Eur. Phys. J. C (2023) 83: 1125
https://doi.org/10.1140/epjc/s10052-023-11949-2

Review

50 Years of quantum chromodynamics

Introduction and Review

¹ Thomas Jefferson National Accelerator Facility, 12000 Jefferson Avenue, 23606, Newport News, VA, USA
² Department of Physics, William and Mary, 23187, Williamsburg, VA, USA
³ Helmholtz-Institut für Strahlen- und Kernphysik, Universität Bonn, Nußallee 14-16, 53115, Bonn, Germany
⁴ Theoretical Physics, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, 94025, Menlo Park, CA, USA
⁵ Institute for Advanced Study, Technische Universität München, Lichtenbergstraße 2a, 85748, Garching b. München, Germany
⁶ Institut für Theoretische Physik, Karlsruher Institut für Technologie (KIT), 76128, Karlsruhe, Germany
⁷ Physikalisches Institut, Universität Freiburg, 79104, Freiburg, Germany
⁸ Carnegie Mellon University, 15213, Pittsburgh, PA, USA
⁹ Department of Physics, Kent State University, 800 E Summit St, 44240, Kent, OH, USA
¹⁰ Physikalisches Institut, Universität Heidelberg, 69120, Heidelberg, Germany
¹¹ Max-Planck-Institut für Physik, Föhringer Ring 6, 80805, Munich, Germany
¹² Physik Department, Technische Universität München, James-Franck-Straße 1, 85748, Garching b. München, Germany
¹³ Munich Data Science Institute, Technische Universität München, Walther-von-Dyck-Straße-10, 85748, Garching b. München, Germany
¹⁴ Extreme Matter Institute EMMI, GSI, 64291, Darmstadt, Germany
¹⁵ Department of Physics, Florida State University, 32306, Tallahassee, FL, USA
¹⁶ Department of Physics, University of Maryland, 20742, College Park, MD, USA
¹⁷ Physics Department, Temple University, 1925 N. 12th Street, 19122, Philadelphia, PA, USA
¹⁸ School of Physics and Astronomy, University of Glasgow, G12 8QQ, Glasgow, UK
¹⁹ Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, EH9 3FD, Edinburgh, UK
²⁰ PRISMA + Cluster of Excellence and Institut für Kernphysik and Helmholtz Institute Mainz, Johannes Gutenberg University Mainz, 55128, Mainz, Germany
²¹ Department of Physics and Astronomy, University of Utah, 84112, Salt Lake City, UT, USA
²² Riga Technical University Center of High Energy Physics and Accelerator Technologies, Riga, Latvia
²³ Petersburg Nuclear Physics Institute, Gatchina, Russia
²⁴ Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
²⁵ Institut für Theoretische Physik II, Ruhr-Universität Bochum, 44780, Bochum, Germany
²⁶ Instituto Galego de Física de Altas Enería (IGFAE), Universidade de Santiago de Compostela, 15782, Galicia, Spain
²⁷ Department für Physik der Universität München, Theresienstraße 37, 80333, Munich, Germany
²⁸ School of Science, University of Tokyo, 113-8654, Bunkyo, Tokyo, Japan
²⁹ Dipartimento di Fisica, Università di Torino and INFN, Sezione di Torino, Via Pietro Giuria 1, 10125, Turin, Italy
³⁰ Department of Physics, Carlton University, 1125 Colonel By Drive, K1S 5B6, Ottawa, ON, Canada
³¹ Department of Physics, Lund University, Lund, Sweden
³² Department of Physics, Indiana University, 47405, Bloomington, IN, USA
³³ CERN, Geneva, Switzerland
³⁴ Dipartimento di Fisica, Università di Bologna, 40126, Bologna, Italy
³⁵ Department of Physics, University of Zurich, Winterthurerstrasse 190, 8057, Zurich, Switzerland
³⁶ Joint Institute for Nuclear Research, 141980, Dubna, Moscow Region, Russia
³⁷ Kobayashi-Maskawa Institute (KMI)/Graduate School of Science Nagoya University, Furocho, Chikusa Ward, 464-8601, Nagoya, Aichi, Japan
³⁸ Physics Department, Bielefeld University, 33615, Bielefeld, Germany
³⁹ Department of Energy, Division of High Energy Physics, 20585, Washington, DC, USA
⁴⁰ Department of Physics-TQHN, University of Maryland, 82 Regents Drive, 20742, College Park, MD, USA
⁴¹ Institute for Particle Physics Phenomenology, Physics Department, Durham University, DH1 3LE, Durham, UK
⁴² Department of Mathematics, Physics, and Computer Science, Faculty of Science, Japan Women’s University, 2-8-1 Mejirodai, Bunkyo-ku, 112-8681, Tokyo, Japan
⁴³ Theory Center, Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), 1-1 Oho, 305-0801, Tsukuba, Ibaraki, Japan
⁴⁴ Centre for the Subatomic Structure of Matter (CSSM), Department of Physics, The University of Adelaide, 5005, Adelaide, SA, Australia
⁴⁵ Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland
⁴⁶ Institute of High Energy Physics, 100049, Beijing, People’s Republic of China
⁴⁷ University of Chinese Academy of Sciences, 100049, Beijing, People’s Republic of China
