11949 10.1140/epjc/s10052-023-11949-2 1125 31 50 Years of quantum chromodynamics Introduction and Review 02 Physical Sciences 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics 02 Physical Sciences 0299 Other Physical Sciences Review 1 636 2023 8 23 2022 12 1 2023 8 21 2023 12 12 The Author(s) 2023 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ . Funded by SCOAP3. SCOAP3 supports the goals of the International Year of Basic Sciences for Sustainable Development. 10052 83 83 12 12 Franz Gross flgros@wm.edu Eberhard Klempt klempt@hiskp.uni-bonn.de Stanley J. Brodsky Andrzej J. Buras Volker D. Burkert Gudrun Heinrich Karl Jakobs Curtis A. Meyer Kostas Orginos Michael Strickland Johanna Stachel Giulia Zanderighi Nora Brambilla Peter Braun-Munzinger Daniel Britzger Simon Capstick Tom Cohen Volker Crede Martha Constantinou Christine Davies Luigi Del Debbio Achim Denig Carleton DeTar Alexandre Deur Yuri Dokshitzer Hans Günter Dosch Jozef Dudek Monica Dunford Evgeny Epelbaum Miguel A. Escobedo Harald Fritzsch Kenji Fukushima Paolo Gambino Dag Gillberg Steven Gottlieb Per Grafstrom Massimiliano Grazzini Boris Grube Alexey Guskov Toru Iijima Xiangdong Ji Frithjof Karsch Stefan Kluth John B. Kogut Frank Krauss Shunzo Kumano Derek Leinweber Heinrich Leutwyler Hai-Bo Li Yang Li Bogdan Malaescu Chiara Mariotti Pieter Maris Simone Marzani Wally Melnitchouk Johan Messchendorp Harvey Meyer Ryan Edward Mitchell Chandan Mondal Frank Nerling Sebastian Neubert Marco Pappagallo Saori Pastore José R. Peláez Andrew Puckett Jianwei Qiu Klaus Rabbertz Alberto Ramos Patrizia Rossi Anar Rustamov Andreas Schäfer Stefan Scherer Matthias Schindler Steven Schramm Mikhail Shifman Edward Shuryak Torbjörn Sjöstrand George Sterman Iain W. Stewart Joachim Stroth Eric Swanson Guy F. de Téramond Ulrike Thoma Antonio Vairo Danny van Dyk James Vary Javier Virto Marcel Vos Christian Weiss Markus Wobisch Sau Lan Wu Christopher Young Feng Yuan Xingbo Zhao Xiaorong Zhou https://ror.org/02vwzrd76 grid.450315.6 0000 0001 2236 1964 Thomas Jefferson National Accelerator Facility 12000 Jefferson Avenue Newport News VA 23606 USA https://ror.org/03hsf0573 grid.264889.9 0000 0001 1940 3051 Department of Physics William and Mary Williamsburg VA 23187 USA grid.10388.32 0000 0001 2240 3300 Helmholtz-Institut für Strahlen- und Kernphysik Universität Bonn Nußallee 14-16 53115 Bonn Germany https://ror.org/05gzmn429 grid.445003.6 0000 0001 0725 7771 Theoretical Physics, SLAC National Accelerator Laboratory 2575 Sand Hill Road Menlo Park CA 94025 USA grid.6936.a 0000000123222966 Institute for Advanced Study Technische Universität München Lichtenbergstraße 2a 85748 Garching b. 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Johannes Gutenberg University Mainz 55128 Mainz Germany https://ror.org/03r0ha626 grid.223827.e 0000 0001 2193 0096 Department of Physics and Astronomy University of Utah Salt Lake City UT 84112 USA https://ror.org/00twb6c09 grid.6973.b 0000 0004 0567 9729 Riga Technical University Center of High Energy Physics and Accelerator Technologies Riga Latvia https://ror.org/037styt87 grid.430219.d 0000 0004 0619 3376 Petersburg Nuclear Physics Institute Gatchina Russia https://ror.org/038t36y30 grid.7700.0 0000 0001 2190 4373 Kirchhoff-Institut für Physik Ruprecht-Karls-Universität Heidelberg Heidelberg Germany https://ror.org/04tsk2644 grid.5570.7 0000 0004 0490 981X Institut für Theoretische Physik II Ruhr-Universität Bochum 44780 Bochum Germany https://ror.org/030eybx10 grid.11794.3a 0000 0001 0941 0645 Instituto Galego de Física de Altas Enería (IGFAE) Universidade de Santiago de Compostela 15782 Galicia Spain grid.5252.0 0000 0004 1936 973X Department für Physik der Universität München Theresienstraße 37 80333 Munich Germany grid.26999.3d 0000 0001 2151 536X School of Science University of Tokyo Bunkyo Tokyo 113-8654 Japan grid.470222.1 0000 0004 7471 9712 Dipartimento di Fisica Università di Torino and INFN, Sezione di Torino Via Pietro Giuria 1 10125 Turin Italy Department of Physics Carlton University 