Quantum Field Theory of the Weak Nuclear Force

The history of physics from ancient times to the modern day, focusing on light and matter. The weak nuclear force stops a neutron from decaying into a proton and an electron. When this happens, an electron leaves the atom. This is known as beta decay. The weak force and the electromagnetic force combined in the early universe, and can now be described by a single theory known as electroweak theory.

Last updated on 5th August 2017 by Dr Helen Klus

1. Fermi's theory of beta decay

The weak nuclear force is the second weakest force, after the force of gravity, and it is the force with the shortest range. It was first devised to explain beta decay, which was discovered by New Zealand physicist Ernest Rutherford in 1899[1].

Rutherford knew that beta decay involved atoms emitting some kind of particles, and the following year French physicist Antoine Henri Becquerel showed that these particles were electrons[2].

In 1911, physicists discovered that an atom loses more energy during beta decay than the energy of the electron that is emitted[3], where mass and energy are related by German-Swiss-American physicist Albert Einstein's theory of special relativity[4].

This suggests that there is another outlet for energy in beta decay, and led Austrian physicist Wolfgang Pauli to predict the existence of a new particle that does not have a charge in 1930[5].

Italian physicist Enrico Fermi named this particle the neutrino, and incorporated it into his theory of beta decay, published in 1933[6]. By then, the nucleus of atoms were known to contain protons and neutrons.

Fermi showed that the electrons emitted in beta decay do not seem to come from the cloud of electrons that orbit the nucleus. The electrons seem to appear as a new electron, emanating from the nucleus.

Fermi considered the weak force to be a force with no range, entirely dependent on physical contact. He showed that during beta decay, a neutron spontaneously decays into a proton and emits an electron, with the electron carrying the negative charge and the proton carrying the positive charge. He predicted that the extra particle emitted in beta decay is the neutrally charged antineutrino.

American physicists Clyde Cowan and Frederick Reines proved that both electrons and antineutrinos are emitted during beta decay, in 1956[7].

Fermi's theory could also be extended to other particles, and described the decay of muons into electrons and neutrinos[8] - all of which were later shown to be leptons, elementary fermions that are not quarks. Fermi showed that the emission of the electron and neutrino was comparable to the emission of a photon by a charged particle.

Beta decay could not be explained by the strong nuclear force, the force that's responsible for holding the atomic nucleus together, because this force doesn't affect electrons. It couldn't be explained by the electromagnetic force, because this does not affect neutrons, and the force of gravity is far too weak to be responsible. Since this new atomic force was not as strong as the strong nuclear force, it was dubbed the weak nuclear force.

2. The weak nuclear force

2.1 Parity

Chinese-American physicist Tsung-Dao Lee and American physicist Chen Ning Yang showed that interactions involving the weak nuclear force do not follow the same symmetry as the other elementary forces in 1956, the same year that Cowan and Reines proved that electrons and antineutrinos are emitted during beta decay[9]. This symmetry is known as parity.

A parity transformation involves transforming the coordinates of an object to negative coordinates e.g. (x, y, z) to (-x, -y, -z). This is the same as reflecting it in a mirror and then turning this image upside down.

  • Objects that cannot be superimposed on their mirror image, like gloves, are called chiral.

  • Objects that can be superimposed on their mirror image are non-chiral, or are said to have negative chirality.

Hungarian-American physicist Eugene Wigner first introduced parity transformations to quantum physics in 1927[10].

The fact that the weak force is not symmetrical under parity transformations was confirmed by Chinese-American physicist Chien-Shiung Wu, who observed beta decay in cobalt-60 in 1957[11]. This meant that Fermi's theory was no longer valid.

Diagram showing chiral and non-chiral objects. Chiral objects, like handprints and footprints, cannot be superimposed on their mirror images. Non-chiral objects, like the silhouette of a bottle of wine, or a spherical ball, can be superimposed on their mirror image.

The images on the left are chiral, and the objects on the right are not. Only one object is symmetrical under parity transformations. This is the object that can still be superimposed on its mirror image once it has been turned upside down, the ball. Image credit: modified by Helen Klus, original images by George Hodan, Karen Arnold & Piotr Siedlecki/Public domain.

