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 \(Q^2\gg \varLambda _{{\textrm{QCD}}} ^2\simeq \) (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 \(q{{\bar{q}}}\) 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!
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This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Data sharing is not applicable to this article as no datasets were generated or analysed for this review.]
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Acknowledgements
The help of many people is acknowledged: Chiara Mariotti thanks A.C. Marini and A. Mecca; Per Grafstrom thanks Peter Jenni, Valery Khoze and Mikhail Ryskin who were kind enough to read his text and given him many useful comments and suggestions to improve his contribution; Andreas Schafer thanks the University of the Basque Country, Bilbao for hospitality; Mikhail Shifman is grateful to Alexander Khodjamirian, Alexander Lenz and Blaženka Melić for very useful discussions and comments; S. Kumano thanks A. Dote, M. Kitazawa, K. Ozawa, S. Sawada, T. Takahashi, M. Takizawa, and S. Yokkaichi for suggestions on the J-PARC experiments; Stanley J. Brodsky, Guy F. de Téramond and Hans Günter Dosch are grateful to Tianbo Liu, Raza Sabbir Sufian and Alexandre Deur, who have greatly contributed to the new applications of the holographic ideas reviewed in this volume. Eberhard Klempt and Ulrike Thoma thank Andrey V. Sarantsev for many years of collaboration on meson and baryon spectroscopy. Peter Braun-Munzinger, Anar Rustamov, and Johanna Stachel acknowledge continued and long-term collaboration with Anton Andronic and Krzysztof Redlich on many of the topics described in their contribution; Daniel Britzger, Klaus Rabbertz and Markus Wobish would like to thank Monica Dunford, Karl Jakobs, and Jürgen Scheins for their careful reading of the manuscript; Kostas Orginos thanks Carl Carlson for many discussions on the charge radius and Anatoly Radyushkin for many discussions on aspects of hadron structure. Volker Burkert expresses his gratitude to Inna Aznauryan for many years of collaboration on the subject of electroproduction of nucleon resonances, which has lead to many of the results discussed in his contribution. He also wishes to acknowledge Victor Mokeev for numerous discussions and collaboration on many aspects of resonance electroproduction. Finally, Volker Burkert thanks Francois-Xavier Girod for contributing Fig. 232 to his section.
The editors wish to thank Brad Sawatzky for setting up the original Overleaf site and for many hours of invaluable technical help, essential to the production of this volume, and Nora Brambilla, Karl Jakobs, and J. Peter LePage for several long discussions at the early stages in the preparation of this volume that influenced its structure and content.
The editors express their gratitude to Dieter Haidt, the Review Editor of the European Physical Journal C, for continuous encouragement and valuable suggestions. The authors received funding from
Australia:
National Computational Infrastructure (NCI) and the Australian Research Council through Grants No. DP190102215 and DP210103706 (D. Leinweber).
People’s Republic of China:
National Natural Science Foundation of China (NSFC) under Contracts Nos. 11935018, 11875054 (H-B. Li).
France
CNRS and ANR (B. Malaescu).
Germany:
The Bundesministerium für Bildung und Forschung (BMBF) (M. Dunford, E. Epelbaum, K. Jakobs, S. Neubert, and K. Rabbertz);
Gesellschaft für Schwerionenforschung Gmb (GSI), Darmstadt, Germany (J. Messchendorp);
The Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the funds provided to the Sino-German Collaborative Research Center TRR110 “Symmetries and the Emergence of Structure in QCD” (DFG Project-ID 196253076-TRR 110) (N. Brambilla, E. Epelbaum, U. Thoma, and A. Vairo);
The DFG Collaborative Research Centre “SFB 1225 (ISOQUANT)” (P. Braun-Munzinger, A. Rustamov, and J. Stachel);
The DFG Collaborative Research Centre 396021762-TRR 257, “Particle Physics Phenomenology after the Higgs Discovery” (G. Heinrich);
The DFG Collaborative Research Centre 315477589-TRR 211, “Strong interaction matter under extreme conditions” (F. Karsch);
The DFG Emmy-Nöther project NE2185/1-1: “Spektroskopie exotischer Baryonen mit LHCb” (S. Neubert)
DFG individual grant, Project Number 455635585
(A. Denig);
The Excellence Cluster ORIGINS (http://www.origins-cluster.de), funded by the DFG, German Research Foundation, Excellence Strategy, EXC-2094, 390783311 (N. Brambilla, A. J. Buras, and A. Vairo);
The Helmholtz Forschungsakademie Hessen für FAIR (HFHF) (F. Nerling and J. Stroth);
The Ministry of Culture and Science of the State of North Rhine-Westphalia (MKW NRW, Germany), project “NRW-FAIR” (S. Neubert and U. Thoma);
European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program through grant agreements 885150-NuclearTheory (E. Epelbaum); 771971-SIMDAMA (H. Meyer); 824093-STRONG2020 (U. Thoma).
