Weak interaction

Weak interaction (often called the weak force or sometimes the weak nuclear force), is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars. Weak interactions affect all known fermions; that is, particles whose spin (a property of all particles) is a half-integer.

In the Standard Model of particle physics the weak interaction is theorised as being caused by the exchange (i.e. emission or absorption) of W and Z bosons; and because it is a consequence of the emission (or absorption) of bosons it is a non-contact force. The best known effect of this emission is beta decay, a form of radioactivity. The Z and W bosons are much heavier than protons or neutrons and it is the heaviness that accounts for the very short range of the weak interaction. It is termed weak because its typical field strength is several orders of magnitude less than that of both electromagnetism and the strong nuclear force. Most particles will decay by a weak interaction over time. It has one unique property – namely quark flavour changing – that does not occur in any other interaction. In addition, it also breaks parity-symmetry and CP-symmetry. Quark flavor changing allows for quarks to swap their 'flavor', one of six, for another.

The weak force was originally described, in the 1930s, by Fermi's theory of a contact four-fermion interaction: which is to say, a force with no range (i.e. entirely dependent on physical contact). But it is now best described as a field, having range, albeit a very short range. In 1968, the electromagnetic force and the weak interaction were unified, when they were shown to be two aspects of a single force, now termed the electro-weak force.

Weak interactions are most noticeable when particles undergo beta decay and in the production of deuterium and then helium from hydrogen that powers the sun's thermonuclear process. Such decay also makes radiocarbon dating possible, as carbon-14 decays through the weak interaction to nitrogen-14. It can also create radioluminescence, commonly used in tritium illumination, and in the related field of betavoltaics.

Properties

A diagram plotting mass against charge for the six quarks of the standard model, and depicting the various decay routes due to the weak interaction and some indication of their likelihood.

The weak interaction is unique in a number of respects:

1. It is the only interaction capable of changing the flavor of quarks (i.e. of changing one type of quark into another).
2. It is the only interaction which violates P or parity-symmetry. It is also the only one which violates CP symmetry.
3. It is propagated by carrier particles that have significant masses (particles called gauge bosons), an unusual feature which is explained in the Standard Model by the Higgs mechanism.

Due to their large mass (approximately 90 GeV/c²) these carrier particles, termed the W and Z bosons, are short-lived: they have a lifetime of under 1×10⁻²⁴ seconds. The weak interaction has a coupling constant (an indicator of interaction strength) of between 10⁻⁷ and 10⁻⁶, compared to the strong interaction's coupling constant of about 1; consequently the weak interaction is weak in terms of strength. The weak interaction has a very short range (around 10⁻¹⁷–10⁻¹⁶ m). At distances around 10⁻¹⁸ meters, the weak interaction has a strength of a similar magnitude to the electromagnetic force; but at distances of around 3×10⁻¹⁷ m the weak interaction is 10,000 times weaker than the electromagnetic.

The weak interaction affects all the fermions of the Standard Model, as well as the hypothetical Higgs boson; neutrinos interact through the weak interaction only. The weak interaction does not produce bound states (nor does it involve binding energy) – something that gravity does on an astronomical scale, that the electromagnetic force does at the atomic level, and that the strong nuclear force does inside nuclei.

Its most noticeable effect is due to its first unique feature: flavor changing. A neutron, for example, is heavier than a proton (its sister nucleon), but it cannot decay into a proton without changing the flavor (type) of one of its two down quarks to up. Neither the strong interaction nor electromagnetism permit flavour changing, so this must proceed by weak decay; without weak decay, quark properties such as strangeness and charm (associated with the quarks of the same name) would also be conserved across all interactions. All mesons are unstable because of weak decay. In the process known as beta decay, a down quark in the neutron can change into an up quark by emitting a virtual
W⁻
boson which is then converted into an electron and an electron antineutrino.

Due to the large mass of a boson, weak decay is much more unlikely than strong or electromagnetic decay, and hence occurs less rapidly. For example, a neutral pion (which decays electromagnetically) has a life of about 10⁻¹⁶ seconds, while a weakly charged pion (which decays through the weak interaction) lives about 10⁻⁸ seconds, a hundred million times longer. In contrast, a free neutron (which decays through the weak interaction) lives about 15 minutes.

