Chapter 24. The Weak Nuclear Force

24.1 Fermi’s theory of beta decay

The weak nuclear force is the second weakest force, after the force of gravity, and it’s 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] (discussed in Chapter 6). 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’s emitted,[3] where mass and energy are related by German-Swiss-American physicist Albert Einstein’s theory of special relativity[4] (discussed in Book I). This suggests that there’s another outlet for energy in beta decay, which 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 nuclei 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 new electrons, 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 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 (discussed in Chapter 23), elementary fermions that are not quarks. Fermi showed that the emission of the electron and antineutrino 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.

Diagram showing the beta decay of a neutron into a proton. In the process, it emits an electron and an antineutrino, where the electron is much easier to detect.

Figure 24.1
Image credit

Diagram showing the beta decay of a neutron (n) into a proton (p). This results in the emission of an electron (e-) and an antineutrino (ν̅e), where the electron is much easier to detect.

24.2 The weak force

24.2.1 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.

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.

Figure 24.2
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The objects 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.

A parity transformation involves transforming the coordinates of an object to negative coordinates e.g. transforming (x, y, z) into (-x, -y, -z). This is the same as reflecting it in a mirror (i.e. reversing the image horizontally) and then turning this image upside down (i.e. rotating the mirror image by 180°).

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

Figure 24.3
Image credit

The red ball represents many cobalt-60 nuclei undergoing beta decay. This cannot be superimposed on its mirror image and is therefore chiral. If the mirror image were turned upside down, it would still not match the original image, and so beta decay is not symmetrical under parity transformations.

An illustration of Wu’s experiment is shown in Figure 24.3. The red ball represents many cobalt-60 nuclei, which all have the same direction of spin (discussed in Chapter 12) 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 that it’s 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.

24.2.2 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, Indian physicist George Sudarshan and American physicist Robert Marshak[12], and American physicists Richard Feynman and Murray Gell-Mann,[13] proposed that the weak nuclear force only acts on left-handed particles, and right-handed antiparticles. It’s 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] (discussed in Book I). 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 who do not accept this have to accept that general relativity is an indeterminate theory like quantum mechanics is thought to be.[17]

24.2.3 CP symmetry and quantum flavordynamics

Pauli, American physicist Julian Schwinger, and German physicist Gerhart Lüders devised the CPT theorem in the 1950s.[18-20] 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.[13] 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 (discussed in Chapter 23) 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.

24.3 Electroweak theory

In the 1960s, American physicists Sheldon Lee Glashow[25] and Steven Weinberg,[26] and Pakistani physicist Abdus Salam[27] 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,[25] 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’. W bosons mediate the weak force when particles with charge are involved, and Z bosons mediate the weak force when neutral particles are involved.

The weak force acts equally on 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 weak isospin of -1/2 or +1/2 via the weak interaction.
Feynman diagram showing a neutron decay into a proton. In the process, it emits a –W boson. This decays into an electron and an antineutrino.

Figure 24.4
Image credit

The Feynman diagram for the beta decay of a neutron (n) into a proton (p). This occurs when a down quark (d) in the neutron decays into an up quark (u) to make a proton. It emits a -W boson (W-) in the process, which decays into an electron (e-) and an antineutrino (ν̅e).

The positively charged up, charm, and top quarks have a weak isospin of +1/2 and always decay via the weak force into down, strange, or bottom quarks that have a weak isospin of -1/2, and vice versa. Positive quarks transform into negative ones by emitting a positive W boson, 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 -W boson is emitted, which almost instantly decays into the electron and antineutrino that are observed.

24.3.1 Leptons

Leptons are part of the ‘standard model’ of particle physics (discussed in Chapter 23), which was devised in the 1960s. A charged lepton - an electron, a muon, or a tau particle - can absorb a W+ boson and be converted into a neutral lepton- an electron neutrino, a muon neutrino, or tau neutrino.

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 at the Super-Kamiokande neutrino observatory in 1998,[34] and confirmed by Canadian physicist Arthur McDonald and his team in 2001.[35]

24.3.2 The Higgs boson

Electroweak theory alone cannot explain how the W and Z bosons acquire mass. 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[26] and Salam[27] were the first to describe how it could successfully apply to electroweak theory.

24.3.3 The Higgs mechanism

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’re 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 (discussed in Chapter 13), 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 (shown in Figure 23.5).

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.

Figure 24.5
Image credit

Spontaneous symmetry breaking.

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.

24.3.4 Completing the standard model

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 Z bosons. 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 Z bosons 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].

