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

This White Paper presents the science case of an Electron-Ion Collider (EIC), focused on the structure and interactions of gluon-dominated matter, with the intent to articulate it to the broader nuclear science community. It was commissioned by the managements of Brookhaven National Laboratory (BNL) and Thomas Jefferson National Accelerator Facility (JLab) with the objective of presenting a summary of scientific opportunities and goals of the EIC as a follow-up to the 2007 NSAC Long Range plan. This document is a culmination of a community-wide effort in nuclear science following a series of workshops on EIC physics over the past decades and, in particular, the focused ten-week program on “Gluons and quark sea at high energies” at the Institute for Nuclear Theory in Fall 2010. It contains a brief description of a few golden physics measurements along with accelerator and detector concepts required to achieve them. It has been benefited profoundly from inputs by the users’ communities of BNL and JLab. This White Paper offers the promise to propel the QCD science program in the US, established with the CEBAF accelerator at JLab and the RHIC collider at BNL, to the next QCD frontier.

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Electron-Ion Collider: The next QCD frontier: Understanding the glue that binds us all

Unraveling hadron structure with generalized parton distributions

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

This article reviews our present understanding of QCD spin physics: the proton spin puzzle and new developments aimed at understanding the transverse structure of the nucleon. Present experimental investigations of the nucleon's internal spin structure, the theoretical interpretation of the different measurements, and the open questions and challenges for future investigation are discussed.

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The Spin Structure of the Nucleon

Hard exclusive π
 + electroproduction is investigated within the handbag approach. The prominent role of the pion-pole contribution is demonstrated. It is also shown that the experimental data require a twist-3 effect which ensues from the helicity-flip generalized parton distribution H
 T
 and the twist-3 pion wave function. The results calculated from this handbag approach are compared in detail with the experimental data on cross sections and spin asymmetries measured with a polarized target. It is also commented on consequences of this approach for exclusive π
 0 and vector-meson electroproduction.

An attempt to understand exclusive π + electroproduction

We analyze electroproduction of light vector mesons (
 $V = \rho, \phi$
 ) at small Bjorken-x in an approach that includes the gluonic generalized parton distributions and a partonic subprocess, $\gamma g \to (q\bar{q}) g$
 , $q\bar{q}\to V$
 . The subprocess is calculated to lowest order of perturbative QCD taking into account the transverse momenta of the quark and antiquark as well as Sudakov suppressions. Our approach allows us to investigate the transition amplitudes for all kinds of polarized virtual photons and polarized vector mesons. Modeling the generalized parton distributions through double distributions and using simple Gaussian wavefunctions for the vector mesons, we compute the longitudinal and transverse cross sections at large photon virtualities as well as the spin-density matrix elements for the vector mesons. Our results are in fair agreement with the findings of recent experiments performed at HERA.

Vector-meson electroproduction at small Bjorken-x and generalized parton distributions

We analyze electroproduction of light vector mesons (V=ρ,φ and ω) at small Bjorken-x in the handbag approach, in which the process factorizes into general parton distributions and partonic subprocesses. The latter are calculated in the modified perturbative approach in which the transverse momenta of the quark and antiquark forming the vector meson are retained and Sudakov suppression is taken into account. Modeling the generalized parton distributions through double distributions and using simple Gaussian wavefunctions for the vector mesons, we compute the longitudinal cross sections at large photon virtualities. The results are in fair agreement with the findings of recent experiments performed at HERA and HERMES.

The longitudinal cross section of vector meson electroproduction

The target asymmetry for electroproduction of vector mesons is investigated within the handbag approach. While the generalized parton distribution (GPD) H is taken from a previous analysis of the electroproduction cross section, we here construct the GPD E from double distributions and constrain it by the Pauli form factors of the nucleon, positivity bounds and sum rules. Predictions for the target asymmetry are given for various vector mesons and it is discussed how experimental data on the asymmetry will further constrain E and what we may learn about the angular momenta the partons carry.

The target asymmetry in hard vector-meson electroproduction and parton angular momenta

The role of transversity or helicity-flip generalized parton distributions (GPDs) in leptoproduction of vector mesons is investigated within the framework of the handbag approach. The transversity GPDs in combination with twist-3 meson wave functions occur in the amplitudes for transitions from a transversely polarized virtual photon to a longitudinal polarized vector meson. The importance of the transversity GPDs can be examined in some of the spin density matrix elements and in transverse target spin asymmetries. Using suitable parametrizations of both helicity-flip and -non-flip GPDs, which are essentially taken from our previous papers, we estimate these observables and compare the results with available data.

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S. V. Goloskokov

Papers

An attempt to understand exclusive π + electroproduction

Vector-meson electroproduction at small Bjorken-x and generalized parton distributions

The longitudinal cross section of vector meson electroproduction

The target asymmetry in hard vector-meson electroproduction and parton angular momenta

Transversity in exclusive vector-meson leptoproduction