum limit. The intermediate and large distance behavior of the energies reflect string breaking and color screening phenomena. This is used to characterize the energies which are needed to dissolve heavy quarkonium states in a thermal medium. Our discussion supports recent findings which suggest that parts of the quarkonium systems may survive the phase transition and dissolve only at higher temperatures.

Motivation & Objective

• To define and compute the quark-antiquark internal energy and entropy as intensive, gauge-invariant observables in finite-temperature QCD.
• To investigate how these thermodynamic quantities reflect the QCD deconfinement crossover, particularly near the critical temperature T_c.
• To compare the behavior of internal energy and entropy with the quark-antiquark free energy, especially regarding quarkonium binding and dissociation.
• To assess the implications of internal energy-based effective potentials for the survival of quarkonium states in the quark-gluon plasma.
• To establish that internal energy and entropy are well-defined in the continuum limit and signal the phase transition clearly.

Proposed method

• Derives internal energy and entropy from thermal derivatives of the QCD partition function with static quark-antiquark sources via Polyakov loop correlation functions.
• Uses lattice QCD simulations with 2-flavor dynamical quarks to compute the expectation values of Wilson line operators in the presence of static sources.
• Defines the internal energy and entropy as gauge-invariant, temperature-dependent observables through the thermodynamic relation U = F + TS, with S obtained via derivative of F with respect to T.
• Analyzes the large-distance behavior of these observables to identify string breaking at low T and color screening at high T.
• Constructs effective potentials from both free energy and internal energy to estimate quarkonium binding energies and their temperature dependence.
• Compares results in full QCD (with dynamical quarks) to quenched QCD, focusing on differences in phase transition structure and thermodynamic singularities.

Experimental results

Research questions

• RQ1 How do the internal energy and entropy of a static quark-antiquark pair behave across the QCD deconfinement crossover?
• RQ2 What is the role of entropy in distinguishing between confinement and deconfinement phases in finite-temperature QCD?
• RQ3 How do internal energy-based effective potentials affect the predicted binding energy and dissociation temperature of quarkonium states?
• RQ4 In what way do internal energy and entropy differ from free energy in signaling the QCD phase transition in full QCD?
• RQ5 To what extent do quarkonium states survive the phase transition when modeled using internal energy rather than free energy?

Key findings

• The internal energy and entropy of a static quark-antiquark pair exhibit a sharp peak at the critical temperature T_c, clearly signaling the crossover nature of the deconfinement transition in 2-flavor QCD.
• Unlike the free energy, which decreases rapidly near T_c, the internal energy and entropy show a pronounced maximum at T_c, indicating non-trivial entropy contributions in the transition region.
• At large distances, the internal energy and entropy approach temperature-dependent plateaus, U_∞(T) and S_∞(T), reflecting color screening at high T and string breaking at low T.
• The difference between internal energy and free energy increases with temperature, with TS_∞(T) ≈ 4m_D(T)α(T)/3 at high T, indicating significant entropy contributions.
• Effective potentials based on internal energy suggest that quarkonium binding energies peak at T_c and decrease only above T_c, implying that quarkonium states may remain bound through the transition and dissociate at higher temperatures than predicted by free energy models.
• The results support recent findings that parts of quarkonium systems may survive the phase transition, with dissociation occurring at temperatures significantly above T_c when internal energy is used in effective potential models.