Quantum Field Theory of the Strong Nuclear Force

The history of physics from ancient times to the modern day, focusing on light and matter. The strong nuclear force holds protons and neutrons together in the nucleus of atoms. This is the force that must be overcome in order to split the atom. The quantum field theory of the strong nuclear force is known as quantum chromodynamics. The strong force is carried by particles known as gluons.

Last updated on 5th August 2017 by Dr Helen Klus

1. The nucleus of atoms

Electromagnetism is responsible for keeping the electron within the atom, and so, at first, people thought it might also be responsible for holding particles together within the nucleus of atoms.

Yet when New Zealand physicist Ernest Rutherford discovered the proton in 1919, he soon realised that electromagnetism should make the nucleus fly apart, as protons are repelled by the positive charge of other protons[1][2].

It was suggested that the nucleus may also contain electrons, and these must be involved in holding the nucleus together[3]. This was partly because they were the only other known sub-atomic particles at the time, and partly because electrons are sometimes emitted from the nucleus, in beta decay.

British physicist James Chadwick discovered that the nucleus of atoms contain neutrons in 1932[4]. Shortly after this, Hungarian-American physicist Eugene Wigner suggested that the electromagnetic force is not involved in holding the nucleus together, and that there are two different nuclear forces[5]. We now refer to these as the strong and weak nuclear forces.

The strong nuclear force is the nuclear binding force, the force that provides the attraction between protons and protons, proton and neutrons, and neutrons and neutrons, keeping the nucleus of atoms together.

The weak nuclear force causes beta decay. It was reasoned that the weak force must be weaker than the strong force because beta decay is relatively common within atoms, yet it requires a lot of energy to break the strong force and split the nucleus of an atom.

1.1 Isospin quantum number

In 1932, German physicist Werner Heisenberg suggested that protons and neutrons are charged and neutral versions of the same particle, which explains why their masses are so similar[6].

Protons and neutrons are differentiated by a property known as isotopic spin, or isospin, a term coined by Wigner in 1937[7]. Isospin is analogous to spin. Protons are said to have clockwise isospin and neutrons have anticlockwise isospin.

The strong force exhibits isospin symmetry, which means that it affects objects with different isospins in the same way. This is not true of the weak nuclear force.

Heisenberg invented isospin as a mathematical convenience, but isospin was proven to be a real property in the 1950s, after another intrinsic property, known as strangeness, was discovered[8a][9a][10a].

2. Hideki Yukawa and early quantum field theory

In 1935, Japanese physicist Hideki Yukawa reasoned that since the strong and weak nuclear forces had never been detected, they must act over a range smaller than the diameter of the atomic nucleus[11].

This suggested that the virtual particles that transmit the nuclear forces must have a rest mass, unlike photons, the particles that transmit the electromagnetic force. This is because it takes more energy to produce a virtual particle with mass, and the more energy needed, the less time a virtual particle can exist according to German physicist Werner Heisenberg's uncertainty principle, hence its short range.

Yukawa developed the first quantum field theory of the strong force, with newly discovered particles known as 'mesons' acting as the force carrying virtual particles.

Yukawa produced evidence of mesons in experiments where he bombarded protons with neutrons. Short-lived particles were emitted. Yukawa calculated their maximum lifetime, and hence their minimum mass, and found them to be at least 200 times more massive than the electron.

In 1936, American physicists Carl David Anderson and Seth Neddermeyer discovered another new particle in cosmic radiation that seemed to have a similar mass to Yukawa's meson[12]. It was soon shown that Anderson's new particle penetrated matter too easily, and was therefore not massive enough to be the same particle Yukawa had predicted[13].

It was suggested that there might be two types of mesons. The first evidence for this came in 1947, when Brazilian physicist Cesar Lattes and his team conducted a high altitude cosmic-ray experiment. Their results showed that Yukawa's heavier meson decays into Anderson's lighter ones[14].