Diagram showing that beta decay has a preferred direction. It is chiral, and so cannot be superimposed on its mirror image. It cannot be superimposed on its mirror image once it has been turned upside down, and so is not symmetrical under parity transformations.

Parity violation during beta decay. Image credit: nagualdesign/CC-SA.

An illustration of Wu's experiment is shown above. The red ball represents many cobalt-60 nuclei, which all spin in the same direction and all emit electrons via beta decay.

When the cobalt nuclei are reversed in the mirror, their spin is reversed. Like a glove, they cannot be superimposed on their mirror image and are therefore chiral.

When this image is turned upside down, the spin is reversed again so it is the same as the original, but the amount of electrons emitted from the top is now higher than at the bottom, rather than the other way around.

This shows that beta decay is not symmetrical under parity transformations.

2.2 Helicity

Particles can be defined as right-handed or left-handed, where a right-handed particle moves in the same direction as its spin, and a left-handed particle moves in the opposite direction to its spin. Right-handed particles are said to have right-handed helicity, and left-handed particles have left-handed helicity.

In 1957 and 1958, American physicist Robert Marshak and Indian physicist George Sudarshan[12], and American physicists Richard Feynman and Murray Gell-Mann[13a], proposed that the weak nuclear force only acts on left-handed particles, and right-handed antiparticles. It is still not understood why there appears to be a preference for left-handed particles.

Some argue that parity violation on a subatomic level means that English natural philosopher Isaac Newton was correct to say that there is such thing as absolute space and time, a view known as spacetime substantivalism[14]. This is because parity violation implies electrons have a preferred spatial direction.

Direction in the quantum world is not the same as direction in the classical world we are used to, for this and other reasons, spacetime substantivalism has not been accepted by all[15].

Einstein considered his theory of general relativity to have disproven the theory of spacetime substantivalism[16]. It was later shown that those that do not accept this have to accept that general relativity is an indeterminate theory like quantum mechanics is thought to be[17].

2.3 CP symmetry and quantum flavordynamics

Pauli, American physicist Julian Schwinger, and German physicist Gerhart Lüders devised the CPT theorem in the 1950s[18][19][20]. This states that particle interactions are symmetrical under two other symmetries, known as charge conjugation, C, and time reversal invariance, T, as well as parity, P.

  • Charge conjugation was introduced by British physicist Paul Dirac in 1931, and states that the laws of physics are the same for particles and their antiparticle partners[21].

  • Time reversal invariance was introduced to quantum mechanics by Wigner in 1932, and states that the laws of physics would be the same if you were able to reverse time[22].

The weak force was known to obey T symmetry and, in 1957, a year after the weak force was shown to violate P symmetry, Russian physicist Lev Landau suggested that it still obeys CP symmetry, where C and P are combined[23].

A field theory of the weak force that incorporated parity violation was formed by Gell-Mann and Feynman in 1958[13b]. This was very successful at low energies but did not work at high energies.

This, and all other attempts to explain the weak force in terms of force carrying particles, gave results that were infinite - much like the first theories of quantum electrodynamics (QED), before they were renormalized.

Another problem was that the force carrying particles were predicted to have mass, and it was still not known how an elementary boson could acquire mass.

In 1964, American physicists James Cronin and Val Fitch showed that Landau was wrong[24]. CP symmetry is violated in kaon decay, which occurs via the weak force.

The fact that the weak force is not symmetrical under CP symmetry means that it does not treat matter and antimatter equally, and this may account for why there is more matter than antimatter in the universe. We still don't know why the weak force favours matter over antimatter.

That same year, quark theory was developed, and it was shown that during beta decay, the weak force turns a down quark into an up quark, and thus turns a neutron into a proton, emitting an electron and antineutrino in the process.

The weak force is the only force that can change the flavour of a quark and the theory of the weak force was named Quantum Flavordynamics (QFD) to match QED and QCD.

3. Electroweak theory

In the 1960s, American physicists Sheldon Lee Glashow[25a] and Steven Weinberg[26a], and Pakistani physicist Abdus Salam[27a] developed a quantum field theory that incorporates the fact that the weak force is not symmetrical under CP transformations at low energies. This theory is known as electroweak theory (EWT).

