Quark Confinement and the Hadron Spectrum

TL;DR

The work addresses how confinement in QCD shapes the hadron spectrum, using heavy quarkonia as a tractable probe of nonperturbative dynamics.It combines gauge-invariant Wilson-loop formalisms, perturbative and lattice analyses of the static potential, and effective field theories (NRQCD, pNRQCD) with vacuum models (MAL, DQCD, SVM) to connect long-range confinement to observable spectra.Key results include the area-law behavior and linear potential with string tension σ from strong-coupling and lattice studies, the validation of flux-tube formation, and the derivation of gauge-invariant spin- and velocity-dependent heavy-quark potentials from Wilson loops.The framework also integrates dual superconductivity ideas and stochastic vacuum concepts, offering multiple coherent pictures of the QCD vacuum that reproduce qualitative and quantitative confinement features on the lattice.Overall, the combination of analytic formalisms, effective theories, and lattice confirmation provides a comprehensive road map for understanding the hadron spectrum and confinement physics in QCD.

Abstract

These lectures contain an introduction to the following topics: 1) Phenomenology of the hadron spectrum; 2) The static Wilson loop in perturbative and in lattice QCD. Confinement and the flux tube formation; 3) Non static properties: effective field theories and relativistic corrections to the quarkonium potential; 4) The QCD vacuum: minimal area law, Abelian projection and dual Meissner effect, stochastic vacuum.

Figures (20)

• Figure 1: The spectrum of the lightest mesons labeled by $({\rm spin})^{\rm parity}$.
• Figure 2: The experimental heavy meson spectrum ($b\bar{b}$ and $c\bar{c}$) relative to the spin-average of the $\chi_b(1P)$ and $\chi_c(1P)$ states.
• Figure 3: The Regge trajectories for the $\rho$, $K^*$ and $\phi$. From Godfrey et al. (1985).
• Figure 4: Picture of the quark-antiquark bound state in the string model.
• Figure 5: $\rho = (E_n- E_1)/(E_2-E_1)$, where $E_n$ is either the $n$th energy level of the physical system or the $n$th eigenvalue of the Schrödinger equation corresponding to the indicated potential.