Yukawa's heavier particle was renamed pi and became known as the pi-meson or pion. The lighter particle was named mu and became known as the mu-meson or muon.

It was later shown that the pion is composed of smaller particles but the muon is an elementary particle with a spin of 1/2, similar to the electron but more massive. It is no longer considered a type of meson.

In 1938, British physicist Nicholas Kemmer had predicted that there are three types of pions: a neutral pion, and pions with a negative and positive charge[15]. This was similar to Heisenberg's idea that protons and neutrons are charged and neutral versions of the same particle.

2.1 Strangeness quantum number

British physicists George Dixon Rochester and Clifford Charles Butler discovered another new particle in 1947[16]. This was the K-meson, or Kaon.

Kaons were produced in large numbers but they did not rapidly decay, and so were dubbed strange particles. It was suggested that the strong nuclear force must be involved in slowing their decay.

By 1953, at least four kinds of strange particle had been discovered[17] and Japanese physicist Kazuhiko Nishijima[8b][9b] and American physicist Murray Gell-Mann[10b] independently showed that these particles have an intrinsic quality, which they dubbed 'strangeness'. Particles were then assigned a strangeness number, S, which must be a whole number.

It was later shown that all mesons, including strange particles, are composed of quarks.

3. The standard model of particle physics

3.1 Bosons and fermions

In the 1920s, particles had been split into bosons and fermions, where bosons have a whole spin number and fermions have a fractional spin number. Fermions obey the Pauli exclusion principle and bosons do not.

Some atoms and composite particles behave like bosons and some like fermions but elementary particles must be one or the other. All elementary bosons are force-carrying particles, like photons, and all the other elementary particles are fermions, like electrons.

3.2 Elementary fermions are either leptons or quarks

Belgian physicist Léon Rosenfeld coined the term 'lepton' in 1948, in order to describe fermions like electrons, which are influenced by the weak, but not the strong, nuclear force [18].

Russian physicist Lev Okun coined the term 'hadron' in 1962, in order to describe particles that experience the strong nuclear force, like protons, neutrons, pions, and kaons[19].

In the early 1960s, it was shown that hadron particles are not elementary.

In 1961-1962, Gell-Mann[20][21], and Israeli physicist Yuval Ne'eman[22], classified hadrons according to their mass, charge, spin, isospin, and strangeness, and independently showed how different hadrons are formed from combinations of 8 or 10 elementary particles. These were split into groups based on the symmetry of their strangeness and charge.

In 1964, Gell-Mann[23] and American physicist George Zweig[24][25] independently showed that the most basic subgroup only contains three particles, from which the octets and decuplets were built. Gell-Mann named these elementary particles quarks, and the three types, or flavours, of quarks were named up and down - for the isospin they carry - and strange - because strange particles contain strange quarks.

It was found that:

  • All hadrons contain quarks, and interact via the strong nuclear force.

  • All leptons are elementary particles, they do not contain quarks, and do not experience the strong force.

  • Only the weak force can change the flavour of a quark.

Diagram showing the standard model of particle physics. Matter is composed of leptons and quarks. There are six quarks and six leptons. There are also four gauge bosons plus the Higgs boson.

The standard model of particle physics. Image credit: MissMJ/CC-A.

3.3 Quarks form mesons and baryons

It was soon shown that mesons are composed of one quark and one antiquark, and all other known hadrons, which were collectively named baryons, are made of three quarks.

  • Baryons are fermions, and hence obey the Pauli exclusion principle.

  • Mesons are bosons, and hence do not obey the Pauli exclusion principle.

Diagram showing hadrons are split into mesons – made of a quark and an antiquark – and baryons, made of three quarks or three antiquarks. Kaons and pions are mesons, and neutrons and protons are baryons.

Different types of hadrons. Image credit: Helen Klus/CC-NC-SA.