EWT shows that the weak force and the electromagnetic force are two manifestations of a more fundamental force, the electro-weak force - just as electricity and magnetism are two manifestations of the electromagnetic force. The weak and electromagnetic forces merge at high energies, like those found in the first 10-36 seconds (a billionth, of a billion, of a billion, of a billion, of a second) after the big bang.

Glashow[25b], and Salam and British-Australian physicist John Ward[28] showed that electroweak theory requires four virtual particles - each with a spin of 1, in order to transmit the electroweak force. Two of these were predicted to be neutral and two charged.

One of the neutral particles is the photon, and the other neutral particle was dubbed the Z boson. The two charged particles were dubbed the +W and -W bosons.

While the photon 'carries' charge, and therefore mediates the electromagnetic force, the Z and W bosons are said to carry a property known as 'weak isospin'.

The W particles mediate the weak force when particles with charge are involved, and the Z particles mediate the weak force when neutral particles are involved.

The weak force acts equally upon leptons and quarks, but not upon left-handed and right-handed particles:

  • Right-handed fermions have a weak isospin of 0 and do not undergo weak interactions.

  • Left-handed fermions have a weak isospin of +1/2 or -1/2, and interact with other particles that have a spin of -1/2 or +1/2 via the weak interaction.

The positively charged up, charm, and top quarks have an isospin of +1/2 and always decay via the weak force into down, strange, or bottom quarks that have an isospin of -1/2, and vice versa.

Positive quarks transform into negative ones by emitting a positive W particle, or absorbing a negative one.

In the case of beta decay, one of the down quarks within the neutron changes to an up quark, changing it into a proton, and a negative W particle is emitted, which almost instantly decays into the electron and antineutrino that are observed.

3.1 Leptons

Leptons are part of the 'standard model' of particle physics, which was devised in the 1960s. Charged leptons have an isospin of -1/2, and neutral leptons have an isospin of +1/2.

A charged lepton, an electron, a muon, or a tau particle, can absorb a W+ boson and be converted into a neutral electron neutrino, muon neutrino, or tau neutrino.

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.

American physicists Carl David Anderson and Seth Neddermeyer discovered the muon in 1936[29], and American physicists Leon Lederman, Melvin Schwartz, and Jack Steinberger detected the muon neutrino in 1962[30].

The tau was not discovered until 1977, in a series of experiments led by American physicist Martin Perl[31], and the tau neutrino was discovered in 2000, by the Direct Observation of the Nu Tau (DONUT) collaboration at Fermilab in the USA[32].

In 1957, Italian physicist Bruno Pontecorvo predicted that neutrinos can change ‘flavour', which means that they can change between being an electron neutrino, a muon neutrino, and a tau neutrino[33]. This means that neutrinos must have a mass. This was proven by Japanese physicist Takaaki Kajita and his team Super-Kamiokande neutrino observatory in 1998[34], and confirmed by Canadian physicist Arthur McDonald and his team in 2001[35].

3.2 The Higgs boson

Electroweak theory alone cannot explain how the W and Z particles acquire mass. The fact that electro-weak theory gives mass to W and Z particles, but not to photons, is yet another way that it appears to be asymmetrical.

The fact that the weak bosons have mass and the photon doesn't means that there must be another force that appears to break this symmetry at low energies, and hence at least one other virtual particle that 'carries' this force. This is the Higgs boson, and the whole process is known as the Higgs mechanism.

American physicist Philip Warren Anderson originally proposed the Higgs mechanism in 1962[36]. It was later developed by British physicist Peter Higgs[37], and two other groups of physicists[38][39]. Weinberg[26b] and Salam[27b] were the first to describe how it could successfully apply to electroweak theory.

The Higgs mechanism does not strictly break the symmetry of the electroweak force, but 'hides' it. Symmetry is dependent on perspective. The gravitational field of the Earth, for example, seems asymmetrical when you are falling, but from space, it clearly pulls in all directions. The symmetry of the Earth's gravity is hidden from certain perspectives.

