nLab QCD

under construction

Idea

Quantum chromodynamics (“QCD”) is the quantum field theory of Yang-Mills theory: it describes the quantum theory of gluons and quarks.

The corresponding effective field theory that describes confined bound states such as protons is quantum hadrodynamics.

Properties

Confinements

See at confinement.

Asymptotic freedom

See at asymptotic freedom.

Trace anomaly

See at QCD trace anomaly.

Phase diagram

QCD has an intricate phase diagram (e.g. Shuryak 96 Hands 01, Schaefer 05), phases including

• quark-gluon plasma,

• colour superconductivity,

• …

Related concepts

• D=2 QCD

• lattice QCD

• super QCD

• confinement

  • chiral perturbation theory, quantum hadrodynamics

  • quark bag model, Cheshire cat principle

• AdS/QCD correspondence

• Gross-Neveu model

• QCD cosmology

• quantum field theory

  • gauge theory

    • Yang-Mills theory

      • quantization of Yang-Mills theory

    • QED

    • QCD

      • quark, gluon

      • bound states:

        glueballs, hadrons (mesons, baryons)

      • colour charge, flavour (particle physics)

      • instanton in QCD, caloron, skyrmion

      • confinement

      • mass gap

      • quark-gluon plasma

      • colour superconductivity

    • electroweak field

• string theory results applied elsewhere

References

General

Introduction and review:

• Jiri Chyla, Quarks, partons and Quantum Chromodynamics, (spire:674163/), pdf)

• Peter Skands, Introduction to QCD (arXiv:1207.2389, doi:10.1142/9789814525220_0008)

• Y. Kurihara, QCD at LHC for beginners Lesson 1 (pdf), Lesson 2 (pdf) Lesson 3 (pdf)

• Particle Data Group, Quantum Chromodynamics (pdf)

• Franz Gross, Eberhard Klempt et al., 50 Years of Quantum Chromodynamics, EJPC [arXiv:2212.11107]

Textbooks:

• Robert E. Marshak, Chapter 5 of: Conceptual Foundations of Modern Particle Physics, World Scientific 1993 (doi:10.1142/1767)

• B. L. Ioffe , V. S. Fadin, L. N. Lipatov, Quantum Chromodynamics – Perturbative and Nonperturbative Aspects, Cambridge University Press (2010) (doi:10.1017/CBO9780511711817)

with emphasis on phenomenology:

• Francis Halzen, Alan Martin, Quarks and Leptons: An Introductory Course in Modern Particle Physics, Wiley 1984 (pdf)

On QCD’s running coupling constant:

• Alexandre Deur, Stanley Brodsky, Guy de Teramond, The QCD Running Coupling, Prog. Part. Nuc. Phys. 90 1 (2016) (arXiv:1604.08082, doi:10.1016/j.ppnp.2016.04.003)

Rigorous construction as a perturbative quantum field theory via causal perturbation theory is discussed in

• Günter Scharf, chapter 3 of Quantum Gauge Theories – A True Ghost Story, Wiley 2001

Survey with emphasis on non-perturbative effects:

• Brambilla et al., QCD and strongly coupled gauge theories - challenges and perspectives, Eur Phys J C Part Fields. 2014; 74(10): 2981 (doi:10.1140/epjc/s10052-014-2981-5)

• Giorgio Comitini, Perturbative methods in non-perturbative Quantum Chromodynamics [arXiv:2306.13624]

Discussion of on-shell methods in QCD perturbation theory includes

• Zvi Bern, Lance Dixon, David Kosower, On-Shell Methods in Perturbative QCD (arXiv:0704.2798)

See also

• Bo-Lun Du, Xing-Gang Wu, Jian-Ming Shen, Stanley J. Brodsky, Extending the Predictive Power of Perturbative QCD (arXiv:1807.11144)

• Christian Drischler, Wick Haxton, Kenneth McElvain, Emanuele Mereghetti, Amy Nicholson, Pavlos Vranas, André Walker-Loud, Towards grounding nuclear physics in QCD (arxiv:1910.07961)