A single proton is composed of three quarks, and has a charge of +1e, the same charge as 1 electron, but positive rather than negative. This implies that quarks have charges of + or - 2/3e, or 1/3e.

Up quarks have a charge of +2/3e, and down and strange quarks have a charge of -1/3e. Strange quarks are distinguished from down quarks by their mass.

  • A proton is composed of two up quarks and one down quark, which add up to have a charge of +1e.

  • A neutron is made of one up quark and two down quarks, which have an overall charge of 0.

  • Positively charged pions are composed of an up quark and an antidown quark, and positively charged kaons are composed of an up quark and an antistrange quark. Both have a charge of +1e.

  • Neutral kaons, with a charge of 0, are composed of a down quark and an antistrange quark.

Diagram of an atom, showing the nucleus composed of quarks that make protons and neutrons. Text states: ‘If the protons and neutrons were 10 cm wide, then the quarks and electrons would be less than 0.1 mm, and the entire atom would be about 10 km in diameter'.

Structure of the atom. Image credit: Helen Klus/CC-NC-SA.

4. Quantum chromodynamics

4.1 Quarks and colour

In 1964, the same year that quarks were first theorised, American physicists Oscar Greenberg[26] and Yoichiro Nambu[27][28] independently showed that quarks must be differentiated by something other than spin, mass, and charge. This is because particles were discovered that are composed entirely of quarks of the same flavour.

The omega-minus particle, for example, is composed of three strange quarks, which should be forbidden by the Pauli exclusion principle.

Greenberg and Yoichiro suggested that this property, which they named colour, has three states, which they named red, green, and blue. There are also three antimatter states: antired, antigreen, and antiblue.

Quarks can only combine in such a way that there is no net colour.

This is done either by combining three different colours - in the case of baryons - or by the combination of a coloured quark and its anticolour partner - which occurs with mesons.

These particles form because quarks of different colours are attracted to each other, and quarks of the same colour repel each other.

Colour is analogous to electric charge, and this similarity led to the idea that colour could be related to the strong nuclear force in the same way that electromagnetism is related to photons. The virtual particles that carry colour, transmitting the strong force, were named gluons.

A new, correct, quantum field theory of the strong nuclear force was devised in the late 1960s and early 1970s, which Gell-Mann named quantum chromodynamics (QCD)[29]. Here, quarks attract or repel each other by exchanging gluons, and protons and neutrons exchange mesons.

Protons and neutrons attract because of a residual strong force, in an analogous way to how neutral atoms attract because of van der Waals forces. This force decreases with distance because it has to compete with the electromagnetic repulsion of the protons.

QCD differs from quantum electrodynamics (QED) as there are three kinds of colour, as opposed to the two states of electric charge and, unlike photons, gluons have a colour themselves - in fact, they carry mixtures of colour and anticolour - and can therefore interact with each other. There must be at least eight types of gluon in order to make all the relevant colour changes.

In contrast to Yukawa's prediction, gluons do not have mass. The short radius of the strong force was explained by American physicists David Gross and Frank Wilczek[30][31], and fellow American physicist Hugh David Politzer[32], in the early 1970s.

Gross, Wilczek, and Politzer showed that the strong force between quarks increases as they move apart (the opposite of the force of gravity, which decreases as the distance between objects increases). The further a quark moves from its origin, the more gluons appear. This creates a stronger force to pull it back, and so it's not possible to split a baryon or meson into its constituent parts.

A quark can radiate a real, rather than virtual, gluon, just as an electron can radiate a real photon, but it will never emerge from the nucleus on its own. The only way for a quark to leave the nucleus is if it combines with the quarks or antiquarks that it emits as it moves away. When quarks are sufficiently close together, there are less gluons, and they have what is known as 'asymptotic freedom'.

4.2 The discovery of quarks

The up, down, and strange quarks were created by the Stanford University Deep inelastic scattering experiments at the Stanford Linear Accelerator Center (SLAC) in the United states, in 1968[33][34]. Here electrons were fired at hadrons, the path of the electrons were analysed, and it seemed as if they were bouncing off three small cores of different masses. These were identified as quarks in the early 1970s[35].

