Quantum Chromodynamics, the theory of quarks and gluons, whose interactions can be described by a local SU(3) gauge symmetry with charges called “color quantum numbers”, is reviewed; the goal of this review is to provide advanced Ph.D. students a comprehensive handbook, helpful for their research. When QCD was “discovered” 50 years ago, the idea that quarks could exist, but not be observed, left most physicists unconvinced. Then, with the discovery of charmonium in 1974 and the explanation of its excited states using the Cornell potential, consisting of the sum of a Coulomb-like attraction and a long range linear confining potential, the theory was suddenly widely accepted. This paradigm shift is now referred to as theNovember revolution. It had been anticipated by the observation of scaling in deep inelastic scattering, and was followed by the discovery of gluons in three-jet events. The parameters of QCD include the running coupling constant, $$\alpha _s(Q^2)$$αs(Q2) , that varies with the energy scale $$Q^2$$Q2 characterising the interaction, and six quark masses. QCD cannot be solved analytically, at least not yet, and the large value of $$\alpha _s$$αs at low momentum transfers limits perturbative calculations to the high-energy region where $$Q^2\gg \varLambda _{{\textrm{QCD}}} ^2\simeq $$Q2≫ΛQCD2≃ (250 MeV) $$^2$$2 . Lattice QCD (LQCD), numerical calculations on a discretized space-time lattice, is discussed in detail, the dynamics of the QCD vacuum is visualized, and the expected spectra of mesons and baryons are displayed. Progress in lattice calculations of the structure of nucleons and of quantities related to the phase diagram of dense and hot (or cold) hadronic matter are reviewed. Methods and examples of how to calculate hadronic corrections to weak matrix elements on a lattice are outlined. The wide variety of analytical approximations currently in use, and the accuracy of these approximations, are reviewed. These methods range from the Bethe–Salpeter, Dyson–Schwinger coupled relativistic equations, which are formulated in both Minkowski or Euclidean spaces, to expansions of multi-quark states in a set of basis functions using light-front coordinates, to the AdS/QCD method that imbeds 4-dimensional QCD in a 5-dimensional deSitter space, allowing confinement and spontaneous chiral symmetry breaking to be described in a novel way. Models that assume the number of colors is very large, i.e. make use of the large $$N_c$$Nc -limit, give unique insights. Many other techniques that are tailored to specific problems, such as perturbative expansions for high energy scattering or approximate calculations using the operator product expansion are discussed. The very powerful effective field theory techniques that are successful for low energy nuclear systems (chiral effective theory), or for non-relativistic systems involving heavy quarks, or the treatment of gluon exchanges between energetic, collinear partons encountered in jets, are discussed. The spectroscopy of mesons and baryons has played an important historical role in the development of QCD. The famous X,Y,Z states – and the discovery of pentaquarks – have revolutionized hadron spectroscopy; their status and interpretation are reviewed as well as recent progress in the identification of glueballs and hybrids in light-meson spectroscopy. These exotic states add to the spectrum of expected $$q{{\bar{q}}}$$qq¯ mesons andqqqbaryons. The progress in understanding excitations of light and heavy baryons is discussed. The nucleon as the lightest baryon is discussed extensively, its form factors, its partonic structure and the status of the attempt to determine a three-dimensional picture of the parton distribution. An experimental program to study the phase diagram of QCD at high temperature and density started with fixed target experiments in various laboratories in the second half of the 1980s, and then, in this century, with colliders. QCD thermodynamics at high temperature became accessible to LQCD, and numerical results on chiral and deconfinement transitions and properties of the deconfined and chirally restored form of strongly interacting matter, called the Quark–Gluon Plasma (QGP), have become very precise by now. These results can now be confronted with experimental data that are sensitive to the nature of the phase transition. There is clear evidence that the QGP phase is created. This phase of QCD matter can already be characterized by some properties that indicate, within a temperature range of a few times the pseudocritical temperature, the medium behaves like a near ideal liquid. Experimental observables are presented that demonstrate deconfinement. High and ultrahigh density QCD matter at moderate and low temperatures shows interesting features and new phases that are of astrophysical relevance. They are reviewed here and some of the astrophysical implications are discussed. Perturbative QCD and methods to describe the different aspects of scattering processes are discussed. The primary parton–parton scattering in a collision is calculated in perturbative QCD with increasing complexity. The radiation of soft gluons can spoil the perturbative convergence, this can be cured by resummation techniques, which are also described here. Realistic descriptions of QCD scattering events need to model the cascade of quark and gluon splittings until