Italy:
Italian Ministry of Research (MIUR) under grant PRIN 20172LNEEZ (P. Gambino and S. Marzani)
Japan:
Japan Society for the Promotion of Science (JSPS) Grants-in-Aid for Scientific Research (KAKENHI):
Grant Number 19K03830 (S. Kumano);
Grant Number 18H05226(T. Iijima).
Spain
MINECO through the “Ramón y Cajal” program RYC-2017-21870, the “Unit of Excellence María de Maeztu 2020–2023” award to the Institute of Cosmos Sciences (CEX2019-000918-M) and from the grants PID2019-105614GB-C21 and 2017-SGR-929 (J. Virto);
The Spanish Ministerio de Ciencia e Innovación grant PID2019-106080GB-C21 and the European Union’s Horizon 2020 research and innovation program under grant agreement No 824093 (STRONG2020) (J. R. Peláez);
European Research Council project ERC-2018-ADG-835105 YoctoLHC, by Maria de Maetzu excellence program under project CEX2020-001035-M, by Spanish Research State Agency under project PID2020-119632GB-I00, and by Xunta de Galicia (Centro singular de investigación de Galicia accreditation 2019–2022), by European Union ERDF (M. Escobedo);
The Spanish Ministerio de Ciencia e Innovación grant PID2021-122134NB-C21 and by the Generalitat Valenciana under grant CIPROM/2021/073 and by CSIC under grant LINKB20065 (M. Vos).
Sweden:
The Swedish Research Council, contract number 2016-05996 (T. Sjöstrand).
Switzerland:
The European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 948254) and from the Swiss National Science Foundation (SNSF) under Eccellenza grant number PCEFP2-194658 (S. Schramm).
UK
Science and Technology Facilities Council (STCF): Ernest Rutherford Fellowship grants
ST/T000945/1 and ST/P000746/1 (C. Davies);
ST/P000630/1 (L. Del Debbio);
ST/V003941/1 (D. Van Dyk);
Royal Society Wolfson fellowship and STFC (F. Krauss).
USA:
The US Department of Energy, Office of Science, Office of Nuclear Physics (contract DE-AC05-06 OR23177-under which Jefferson Science Associates operates, LLC, operates Jefferson Lab) (V. Burkert, J. Dudek, F. Gross, W. Melnitchouk, J. Qiu, and P. Rossi);
DE-AC02-76SF00515 (S. J. Brodsky);
Early Career Award under Grant No. DE-SC0020405 (M. Constantinou);
DE-FG02-92ER40735 V. Crede);
DE-SC0018416 (J. Dudek);
DESC0018223 (P. Maris and J. Vary)
DE-SC0023495 (P. Maris and J. Vary)
DE-FG02-87ER40315 (C. Meyer);
DE-FG02-04ER41302 (K. Orginos);
DE-SC0021027 (S. Pastore);
DE-SC0021200 (A. Puckett);
DE-SC0019647 (M. Schindler);
DE-AC02-05CH11231 (A. Schafer, F. Yuan);
DE-SC0011842 (M. Shifman);
DE-SC0013470 (M. Strickland)
DE-SC0011090 and Simons Foundation Investigator grant 327942 (I. Stewart);
DE-FG02-87ER40371 (J. Vary)
DE-FG02-95ER40896, (S. L. Wu);
University of Wisconsin through the Wisconsin Alumni Research Foundation and the Vilas Foundation (S. L. Wu);
The National Science Foundation under grants PHY-1915093 and PHY-2210533 (G. Sterman);
NSF grant PHY20-13064 (C. DeTar).
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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
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Gross, F., Klempt, E., Brodsky, S.J. et al. 50 Years of quantum chromodynamics. Eur. Phys. J. C 83, 1125 (2023). https://doi.org/10.1140/epjc/s10052-023-11949-2
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DOI: https://doi.org/10.1140/epjc/s10052-023-11949-2