The Higgs mechanism is a type of superconductivity, and the symmetry between the W and Z bosons and the photon is 'hidden' at low energies, when the Higgs field stops superconducting. This occurs through a process known as spontaneous symmetry breaking.

Spontaneous symmetry breaking occurs when a system obeying symmetrical laws becomes locally asymmetrical in its lowest energy state.

This can be seen in the example of a pencil balanced on its end. This system appears symmetrical, but when the pencil falls, it must fall in one direction, apparently at random.

Another example is a ball placed inside of a bowl that rises in the centre, until the ball must fall one way or the other.

Like all other fields, the Higgs field fills all of space, and the lowest energy state always seems to 'fall' in the same 'direction', giving the W and Z particles, but not the photons, mass.

Diagram showing a bowl-shape with a ball inside. The ball is in the centre. As the bottom of the bowl rises, the ball must fall one way or the other, seemingly at random.

Spontaneous symmetry breaking. Image credit: FT2/CC-A.

The Higgs boson also acquires mass from the Higgs field, in a similar way to how gluons - the bosons that carry the colour charge, and therefore transmit the strong force - also have a colour, and therefore experience the force they carry. Unlike all other elementary particles, however, the Higgs boson has a spin of 0.

Leptons and quarks acquire mass from the Higgs field in a similar way to how protons and neutrons are affected by the strong nuclear force, despite the fact that it primarily affects quarks.

3.3 Completing the standard model of particle physics

Dutch physicists Gerard 't Hooft and Martinus Veltman solved the last problem with electroweak theory in 1971, by proving that it could be renormalized[40][41]. Electroweak theory was experimentally verified in the 1970s and 1980s.

Physicists working at CERN (The European Organization for Nuclear Research) detected evidence of a neutral current, predicted to be produced by the Z boson, in 1973[42][43]. A beam of muon-antineutrinos was fired at a large bubble chamber known as Gargamelle. An electron should be set in motion by the effect of the neutral current produced by the Z particle. The electron would leave a track, which should seem to appear from nowhere. Over fifty physicists from all around the world looked at over a million images, and in the end, they found three examples of this happening.

In 1983, hundreds of physicists working at CERN discovered evidence of W and Z bosons, in collisions between protons and antiprotons[44][45].

Electroweak theory shows that quarks and leptons are grouped in pairs of increasing mass, but it doesn't show how many pairs exist. This was addressed in 1989, in another experiment at CERN[46]. This showed that the Z particle can only decay into three types of neutrino, which suggests that there are probably only three pairs of leptons and quarks.

Physicists at CERN discovered the Higgs boson in 2012[47]. This was confirmed in 2013[48]. The Higgs boson was found to have a mass between that of the top and bottom quarks at about 126 GeV/c2 (in units of energy/c2, where c is the speed of light).

The fact that the electromagnetic and the weak forces combine to become the electroweak force at high energies led to the idea that the electroweak and strong force may combine at even higher energies. Theories that propose this are known as grand unified theory (GUTs).

GUTs show that at very high energies quarks may convert into leptons and vice versa, and predict that a new boson, dubbed the X boson, must be involved in this process[49].

4. References

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  2. Becquerel, H., 1900, 'Deviation du rayonnement du radium dans un champ electrique' ('Deviation of radiation from radium in an electric field'), Comptes Rendus hebdomadaires des Seances de l'Academie des Sciences, 130, pp.809-815.

  3. Hahn, O. and Meitner, L., 1911, 'New Beta-Radiation from Thorium X', Journal of the Röntgen Society, 7, pp.51.

  4. Einstein, A., 1905, 'On the electrodynamics of moving bodies', Annalen der Physik, 17, pp.891-921, reprinted in 'The principle of relativity; original papers', 1920, The University of Calcutta.

  5. Pauli, W. and Riesselmann, K. (trans), 1930, 'Open letter to the group of radioactive people at the Gauverein meeting in Tübingen', 15 December 1930.

  6. Fermi, E., 1933, 'Tentativo di una teoria dei raggi beta' (Attempt at a theory of beta-rays), Ricerca Scientifica, 2, pp.12.