In 1964, American physicists James Bjørken and Sheldon Lee Glashow predicted that another quark with a charge of +2/3e must exist in order to better describe how quarks decay via the weak nuclear force[36].

They named this quark the charm quark because they were pleased to find a partner for the strange quark. Glashow, Greek physicist John Iliopoulos, and San Marino physicist Luciano Maiani provided further evidence in 1970[37].

Charm quarks were discovered by two independent teams of particle physicists in 1974, in similar experiments to those that proved the existence of the up, down, and strange quarks[38][39].

Japanese physicists Makoto Kobayashi and Toshihide Maskawa predicted the existence of two new quarks in 1973, in order to explain CP violation[40]. These were named top and bottom - as they were similar to the names up and down - by Israeli physicist Haim Harari in 1975[41].

The top and bottom quarks are the most massive quarks, and so they require a lot of energy to be created. The bottom quark, with a charge of -1/3e, was first observed by American physicist Leon Lederman and his team at Fermilab in the United States in 1977[42]. This indirectly implied the existence of the top quark, with a charge of +2/3 e, since quarks seem to come in pairs. The top quark was finally observed by a team at Fermilab in 1995[43][44].

Diagram of quarks, where the size is representative of the mass. The top quark is the largest, and the down quark is the smallest.

Bare masses of all six flavours of quarks, with a proton and electron for comparison, depicted as spheres of proportional volumes. Image credit: Incnis Mrsi/CC-A.

Gluons were observed during the TASSO experiment, which was conducted in Germany in 1979[45]. In the 1970s, physicists predicted that a quark-gluon plasma, which consists of asymptotically free quarks and gluons, could exist[46].

A quark-gluon plasma should have existed for 10 microseconds or so after the big bang, and was created in 2015 by physicists at CERN, who found that it behaved like a fluid[47].

In 2015, data from CERN's Large Hadron Collider (LHC) showed evidence for a new class of hadrons that are composed of five quarks - specifically, two up quarks, one down quark, one charm quark, and one anti-charm quark[48]. These are known as pentaquarks, and may be composed of a meson and a baryon that are weakly bound together.

Illustration showing two connected particles that are made of quarks.

Artist's impression of a loosely bound pentaquark composed of a meson (left) and a baryon (right). Image credit: CERN/CC-A.

Illustration showing one particle composed of five quarks.

Artist's impression of a tightly bound pentaquark. Image credit: CERN/CC-A.

Over 200 subatomic particles have now been discovered, and all are made from a selection of only 12 particles, the 6 elementary quarks, and the 6 elementary leptons[49].

5. References

  1. Rutherford, E., 1919, 'Collision of alpha Particles with Light Atoms IV. An Anomalous Effect in Nitrogen', The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 37, pp.581-587.

  2. Soddy, F., 1920, 'Name for the Positive Nucleus', Nature, 106, pp.502-503.

  3. Nye, M. J., 2003, 'The Cambridge History of Science: Volume 5, The Modern Physical and Mathematical Sciences', Cambridge University Press.

  4. Chadwick, J., 1932, 'The existence of a neutron', Proceedings of the Royal Society of London, Series A, 136, pp.692-708.

  5. Wigner, E., 1933, 'On the mass defect of helium', Physical Review, 43, pp.252-257.

  6. Heisenberg, W., 1932, 'Über den Bau der Atomkerne' ('About the construction of atomic nuclei'), Zeitschrift für Physik, 47, pp.1-11.

  7. Wigner, E., 1937, 'On the Consequences of the Symmetry of the Nuclear Hamiltonian on the Spectroscopy of Nuclei', Physical Review, 51, pp.106-129.

  8. (a, b) Nakano, T. and Nishijima, K., 1953, 'Charge Independence for V-particles', Progress of Theoretical Physics, 10, pp.581-582.