hadron formation sets in, which is done by parton showers. The full event simulation can be performed with Monte Carlo event generators, which simulate the full chain from the hard interaction to the hadronic final states, including the modelling of non-perturbative components. The contribution of the LEP experiments (and of earlier collider experiments) to the study of jets is reviewed. Correlations between jets and the shape of jets had allowed the collaborations to determine the “color factors” – invariants of the SU(3) color group governing the strength of quark–gluon and gluon–gluon interactions. The calculated jet production rates (using perturbative QCD) are shown to agree precisely with data, for jet energies spanning more than five orders of magnitude. The production of jets recoiling against a vector boson, $$W^\pm $$W± orZ, is shown to be well understood. The discovery of the Higgs boson was certainly an important milestone in the development of high-energy physics. The couplings of the Higgs boson to massive vector bosons and fermions that have been measured so far support its interpretation as mass-generating boson as predicted by the Standard Model. The study of the Higgs boson recoiling against hadronic jets (without or with heavy flavors) or against vector bosons is also highlighted. Apart from the description of hard interactions taking place at high energies, the understanding of “soft QCD” is also very important. In this respect, Pomeron – and Odderon – exchange, soft and hard diffraction are discussed. Weak decays of quarks and leptons, the quark mixing matrix and the anomalous magnetic moment of the muon are processes which are governed by weak interactions. However, corrections by strong interactions are important, and these are reviewed. As the measured values are incompatible with (most of) the predictions, the question arises: are these discrepancies first hints for New Physics beyond the Standard Model? This volume concludes with a description of future facilities or important upgrades of existing facilities which improve their luminosity by orders of magnitude. The best is yet to come!

We review the present understanding of the spin structure of protons and neutrons, the fundamental building blocks of nuclei collectively known as nucleons. The field of nucleon spin provides a critical window for testing Quantum Chromodynamics (QCD), the gauge theory of the strong interactions, since it involves fundamental aspects of hadron structure which can be probed in detail in experiments, particularly deep inelastic lepton scattering on polarized targets. QCD was initially probed in high energy deep inelastic lepton scattering with unpolarized beams and targets. With time, interest shifted from testing perturbative QCD to illuminating the nucleon structure itself. In fact, the spin degrees of freedom of hadrons provide an essential and detailed verification of both perturbative and nonperturbative QCD dynamics. Nucleon spin was initially thought of coming mostly from the spin of its quark constituents, based on intuition from the parton model. However, the first experiments showed that this expectation was incorrect. It is now clear that nucleon physics is much more complex, involving quark orbital angular momenta as well as gluonic and sea quark contributions. Thus, the nucleon spin structure remains a most active aspect of QCD research, involving important advances such as the developments of generalized parton distributions (GPD) and transverse momentum distributions (TMD). Elastic and inelastic lepton-proton scattering, as well as photoabsorption experiments provide various ways to investigate non-perturbative QCD. Fundamental sum rules—such as the Bjorken sum rule for polarized photoabsorption on polarized nucleons—are also in the non-perturbative domain. This realization triggered a vigorous program to link the low energy effective hadronic description of the strong interactions to fundamental quarks and gluon degrees of freedom of QCD. This has also led to advances in lattice gauge theory simulations of QCD and to the development of holographic QCD ideas based on the AdS/CFT or gauge/gravity correspondence, a novel approach providing a well-founded semiclassical approximation to QCD. Any QCD-based model of the nucleon’s spin and dynamics must also successfully account for the observed spectroscopy of hadrons. Analytic calculations of the hadron spectrum, a long sought goal of QCD research, have now being realized using light-front holography and superconformal quantum mechanics, a formalism consistent with the results from nucleon spin studies. We begin this review with a phenomenological description of nucleon structure in general and of its spin structure in particular, aimed to engage non-specialist readers. Next, we discuss the nucleon spin structure at high energy, including topics such as Dirac’s front form and light-front quantization which provide a frame-independent, relativistic description of hadron structure and dynamics, the derivation of spin sum rules, and a direct connection to the QCD Lagrangian. We then discuss experimental and theoretical advances in the nonperturbative domain—in particular the development of light-front holographic QCD and superconformal quantum mechanics, their predictions for the spin content of nucleons, the computation of PDFs and of hadron masses.