  7. Reines, F. and Cowan, C. L., 1956, 'The neutrino', Nature, 178, pp.446-449.

  8. Gershtein, S. S. and Zel'dovich, I. B., 1956, 'Meson corrections in the theory of beta decay', Soviet Phys, 2, pp.698-699.

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  10. Wigner, E., 1927, 'Ueber die Erhaltungssätze in der Quantenmechanik' ('About the conservation laws in quantum mechanics'), Mathematisch-Physikalische Klasse, 1, pp.375-381.

  11. Wu, C. S., et al, 1957, 'Experimental test of parity conservation in beta decay', Physical Review, 105, pp.1413-1415.

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  15. Huggett, N. and Hoefer, C., 'Absolute and Relational Theories of Space and Motion', Stanford Encyclopedia of Philosophy, last accessed 01-06-17.

  16. Einstein, A., 1916, 'The foundation of the generalised theory of relativity', Annalen der Physik, 354, pp.769-822, reprinted in 'The principle of relativity; original papers', 1920, The University of Calcutta.

  17. Norton, J. D., 'The Hole Argument', Stanford Encyclopedia of Philosophy, last accessed 01-06-17.

  18. Schwinger, J., 1951, 'The theory of quantized fields I', Physical Review, 82, pp.914.

  19. Lüders, G., 1954, 'On the Equivalence of Invariance under Time Reversal and under Particle-Antiparticle Conjugation for Relativistic Field Theories', Dan. Mat. Fys. Medd, 28, pp.1-17.

  20. Pauli, W., 1955, 'Niels Bohr and the Development of Physics: Essays Dedicated to Niels Bohr on the Occasion of His Seventieth Birthday', McGraw-Hill.

  21. Dirac, P. A., 1931, 'Quantised singularities in the electromagnetic field', Proceedings of the Royal Society of London, Series A, 133, pp.60-72.

  22. Wigner, E., 1932, 'Über die Operation der Zeitumkehr in der Quantenmechanik' ('About the operation of time reversal in quantum mechanics'), Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 1932, pp.546-559.

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  27. (a, b) Salam, A., and Svartholm, N. (ed), 1968, 'Elementary Particle Theory: Proceedings of the Eighth Nobel Symposium', Almqvist & Wiksell.

  28. Salam, A. and Ward, J. C., 1964, 'Electromagnetic and weak interactions', Physics Letters, 13, pp.168-171.

  29. 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.

  30. Danby, G., et al, 1962, 'Observation of high-energy neutrino reactions and the existence of two kinds of neutrinos', Physical Review Letters, 9, pp.36-49.

  31. Perl, M. L., 1977, 'Evidence for, and properties of, the new charged heavy lepton', SLAC-PUB-1923.

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  39. Guralnik, G. S., Hagen, C. R. and Kibble, T. W., 1964, 'Global conservation laws and massless particles', Physical Review Letters, 13, pp.585–587.

  40. Hooft, G. T., 1971, 'Renormalization of massless Yang-Mills fields', Nuclear physics B, 33, pp.173-199.

  41. Hooft, G. T., 1971, 'Renormalizable lagrangians for massive Yang-Mills fields', Nuclear physics B, 35, pp.167-188.

  42. Hasert, F. J., et al, 1973, 'Search for elastic muon-neutrino electron scattering', Physics letters B, 46, pp.121-124.

  43. Hasert, F. J., et al, 1973, 'Observation of neutrino-like interactions without muon or electron in the Gargamelle neutrino experiment', Physics letters B, 46, pp.138-140.

  44. Arnison, G., et al, 1983, 'Experimental observation of isolated large transverse energy electrons with associated missing energy at sqrt (s)= 540 GeV', Physics Letters B, 122, pp.103-116.

  45. Banner, M., et al, 1983, 'Observation of single isolated electrons of high transverse momentum in events with missing transverse energy at the CERN pp collider', Physics Letters B, 122, pp.476-485.

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

  47. CERN, 2012, 'CERN experiments observe particle consistent with long-sought Higgs boson', 4 July 2012.

  48. CERN, 2013, 'New results indicate that new particle is a Higgs boson', 14 March 2013.

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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.

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Pre 20th Century theories

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1. Field Concept in Physics

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3. Strong Nuclear Force

4. Weak Nuclear Force

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