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

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

This report reviews the study of open heavy-flavour and quarkonium production in high-energy hadronic collisions, as tools to investigate fundamental aspects of Quantum Chromodynamics, from the proton and nucleus structure at high energy to deconfinement and the properties of the Quark–Gluon Plasma. Emphasis is given to the lessons learnt from LHC Run 1 results, which are reviewed in a global picture with the results from SPS and RHIC at lower energies, as well as to the questions to be addressed in the future. The report covers heavy flavour and quarkonium production in proton–proton, proton–nucleus and nucleus–nucleus collisions. This includes discussion of the effects of hot and cold strongly interacting matter, quarkonium photoproduction in nucleus–nucleus collisions and perspectives on the study of heavy flavour and quarkonium with upgrades of existing experiments and new experiments. The report results from the activity of the SaporeGravis network of the I3 Hadron Physics programme of the European Union 7
 $$\mathrm{th}$$
 Framework Programme.

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Heavy-flavour and quarkonium production in the LHC era: from proton–proton to heavy-ion collisions

Phenomenology of heavy meson chiral lagrangians

We present predictions for a variety of single-inclusive observables that stem from the production of charm and bottom quark pairs at the 7 TeV LHC. They are obtained within the FONLL semi-analytical framework, and with two "Monte Carlo + NLO" approaches, MC@NLO and POWHEG. Results are given for final states and acceptance cuts that are as close as possible to those used by experimental collaborations and, where feasible, are compared to LHC data.

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Theoretical predictions for charm and bottom production at the LHC

The dominant production mechanism for heavy-quark--antiquark bound states with large transverse momentum is fragmentation, the splitting of a high energy parton into a quarkonium state and other partons. We show that the fragmentation functions D(z,\ensuremath{\mu}) describing these processes can be calculated using perturbative QCD. We calculate the fragmentation functions for a gluon to split into S-wave quarkonium states to leading order in the QCD coupling constant.

Gluon fragmentation into heavy quarkonium

The perturbative QCD fragmentation functions for a heavy quark to fragment into heavy-light mesons are studied in the heavy-quark limit. The fragmentation functions for {ital S}-wave pseudoscalar and vector mesons are calculated to next-to-leading order in the heavy-quark mass expansion using the methods of heavy-quark effective theory. The results agree with the {ital m}{sub {ital b}}{r_arrow}{infinity} limit of the perturbative QCD fragmentation functions for {ital {bar b}} into {ital B}{sub {ital c}} and {ital B}{sub {ital c}}{sup *}. We discuss the application of the perturbative QCD fragmentation functions as a model for the fragmentation of heavy quarks into heavy-light mesons. Using this model we predict the fraction {ital P}{sub {ital V}} of heavy-light mesons that are produced in the vector meson state as functions of the longitudinal momentum fraction {ital z} and the transverse momentum relative to the jet axis. The fraction {ital P}{sub {ital V}} is predicted to vary from about 1/2 at small {ital z} to almost 3/4 near {ital z}=1.

Perturbative QCD fragmentation functions as a model for heavy-quark fragmentation

▪ Abstract Recent data from the Tevatron collider have revealed that the production rate of prompt charmonium at large transverse momentum is orders of magnitude larger than the best theories of a few years ago had predicted. These surprising results can be understood by taking into account two recent developments that have dramatically revised the theoretical description of heavy-quarkonium production. The first is the realization that fragmentation must dominate at large transverse momentum, which implies that most charmonium in this kinematic region is produced by the hadronization of individual high-pT partons. The second is the development of a factorization formalism for quarkonium production based on nonrelativistic QCD that allows the formation of charmonium from color-octet pairs to be treated systematically. This review summarizes these theoretical developments and their implications for quarkonium production in high-energy colliders.

Production of heavy quarkonium in high-energy colliders

The fragmentation functions for gluons to split into P-wave heavy quarkonium states are calculated to leading order in the QCD coupling constant. Long-distance effects are factored into two nonperturbative parameters: the derivative of the radial wavefunction at the origin and a second parameter related to the probability for a heavy-quark-antiquark pair that is produced in a color-octet S-wave state to form a color-singlet P-wave bound state. The fragmentation probabilities for a high transverse momentum gluon to split into the P-wave charmonium states \chi_{c0}, \chi_{c1}, and \chi_{c2} are estimated to be 0.4 \times 10^{-4}, 1.8 \times 10^{-4}, and 2.4 \times 10^{-4}, respectively. This fragmentation process may account for a significant fraction of the rate for the inclusive production of \chi_{cJ} at large transverse momentum in p \bar p colliders.

Gluon fragmentation into P-wave heavy quarkonium.

The direct production rate of {ital J}/{psi} via the color-octet mechanism is calculated at the {ital Z} resonance. The color-octet production process {ital Z}{r_arrow}{ital J}/{psi}{bar {ital qq}} is shown to have a substantial branching ratio as well as a distinctive energy spectrum, which can be used as a powerful tool to distinguish from the color-singlet direct production of the {ital J}/{psi}. {copyright} {ital 1996 The American Physical Society.}

Tzu Chiang Yuan

Papers

Gluon fragmentation into heavy quarkonium

Perturbative QCD fragmentation functions as a model for heavy-quark fragmentation

Production of heavy quarkonium in high-energy colliders

Gluon fragmentation into P-wave heavy quarkonium.

Color-octet quarkonium production at the Z pole.