We report the total and differential cross sections for $J/\psi$ photoproduction with the large acceptance GlueX spectrometer for photon beam energies from the threshold at 8.2 GeV up to 11.44 GeV and over the full kinematic range of momentum transfer squared, $t$. Such coverage facilitates the extrapolation of the differential cross sections to the forward ($t=0$) point beyond the physical region. The forward cross section is used by many theoretical models and plays an important role in understanding $J/\psi$ photoproduction and its relation to the $J/\psi$-proton interaction. These measurements of $J/\psi$ photoproduction near threshold are also crucial inputs to theoretical models that are used to study important aspects of the gluon structure of the proton, such as the gluon generalized parton distribution of the proton, the mass radius of the proton, and the trace anomaly contribution to the proton mass. We observe possible structures in the total cross section energy dependence and find evidence for contributions beyond gluon exchange in the differential cross section close to threshold, both of which are consistent with contributions from open-charm intermediate states.

Establishing an explicit connection between the long distance physics of confinement and the dynamical interactions of quarks and gluons at short distances has been a long-sought goal of quantum chromodynamics. Using holographic QCD, we derive a direct analytic relation between the scale $\kappa$ which determines the masses of hadrons and the scale $\Lambda_{s}$ which controls the predictions of perturbative QCD at very short distances. The resulting prediction $\Lambda_{s}=0.341\pm0.032$ GeV in the $\overline{MS}$ scheme agrees well with the experimental average $0.339\pm0.016$ GeV. We also derive a relation between $\Lambda_{s}$ and the QCD string tension $\sigma$. This connection between the fundamental hadronic scale underlying the physics of quark confinement and the perturbative QCD scale controlling hard collisions can be carried out in any renormalization scheme.Comment: 11 pages, 4 figures. Final version published in Phys. Lett.

The QCD running coupling αs(Q2) sets the strength of the interactions of quarks and gluons as a function of the momentum transfer Q. The Q2 dependence of the coupling is required to describe hadronic interactions at both large and short distances. In this article we adopt the light-front holographic approach to strongly-coupled QCD, a formalism which incorporates confinement, predicts the spectroscopy of hadrons composed of light quarks, and describes the low-Q2 analytic behavior of the strong coupling αs(Q2). The high-Q2 dependence of the coupling αs(Q2) is specified by perturbative QCD and its renormalization group equation. The matching of the high and low Q2 regimes of αs(Q2) then determines the scale Q0 which sets the interface between perturbative and nonperturbative hadron dynamics. The value of Q0 can be used to set the factorization scale for DGLAP evolution of hadronic structure functions and the ERBL evolution of distribution amplitudes. We discuss the scheme-dependence of the value of Q0 and the infrared fixed-point of the QCD coupling. Our analysis is carried out for the MS‾, g1, MOM and V renormalization schemes. Our results show that the discrepancies on the value of αs at large distance seen in the literature can be explained by different choices of renormalization schemes. We also provide the formulae to compute αs(Q2) over the entire range of space-like momentum transfer for the different renormalization schemes discussed in this article