[Paper Review] Heavy Quark Potentials and Quarkonia Binding

P. Petreczky|OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)|Feb 16, 2005

Quantum Chromodynamics and Particle Interactions4 citations

TL;DR

This paper reviews lattice QCD studies of finite-temperature heavy quark potentials, focusing on the free energy of static quark-antiquark pairs as a probe of in-medium quarkonium binding. It evaluates the validity of using free energy or internal energy as effective potentials in quarkonium spectral function calculations, concluding that internal energy provides better agreement with lattice spectral functions and suggests J/ψ can survive up to 1.7T_c.

ABSTRACT

I review recent progress in studying in-medium modification of inter-quark forces at finite temperature in lattice QCD. Some applications to the problem of quarkonium binding in potential models is also discussed.

Motivation & Objective

• To assess the validity of using finite-temperature free energy of static quark-antiquark pairs as an effective potential in quarkonium potential models.
• To investigate how many-body effects in the medium modify inter-quark forces, particularly near the deconfinement transition.
• To compare predictions of potential models with lattice QCD calculations of quarkonium spectral functions and Euclidean correlators.
• To determine whether the free energy or the internal energy provides a more reliable description of quarkonium binding in the Quark-Gluon Plasma.
• To evaluate the survival temperature of J/ψ states using different potential models and compare with lattice spectral function data.

Proposed method

• Uses lattice QCD to compute the singlet and octet free energies of static quark-antiquark pairs via Wilson loops and Polyakov loops in Coulomb gauge.
• Applies projection operators to separate color-singlet and color-octet contributions to the partition function.
• Calculates the internal energy and entropy of the static pair from the free energy using thermodynamic relations.
• Uses the internal energy as an effective potential in the Schrödinger equation to compute quarkonium bound states and spectral functions.
• Compares model-derived Euclidean meson correlators with direct lattice QCD calculations to test consistency.
• Relies on the spectral function decomposition involving bound states and continuum thresholds to model quarkonium correlators.

Experimental results

Research questions

• RQ1 Can the free energy of static quark-antiquark pairs in medium be reliably used as an effective potential in quarkonium potential models?
• RQ2 How do many-body effects in the Quark-Gluon Plasma modify the inter-quark potential beyond simple screening?
• RQ3 What is the correct thermodynamic quantity—free energy or internal energy—to use as a potential in quarkonium binding calculations?
• RQ4 To what temperature can the J/ψ state survive in the Quark-Gluon Plasma according to potential models based on lattice potentials?
• RQ5 How well do model spectral functions derived from lattice potentials reproduce the behavior of Euclidean correlators observed in lattice QCD?

Key findings

• The free energy of the static quark-antiquark pair in the color singlet channel shows a strong temperature dependence, with screening effects becoming significant above T_c.
• The internal energy exceeds the free energy at finite temperature, especially near T_c, indicating that entropy contributions are large and the free energy is not a reliable potential in this regime.
• Using the internal energy as the potential in the Schrödinger equation yields a J/ψ survival temperature of up to 1.7T_c, consistent with lattice spectral function calculations.
• The color-averaged free energy, while gauge-invariant and widely studied, contains less direct information about medium-modified two-body forces due to its statistical averaging over color channels.
• The internal energy's lack of a constant term at large distances at high T makes it a more physically plausible effective potential than the free energy.
• Model spectral functions based on the internal energy potential successfully reproduce features such as the enhancement of the scalar correlator above T_c, as seen in lattice data.