  9. (a, b) Nishijima, K., 1955, 'Charge Independence Theory of V Particles', Progress of Theoretical Physics, 13, pp.285-304.

  10. (a, b) Gell-Mann, M., 1956, 'The interpretation of the new particles as displaced charge multiplets', Il Nuovo Cimento, 4, pp.848-866.

  11. Yukawa, H., 1935, 'On the interaction of elementary particles', Nippon Sugaku-Buturigakkwai Kizi Dai 3 Ki, 17, pp.48-57.

  12. Anderson, C. D. and Neddermeyer, S. H., 1936, 'Cloud chamber observations of cosmic rays at 4300 meters elevation and near sea-level', Physical Review, 50, pp.263.

  13. Conversi, M., Pancini, E. and Piccioni, O., 1945, 'On the decay process of positive and negative mesons', Physical Review, 68, pp.232.

  14. Lattes, C. M. G., Occhialini, G. P. S. and Powell, C. F., 1947, 'Observations on the tracks of slow mesons in photographic emulsions', Nature, 160, pp.453-456.

  15. Kemmer, N., 1938, 'Nature of the nuclear field', Nature, 141, pp.116-117.

  16. Rochester, G. D. and Butler, C. C., 1947, 'Evidence for the existence of new unstable elementary particles', Nature, 160, pp.855.

  17. Kragh, H., 2002, 'Quantum Generations: A History of Physics in the Twentieth Century', Princeton University Press.

  18. Rosenfeld, L., 1948, 'Nuclear forces', North-Holland Publishing Company.

  19. Okun, L. B., 1962, 'Theory of weak interactions : thirteen lectures', Oak Ridge.

  20. Gell-Mann, M., 1961, 'The eightfold way: A theory of strong interaction symmetry', California Inst. of Tech., Pasadena. Synchrotron Lab.

  21. Gell-Mann, M., 1962, 'Symmetries of baryons and mesons', Physical Review, 125, pp.1084.

  22. Ne'eman, Y., 1961, 'Derivation of strong interactions from a gauge invariance', Nuclear physics, 26, pp.222-229.

  23. Gell-Mann, M., 1964, 'A Schematic Model of Baryons and Mesons', Physics Letters, 8, pp.214–215.

  24. Zweig, G., 1964, 'An SU(3) Model for Strong Interaction Symmetry and its Breaking: I', CERN-TH-401.

  25. Zweig, G., 1964, 'An SU(3) Model for Strong Interaction Symmetry and its Breaking: II', CERN-TH-412.

  26. Greenberg, O. W., 1964, 'Spin and unitary-spin independence in a paraquark model of baryons and mesons', Physical Review Letters, 13, pp.598-602.

  27. Nambu, Y., 1966, 'A systematics of hadrons in subnuclear physics' in 'Preludes in Theoretical Physics in honor of VF Weisskopf', North-Holland Publishing Company.

  28. Han, M. Y. and Nambu, Y., 1965, 'Three-triplet model with double SU (3) symmetry', Physical Review, 139, pp.B1006-B1010.

  29. Muta, T., 2010, 'Foundations of Quantum Chromodynamics: An Introduction to Perturbative Methods in Gauge Theories', World Scientific.

  30. Gross, D. J. and Wilczek, F., 1973, 'Ultraviolet behavior of non-abelian gauge theories', Physical Review Letters, 30, pp.1343.

  31. Gross, D. J. and Wilczek, F., 1973, 'Asymptotically free gauge theories', Physical Review D, 8, pp.3633-3706.

  32. Politzer, H. D., 1973, 'Reliable perturbative results for strong interactions?', Physical Review Letters, 30, pp.1346.

  33. Bloom, E. D., et al, 1969, 'High-Energy Inelastic e− p Scattering at 6 and 10', Physical Review Letters, 23, pp.930-941.

