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QCD forces and heavy quark bound states

Gunnar S. Bali

TL;DR

This work surveys how QCD confining forces between static color charges underpin heavy quark bound states, emphasizing lattice results and effective field theory links to quarkonium spectra. It articulates how Wilson-loop derived static potentials, strong-coupling and string pictures, and perturbative insights cohere into the Cornell-like potentials that describe quarkonia, while detailing relativistic corrections via NRQCD and pNRQCD. The review highlights lattice methodologies, continuum and finite-volume extrapolations, and the impact of sea quarks, including string breaking and Casimir scaling, on static and hybrid potentials. Collectively, these threads connect nonperturbative QCD vacuum structure to observable spectra, validating a potential-based, Adiabatic framework for heavy quarkonia and signaling areas—like nonperturbative matching and hybrid dynamics—where further progress is both possible and necessary.

Abstract

The present knowledge of QCD confining forces between static test charges is summarised, with an emphasis on lattice results. Recent developments in relating QCD potentials to quarkonium properties by use of effective field theory methods are presented. The validity of non-relativistic QCD and the adiabatic approximation with respect to heavy quark bound states is explored. Besides the static potential and relativistic correction terms, the spectra of glueballs and gluinoballs, hybrid excitations of the QCD flux tube between fundamental colour sources, potentials between charges in various representations of the SU(3) gauge group, and multi-particle interactions are discussed. Some implications for quarkonia systems and quark-gluon hybrid mesons are drawn.

QCD forces and heavy quark bound states

TL;DR

This work surveys how QCD confining forces between static color charges underpin heavy quark bound states, emphasizing lattice results and effective field theory links to quarkonium spectra. It articulates how Wilson-loop derived static potentials, strong-coupling and string pictures, and perturbative insights cohere into the Cornell-like potentials that describe quarkonia, while detailing relativistic corrections via NRQCD and pNRQCD. The review highlights lattice methodologies, continuum and finite-volume extrapolations, and the impact of sea quarks, including string breaking and Casimir scaling, on static and hybrid potentials. Collectively, these threads connect nonperturbative QCD vacuum structure to observable spectra, validating a potential-based, Adiabatic framework for heavy quarkonia and signaling areas—like nonperturbative matching and hybrid dynamics—where further progress is both possible and necessary.

Abstract

The present knowledge of QCD confining forces between static test charges is summarised, with an emphasis on lattice results. Recent developments in relating QCD potentials to quarkonium properties by use of effective field theory methods are presented. The validity of non-relativistic QCD and the adiabatic approximation with respect to heavy quark bound states is explored. Besides the static potential and relativistic correction terms, the spectra of glueballs and gluinoballs, hybrid excitations of the QCD flux tube between fundamental colour sources, potentials between charges in various representations of the SU(3) gauge group, and multi-particle interactions are discussed. Some implications for quarkonia systems and quark-gluon hybrid mesons are drawn.

Paper Structure

This paper contains 67 sections, 261 equations, 46 figures, 13 tables.

Table of Contents

  1. Motivation
  2. The hadron spectrum
  3. Regge trajectories
  4. Quarkonia
  5. Lattice methods
  6. What can the lattice do?
  7. The method
  8. Getting the physics right
  9. Mass determinations
  10. The continuum limit
  11. The static QCD potential
  12. Wilson loops
  13. Exact results
  14. Strong coupling expansions
  15. String picture
  16. ...and 52 more sections

Figures (46)

  • Figure 2.1: Regge trajectories.
  • Figure 2.2: Rotating quarks, connected by a string of constant energy density.
  • Figure 2.3: Energy splittings, $\Delta E$, for charmonia and bottomonia with respect to the $\Upsilon$ and $J/\psi$ triplet $S$ wave states.
  • Figure 3.1: Examples of gauge invariant objects. Lines correspond to gauge transporters.
  • Figure 3.2: The plaquette, $U_{x,\mu\nu}$.
  • ...and 41 more figures