As thermal field theory:

• Jacopo Ghiglieri, Aleksi Kurkela, Michael Strickland, Aleksi Vuorinen, Perturbative Thermal QCD: Formalism and Applications (arXiv:2002.10188)

Phase diagram

On the phase diagram of QCD:

• Edward Shuryak, The Phases of QCD (arXiv:hep-ph/9609249)

• Simon Hands, The Phase Diagram of QCD, Contemp. Phys. 42:209-225, 2001 (arXiv:physics/0105022)

• Thomas Schaefer, Phases of QCD (arXiv:hep-ph/0509068)

Via lattice QCD:

• Jana N. Guenther, Overview of the QCD phase diagram – Recent progress from the lattice (arXiv:2010.15503)

History

On the early history of the development of quantum chromodynamics (the quark-model):

• George Zweig, Origins of the quark model, 1980 (pdf, pdf)

• Mikhail Shifman, OPE-based Methods in Nonperturbative QCD, Eur. Phys. J. C (2022) [arXiv:2208.10600]

Lattice QCD

Due to confinement, the fundamental degrees of freedom in terms of which QCD is formulated, namely the quarks, are actually not the low-energy bound states of the theory, which instead are the hadrons. This leaves room to speculate that QCD is not really the fundamental theory of the strong nuclear force.

However, brute-force computation in lattice QCD shows that the quark-model does reproduce these hadron bound states somehow (even if the real understanding of how it does so remains open, this is the mass gap problem):

• S. Durr, Z. Fodor, J. Frison, C. Hoelbling, R. Hoffmann, S.D. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, K.K. Szabo, G. Vulvert,

  Ab-initio Determination of Light Hadron Masses,

  Science 322:1224-1227,2008 (arXiv:0906.3599)

  conclusion on p. 4:

our study strongly suggests that QCD is the theory of the strong interaction, at low energies as well

• Zoltan Fodor, Christian Hoelbling, Light Hadron Masses from Lattice QCD, Rev. Mod. Phys. 84, 449, (arXiv:1203.4789)

• S. Aoki et. al. Review of lattice results concerning low-energy particle physics (arXiv:1607.00299)

On string diagram-calculus (Cvitanović 2008: “bird tracks”) for the representation theory involved in quantum chromodynamics

• Stéphane Peigné, Introduction to color in QCD: Initiation to the birdtrack pictorial technique [arXiv:2302.07574]

Light-cone quantization

Non-perturbative QCD and hadron bound states by light-cone quantization (see there for more):

• G. Peter Lepage, Stanley J. Brodsky, Exclusive processes in perturbative quantum chromodynamics, Phys. Rev. D 22 (1980) 2157 [doi:10.1103/PhysRevD.22.2157]

• Hans-Christian Pauli, Stanley J. Brodsky, Discretized light-cone quantization: Solution to a field theory in one space and one time dimension, Phys. Rev. D 32 (1985) 2001 [doi:10.1103/PhysRevD.32.2001]

• Stanley J. Brodsky, Gary McCartor, Hans-Christian Pauli, Stephen S. Pinsky, The challenge of light-cone quantization of gauge field theory, Particle World 3 3 (1993) 109-124 [cds:240388, inspire:335247]

• Stanley Brodsky, Hans-Christian Pauli, Stephen S. Pinsky, Quantum Chromodynamics and Other Field Theories on the Light Cone, Phys. Rept. 301 (1998) 299-486 [arXiv:hep-ph/9705477, doi:10.1016/S0370-1573(97)00089-6]

• Stanley Brodsky, Thomas Heinzl et al. Light-Front Quantum Chromodynamics: A framework for the analysis of hadron physics, White Paper of International Light Cone Advisory Committee, Nuclear Physics B - Proceedings Supplements 251, 252 (2014) 165-174 [doi:10.1016/j.nuclphysbps.2014.05.004, arXiv:1309.6333]