  34. Breidenbach, M., et al, 1969, 'Observed behavior of highly inelastic electron-proton scattering', Physical Review Letters, 23, pp.935-947.

  35. Riordan, E. M., 1992, 'The discovery of quarks', Science, 256, pp.1287-1293.

  36. Bjørken, B. J. and Glashow, S. L., 1964, 'Elementary particles and SU (4)', Physics Letters, 11, pp.255-257.

  37. Glashow, S. L., Iliopoulos, J. and Maiani, L., 1970, 'Weak interactions with lepton-hadron symmetry', Physical Review D, 2, pp.1285.

  38. Augustin, J. E., et al, 1974, 'Discovery of a Narrow Resonance in e+ e− Annihilation', Physical Review Letters, 33, pp.1406-1412.

  39. Aubert, J. J., et al, 1974, 'Experimental observation of a heavy particle J', Physical Review Letters, 33, pp.1404.

  40. Kobayashi, M. and Maskawa, T., 1973, 'CP-violation in the renormalizable theory of weak interaction', Progress of Theoretical Physics, 49, pp.652-657.

  41. Harari, H., 1975, 'A new quark model for hadrons', Physics Letters B, 57, pp.265-269.

  42. Herb, S. W., et al, 1977, 'Observation of a dimuon resonance at 9.5 GeV in 400-GeV proton-nucleus collisions', Physical Review Letters, 39, pp.252.

  43. Abe, F., et al, 1995, 'Observation of top quark production in Pbar-P collisions with the collider detector at Fermilab', Physical Review Letters, 74, pp.2626.

  44. Abachi, S., et al, 1995, 'Search for High Mass Top Quark Production in P-Pbar Collisions at s= 1.8 TeV', Physical Review Letters, 74, pp.2422.

  45. Brandelik, R., et al, 1979, 'Evidence for planar events in e+ e− annihilation at high energies', Physics Letters B, 86, pp.243-249.

  46. Cabibbo, N. and Parisi, G., 1975, 'Exponential hadronic spectrum and quark liberation', Physics Letters B, 59, pp.67-69.

  47. Ollitrault, J. Y., 2015, 'Viewpoint: The Littlest Liquid', Physics, 8, pp.61.

  48. Aaij, R., et al, 2015, 'Observation of J/Ω p Resonances Consistent with Pentaquark States in Λ b 0 → J/ψ K− p Decays', Physical Review Letters, 115, pp.07200101-0720115.

  49. CERN Courier, 1989, 'First physics from LEP', December 1989, pp.18–19.

Back to top

The Star Garden is a science news and science education website run by Dr Helen Klus.

How we came to know the cosmos covers the history of physics focusing on space and time, light and matter, and the mind. It explains the simple discoveries we made in prehistoric times, and how we built on them, little by little, until the conclusions of modern theories seem inevitable. This is shown in a timeline of the universe.

The Star Garden covers the basics for KS3, KS4, and KS5 science revision including SATs, GCSE science, and A-level physics.

Light & Matter

Pre 20th Century theories

1. Atoms and Waves

2. Reflection, Refraction, and Diffraction

3. Newton's theory of Light

4. Measuring the Speed of Light

5. 19th Century Wave Theories

6. 19th Century Particle Theories

7. Spectral Lines and Spectroscopy

Quantum Mechanics

1. Origin of Quantum Mechanics

2. Development of Atomic theory

3. Quantum Mechanical model

4. Sommerfeld's model

5. History of Quantum Spin

6. Superconductivity

7. History of Nuclear Physics

8. De Broglie's Matter Waves

9. Heisenberg's Uncertainty Principle

10. Schrödinger's Wave Equation

11. Quantum Entanglement

12. Schrödinger's Cat

Quantum field theories

1. Field Concept in Physics

2. Electromagnetic Force

3. Strong Nuclear Force

4. Weak Nuclear Force

5. Quantum Gravity