1125 Colonel By Drive Ottawa ON K1S 5B6 Canada https://ror.org/012a77v79 grid.4514.4 0000 0001 0930 2361 Department of Physics Lund University Lund Sweden grid.411377.7 0000 0001 0790 959X Department of Physics Indiana University Bloomington IN 47405 USA grid.9132.9 0000 0001 2156 142X CERN Geneva Switzerland https://ror.org/01111rn36 grid.6292.f 0000 0004 1757 1758 Dipartimento di Fisica Università di Bologna 40126 Bologna Italy https://ror.org/02crff812 grid.7400.3 0000 0004 1937 0650 Department of Physics University of Zurich Winterthurerstrasse 190 8057 Zurich Switzerland https://ror.org/044yd9t77 grid.33762.33 0000 0004 0620 4119 Joint Institute for Nuclear Research 141980 Dubna Moscow Region Russia grid.27476.30 0000 0001 0943 978X Kobayashi-Maskawa Institute (KMI)/Graduate School of Science Nagoya University Furocho, Chikusa Ward Nagoya Aichi 464-8601 Japan https://ror.org/02hpadn98 grid.7491.b 0000 0001 0944 9128 Physics Department Bielefeld University 33615 Bielefeld Germany grid.85084.31 0000000123423717 Department of Energy, Division of High Energy Physics Washington DC 20585 USA https://ror.org/047s2c258 grid.164295.d 0000 0001 0941 7177 Department of Physics-TQHN University of Maryland 82 Regents Drive College Park MD 20742 USA https://ror.org/01v29qb04 grid.8250.f 0000 0000 8700 0572 Institute for Particle Physics Phenomenology, Physics Department Durham University Durham DH1 3LE UK https://ror.org/04gpcyk21 grid.411827.9 0000 0001 2230 656X Department of Mathematics, Physics, and Computer Science, Faculty of Science Japan Women’s University 2-8-1 Mejirodai, Bunkyo-ku Tokyo 112-8681 Japan grid.410794.f 0000 0001 2155 959X Theory 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N. Yang Institute for Theoretical Physics and Department of Physics and Astronomy Stony Brook University, Stony Brook New York 11794 USA https://ror.org/042nb2s44 grid.116068.8 0000 0001 2341 2786 Center for Theoretical Physics Massachusetts Institute of Technology Cambridge MA 02139 USA https://ror.org/01an3r305 grid.21925.3d 0000 0004 1936 9000 Department of Physics and Astronomy University of Pittsburgh Pittsburgh PA 15260 USA https://ror.org/02yzgww51 grid.412889.e 0000 0004 1937 0706 Laboratorio de Física Teórica y Computacional Universidad de Costa Rica 11501 San José Costa Rica https://ror.org/02kkvpp62 grid.6936.a 0000 0001 2322 2966 Physik Department Technische Universität München James-Franck-Straße 1 85748 Garching b. München Germany https://ror.org/021018s57 grid.5841.8 0000 0004 1937 0247 Departament de Física Quántica i Astrofísica Universitat de Barcelona Martí i Franqués 1 08028 Barcelona Catalunya Spain https://ror.org/021018s57 grid.5841.8 0000 0004 1937 0247 Institut de Ciències del Cosmos (ICCUB) Universitat de Barcelona Martí i Franqués 1 08028 Barcelona Catalunya Spain grid.470047.0 0000 0001 2178 9889 IFIC (UVEG/CSIC) Valencia 46980 Paterna Spain https://ror.org/04q9esz89 grid.259237.8 0000 0001 2150 6076 Departmant of Physics Louisiana Tech University 201 Mayfield Ave Ruston LA 71272 USA https://ror.org/01y2jtd41 grid.14003.36 0000 0001 2167 3675 Department of Physics University of Wisconsin Madison WI 53706 USA https://ror.org/0245cg223 grid.5963.9 0000 0004 0491 7203 Institute of Physics Albert Ludwig University of Freiburg Freiburg im Breisgau Germany https://ror.org/02jbv0t02 grid.184769.5 0000 0001 2231 4551 Nuclear Science Division Lawrence Berkeley National Laboratory 1 Cyclotron Rd Berkeley CA 94720 USA 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,

α_{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

α_{s}

at low momentum transfers limits perturbative calculations to the high-energy region where

Q^{2} ≫ Λ_{QCD}^{2} ≃

(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 \bar{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! Harald Fritzsch: Deceased. Stanley J. Brodsky, Andrzej J. Buras, Volker D. Burkert, Gudrun Heinrich, Karl Jakobs, Curtis A. Meyer, Kostas Orginos, Michael Strickland, Johanna Stachel, Giulia Zanderighi: Convenor.