A Brief History of CERN

Forming CERN

CERN was first envisioned in 1949 by French engineer Raoul Dautry, French physicists Pierre Auger and Lew Kowarski, Italian physicist Edoardo Amaldi, and Danish physicist Niels Bohr. They wished to create a laboratory to study atomic physics with particle accelerators so large, and expensive, that they could not be built by a single county alone. The first official proposal was put forward by French physicist Louis de Broglie in December of that year.[50]

In June of 1950, American physicist Isidor Isaac Rabi asked UNESCO (the United Nations Educational, Scientific and Cultural Organization) for assistance in the creation of the laboratory in order to encourage the collaboration of scientists from across Europe. By December the following year, members of UNESCO adopted the first resolution to establish a European Council for Nuclear Research (or Conseil Européen pour la Recherche Nucléaire in French, which is where the acronym CERN came from).[50]

This council came into effect in February 1952, and 11 counties agreed to participate. These were: Belgium, Denmark, France, the Federal Republic of Germany, Greece, Italy, the Netherlands, Norway, Sweden, Switzerland, and Yugoslavia. Geneva was selected as a site for the laboratory, and the United Kingdom joined the council the following year.[51] Construction began in May 1954, and by September of that year, the Council officially became an Organisation.[52]

The highest energy particle accelerator

CERN’s first accelerator - the Synchrocyclotron (SC) - was switched on in 1957 and remained in operation for 33 years.[50] A second accelerator, the Proton Synchrotron (PS), was switched on in 1959 and briefly became the highest energy accelerator in the world. It is still in operation, feeding particles to newer, higher-powered accelerators.

The first hadron collider

Physicists knew they would be able to create higher energy collisions if they fired two moving targets at each other, instead of firing accelerated particles at a fixed target. The first collider accelerator, Anello Di Accumulazione (ADA), was developed by Austrian physicist Bruno Touschek for the National Institute of Nuclear Physics in Italy, and was switched on in 1961.[53] This collided electrons and positrons (both of which are leptons, not hadrons). The beams of particles must be lined up very precisely in order for them to collide. This is easier to do in lepton collisions, since leptons are elementary particles.

Hadron collisions may be more difficult than lepton collisions, but hadrons can collide at a wide range of energies, and so are more useful when physicists are trying to create new particles. Physicists at CERN suggested that protons (which are hadrons) could be made to collide by using the PS to feed two rings - known as the Intersecting Storage Rings (ISR) - where beams of protons could be fired in different directions. This project was approved in 1965, construction on the ISR began the following year, and it became operational in January of 1971, becoming the first hadron collider in the world.[50]

The following month, the Super Proton Synchrotron (SPS) was commissioned. This was to be CERN’s largest accelerator yet, built about 40 metres below the ground with a circumference of 7 km. The SPS crossed the border into France becoming the first accelerator to cross an international border. It became operational in 1976.[50]

The first bubble chamber for neutral particles

After the development of electroweak theory in the 1960s, physicists at CERN created a bubble chamber that could detect neutral particles, known as Gargamelle, which was operational from 1970 until 1979. It was attached to the PS until 1976 when it was moved to the SPS.[54]

Gargamelle worked by measuring the effects of charged particles that were affected by collisions with neutrinos. It used heavy-liquid Freon instead of liquid hydrogen, which is lighter, in order to increase the number of collisions. Gargamelle first showed evidence of neutral currents via the detection of neutrinos in 1973.[43] The discovery of W and Z bosons was not possible, however, until they could be produced in more powerful collisions.

The first proton-antiproton collisions

The SPS was converted into a proton-antiproton collider in 1979.[55] The first proton-antiproton collisions occurred in 1981, and W and Z bosons were discovered in these collisions in 1983.[45] Once W and Z bosons had been discovered using a hadron collider, more precise collisions using a lepton collider were needed in order to determine their mass.

The Large Electron-Positron Collider

The Large Electron-Positron Collider (LEP) was first proposed in order to measure the mass of the Z boson produced in collisions between electrons and positrons.[56] The LEP would be the largest lepton collider in the world, located about 100 metres below the ground, with a circumference of 27 km. It had been approved in 1981, and became operational in 1989, at energies of about 100 GeV. Millions of Z bosons were produced, and it was shown that they produced only three generations of particles of matter.[46] W bosons required more energy, and these were not produced until the 1990s when the LEP was improved, with more cavities added so that the collisions doubled in energy.[56]

The Large Hadron Collider

Even before the LEP became operational in 1989, physicists considered how they could create higher energy collisions if it were converted into a hadron collider. Experiments that could be conducted in such a machine were first considered in 1984, although the construction of the Large Hadron Collider (LHC) was not approved until 1994.[57]

The LHC was initially planned to be developed in two stages, but donations from non-European counties such as Japan, India, Russia, the United States, and Canada meant that it was completed in one stage, becoming operational in 2009. The PS and SPS are used to accelerate particles before they are injected into the LHC. The first attempt to circulate a beam of protons was conducted in 2008, but it failed due to a faulty magnet connection, which took a year to repair.[57]

In November 2009, two beams successfully circulated the LHC, and by March of 2010, physicists were able to make two beams collide with an energy of 7 trillion eV (7 TeV), beating Fermilab’s Tevatron, which reached about 2 trillion eV (2 TeV). This made the LHC the highest energy accelerator in the world. The LHC produced so much data that it took years to analyse.[57]

The LHC was designed to run a number of experiments, all with their own detectors. These detectors are more complicated than bubble or wire chambers, and are much larger, the largest, ATLAS (A Toroidal LHC Apparatus), is the size of a seven-story building.[58]

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