A golden age for heavy-quarkonium physics dawned a decade ago, initiated by the confluence of exciting advances in quantum chromodynamics (QCD) and an explosion of related experimental activity. The early years of this period were chronicled in the Quarkonium Working Group (QWG) CERN Yellow Report (YR) in 2004, which presented a comprehensive review of the status of the field at that time and provided specific recommendations for further progress. However, the broad spectrum of subsequent breakthroughs, surprises, and continuing puzzles could only be partially anticipated. Since the release of the YR, the BESII program concluded only to give birth to BESIII; the B-factories and CLEO-c flourished; quarkonium production and polarization measurements at HERA and the Tevatron matured; and heavy-ion collisions at RHIC have opened a window on the deconfinement regime. All these experiments leave legacies of quality, precision, and unsolved mysteries for quarkonium physics, and therefore beg for continuing investigations at BESIII, the LHC, RHIC, FAIR, the Super Flavor and/or Tau-Charm factories, JLab, the ILC, and beyond. The list of newly found conventional states expanded to include h(c)(1P), chi(c2)(2P), B-c(+), and eta(b)(1S). In addition, the unexpected and still-fascinating X(3872) has been joined by more than a dozen other charmonium- and bottomonium-like "XYZ" states that appear to lie outside the quark model. Many of these still need experimental confirmation. The plethora of new states unleashed a flood of theoretical investigations into new forms of matter such as quark-gluon hybrids, mesonic molecules, and tetraquarks. Measurements of the spectroscopy, decays, production, and in-medium behavior of c (c) over bar, b (b) over bar, and b (c) over bar bound states have been shown to validate some theoretical approaches to QCD and highlight lack of quantitative success for others. Lattice QCD has grown from a tool with computational possibilities to an industrial-strength effort now dependent more on insight and innovation than pure computational power. New effective field theories for the description of quarkonium in different regimes have been developed and brought to a high degree of sophistication, thus enabling precise and solid theoretical predictions. Many expected decays and transitions have either been measured with precision or for the first time, but the confusing patterns of decays, both above and below open-flavor thresholds, endure and have deepened. The intriguing details of quarkonium suppression in heavy-ion collisions that have emerged from RHIC have elevated the importance of separating hot- and cold-nuclear-matter effects in quark-gluon plasma studies. This review systematically addresses all these matters and concludes by prioritizing directions for ongoing and future efforts.

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Heavy quarkonium: progress, puzzles, and opportunities

The QCD transition temperature: Results with physical masses in the continuum limit

We briefly review how nonrelativistic effective field theories give us a definition of the QCD potentials and a coherent field-theory-derived quantum-mechanical scheme to calculate the properties of bound states made by two or more heavy quarks. In this framework heavy quarkonium properties depend only on the QCD parameters (quark masses and αs) and nonpotential corrections are systematically accounted for. The relation between the form of the nonperturbative potentials and the low-energy QCD dynamics is also discussed.

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Effective field theories for heavy quarkonium

We extend our previous study [Phys. Lett. B 643 (2006) 46] of the cross-over temperatures (Tc) of QCD. We improve our zero temperature analysis by using physical quark masses and finer lattices. In addition to the kaon decay constant used for scale setting we determine four quantities (masses of the Ω baryon, K*(892) and (1020) mesons and the pion decay constant) which are found to agree with experiment. This implies that — independently of which of these quantities is used to set the overall scale — the same results are obtained within a few percent. At finite temperature we use finer lattices down to a0.1 fm (Nt = 12 and Nt = 16 at one point). Our new results confirm completely our previous findings. We compare the results with those of the 'hotQCD' collaboration.

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The QCD transition temperature: results with physical masses in the continuum limit II.

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.

QCD and strongly coupled gauge theories: challenges and perspectives

The relativistic correction to the QCD static interquark potential at O(1/m) is investigated nonperturbatively for the first time by using lattice Monte Carlo QCD simulations. The correction is found to be comparable with the Coulombic term of the static potential when applied to charmonium, and amounts to one-fourth of the Coulombic term for bottomonium.

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Nonperturbative determination of the QCD potential at O(1/m).

Spin-dependent potentials from lattice QCD

Overlap fermions have an exact chiral symmetry on the lattice and are thus an appropriate tool for investigating the chiral and topological structure of the QCD vacuum. We study various chiral and topological aspects of quenched gauge field configurations. This includes the localization and chiral properties of the eigenmodes, the local structure of the ultraviolet-filtered field strength tensor, as well as the structure of topological charge fluctuations. We conclude that the vacuum has a multifractal structure.

Exploring the structure of the quenched QCD vacuum with overlap fermions

Static potential, force, and flux-tube profile in 4D compact U(1) lattice gauge theory with the multi-level algorithm

The color-electric flux tube of Abelian-projected (AP) SU(2) lattice gauge theory in the maximally Abelian gauge (MAG) is examined. It is shown that the lattice Gribov copy effect in the MAG is crucial for the monopole-related parts of the flux-tube profiles. Taking into account both the gauge fixing procedure and the effect of finite quark-antiquark distance properly, the scaling property of the flux-tube profile is confirmed. The quantitative relation between the measured AP flux tube and the flux-tube solution of the U(1) dual Abelian Higgs (DAH) model is also discussed. The fitting of the AP flux tube in terms of the DAH flux tube indicates that the vacuum can be classified as a weakly type-I dual superconductor.

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Yoshiaki Koma

Papers

Nonperturbative determination of the QCD potential at O(1/m).

Spin-dependent potentials from lattice QCD

Exploring the structure of the quenched QCD vacuum with overlap fermions

Static potential, force, and flux-tube profile in 4D compact U(1) lattice gauge theory with the multi-level algorithm

Detailed study of the Abelian-projected SU(2) flux tube and its dual Ginzburg-Landau analysis