⁴⁸ University of Science and Technology of China, No. 96, JinZhai Road, Baohe District, 230026, Hefei, Anhui, People’s Republic of China
⁴⁹ LPNHE, Sorbonne Université, Université de Paris Cité, CNRS/IN2P3, 75252, Paris, France
⁵⁰ INFN, Sezione di Torino, Via Pietro Giuria 1, 10125, Turin, Italy
⁵¹ Deptarment of Physics and Astronomy, Iowa State University, 50011, Ames, IA, USA
⁵² Dipartimento di Física, Università di Genova and INFN, Sezione di Genova, Via Dodecaneso 33, 16146, Genoa, Italy
⁵³ GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstraße 1, 64291, Darmstadt, Germany
⁵⁴ Department of Physics, Indiana University Bloomington, 107 S. Indiana Avenue, 47405, Bloomington, IN, USA
⁵⁵ Institute of Modern Physics, Chinese Academy of Sciences, 730000, Lanzhou, Gansu, People’s Republic of China
⁵⁶ Helmholtz Forschungsakademie Hessen für FAIR (HFHF), GSI Helmholtzzentrum für Schwerionenforschung, Campus Frankfurt, Frankfurt, Germany
⁵⁷ Goethe Universität, Institut für Kernphysik, Max-von-Laue-Str. 1, 60438, Frankfurt, Germany
⁵⁸ Dipartimento Interateneo di Fisica, Università di Bari and INFN, Sezione di Bari, Via Amendola 173, 70125, Bari, Italy
⁵⁹ Department of Physics and McDonnell Center for the Space Sciences, Washington University in Saint Louis, 63130, Saint Louis, MO, USA
⁶⁰ Departamento de Física Teórica and IPARCOS, Universidad Complutense, 28040, Madrid, Spain
⁶¹ University of Connecticut, 06269, Storrs, CT, USA
⁶² ETP, KIT, Postfach 6980, 76128, Karlsruhe, Germany
⁶³ IFIC (UVEG/CSIC) Valencia, C. del Catedrático José Beltrán 2, 46980, Paterna, Spain
⁶⁴ INFN, Laboratori Nazionali di Frascati, 00044, Frascati, Italy
⁶⁵ National Nuclear Research Center, 1000, Baku, Azerbaijan
⁶⁶ Institut für Theoretische Physik, Universität Regensburg, 93040, Regensburg, Germany
⁶⁷ Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, 55099, Mainz, Germany
⁶⁸ Department of Physics and Astronomy, University of South Carolina, 29208, Columbia, SC, USA
⁶⁹ Département de Physique Nucléaire et Corpusculaire, Université de Genève, 1205, Geneva, Switzerland
⁷⁰ School of Physics and Astronomy, University of Minnesota, 55455, Minneapolis, MN, USA
⁷¹ Department of Physics and Astronomy, Stony Brook University, 11794, Stony Brook, NY, USA
⁷² Department of Astronomy and Theoretical Physics, Lund University, Box 43, 221 00, Lund, Sweden
⁷³ C. N. Yang Institute for Theoretical Physics and Department of Physics and Astronomy Stony Brook University, Stony Brook, 11794, New York, USA
⁷⁴ Center for Theoretical Physics, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA
⁷⁵ Department of Physics and Astronomy, University of Pittsburgh, 15260, Pittsburgh, PA, USA
⁷⁶ Laboratorio de Física Teórica y Computacional, Universidad de Costa Rica, 11501, San José, Costa Rica
⁷⁷ Physik Department, Technische Universität München, James-Franck-Straße 1, 85748, Garching b. München, Germany
⁷⁸ Departament de Física Quántica i Astrofísica, Universitat de Barcelona, Martí i Franqués 1, 08028, Barcelona, Catalunya, Spain
⁷⁹ Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, Martí i Franqués 1, 08028, Barcelona, Catalunya, Spain
⁸⁰ IFIC (UVEG/CSIC) Valencia, 46980, Paterna, Spain
⁸¹ Departmant of Physics, Louisiana Tech University, 201 Mayfield Ave, 71272, Ruston, LA, USA
⁸² Department of Physics, University of Wisconsin, 53706, Madison, WI, USA
⁸³ Institute of Physics, Albert Ludwig University of Freiburg, Freiburg im Breisgau, Germany
⁸⁴ Nuclear Science Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Rd, 94720, Berkeley, CA, USA

^b klempt@hiskp.uni-bonn.de

Received: 1 December 2022
Accepted: 21 August 2023
Published online: 12 December 2023

Abstract

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 the November 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, ${\alpha }_s(Q^2)$, that varies with the energy scale $Q^2$ characterising the interaction, and six quark masses. QCD cannot be solved analytically, at least not yet, and the large value of ${\alpha }_s$ at low momentum transfers limits perturbative calculations to the high-energy region where $Q^2\gg {\Lambda }_{\text{QCD}}^2\simeq$ (250 MeV)${}^2$. 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 $N_c$-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 $q\overline{q}$ mesons and qqq baryons. 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, $W^{\pm }$ or Z, 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!