Weak isospin and weak hypercharge

Main article: Weak isospin

Left-handed fermions in the Standard Model.

Generation 1			Generation 2			Generation 3
Fermion	Symbol	Weak isospin	Fermion	Symbol	Weak isospin	Fermion	Symbol	Weak isospin
Electron	$e^{-}\,$	$-1/2\,$	Muon	$\mu ^{-}\,$	$-1/2\,$	Tau	$\tau ^{-}\,$	$-1/2\,$
Electron neutrino	$\nu _{e}\,$	$+1/2\,$	Muon neutrino	$\nu _{\mu }\,$	$+1/2\,$	Tau neutrino	$\nu _{\tau }\,$	$+1/2\,$
Up quark	$u\,$	$+1/2\,$	Charm quark	$c\,$	$+1/2\,$	Top quark	$t\,$	$+1/2\,$
Down quark	$d\,$	$-1/2\,$	Strange quark	$s\,$	$-1/2\,$	Bottom quark	$b\,$	$-1/2\,$
All left-handed antiparticles have weak isospin of 0. Right-handed antiparticles have the opposite weak isospin.

Weak isospin (T₃) is a property (quantum number) of all particles, which governs how particles interact in the weak interaction. Weak isospin is to the weak interaction what electric charge is to the electromagnetism, and what color charge is to strong interaction. Other elementary particles have weak isospin values of ±1⁄2. For example, up-type quarks (u, c, t) have T₃ = +1⁄2 and always transform into down-type quarks (d, s, b), which have T₃ = −1⁄2, and vice-versa. On the other hand, a quark never decays weakly into a quark of the same T₃. As is the case with electric charge, these two possible values are equal except for sign.

π⁺
decay through the weak interaction

Weak isospin is conserved: the sum of the weak isospin numbers of the particles exiting a reaction equals the sum of the weak isospin numbers of the particles entering that reaction. For example, a (left-handed)
π⁺
, with an weak isospin of +1⁄2 normally decays into a
ν
_μ (+1/2) and a
μ⁺
(as a left-handed antiparticle, 0).

Following the development of the electroweak theory, another property, weak hypercharge, was developed. It is dependent on a particle's electrical charge and weak isospin, and is defined as:

$\qquad Y_{W}=2(Q-T_{3})$

where Y_W is the weak hypercharge of a given type of particle, Q is its electrical charge (in elementary charge units) and T₃ is its weak isospin. Whereas some particles have a weak isospin of zero, all particles have non-zero weak hypercharge. Weak hypercharge is the generator of the U(1) component of the electroweak gauge group.

Violation of symmetry

Left- and right-handed particles: p is the particle's momentum and S is its spin. Note the lack of reflective symmetry between the states.

The laws of nature were long thought to remain the same under mirror reflection, the reversal of all spatial axes. The results of an experiment viewed via a mirror were expected to be identical to the results of a mirror-reflected copy of the experimental apparatus. This so-called law of parity conservation was known to be respected by classical gravitation, electromagnetism and the strong interaction; it was assumed to be a universal law. However, in the mid-1950s Chen Ning Yang and Tsung-Dao Lee suggested that the weak interaction might violate this law. Chien Shiung Wu and collaborators in 1957 discovered that the weak interaction violates parity, earning Yang and Lee the 1957 Nobel Prize in Physics.

Although the weak interaction used to be described by Fermi's theory, the discovery of parity violation and renormalization theory suggested a new approach was needed. In 1957, Robert Marshak and George Sudarshan and, somewhat later, Richard Feynman and Murray Gell-Mann proposed a V−A (vector minus axial vector or left-handed) Lagrangian for weak interactions. In this theory, the weak interaction acts only on left-handed particles (and right-handed antiparticles). Since the mirror reflection of a left-handed particle is right-handed, this explains the maximal violation of parity. Interestingly, the V−A theory was developed before the discovery of the Z boson, so it did not include the right-handed fields that enter in the neutral current interaction.

However, this theory allowed a compound symmetry CP to be conserved. CP combines parity P (switching left to right) with charge conjugation C (switching particles with antiparticles). Physicists were again surprised when in 1964, James Cronin and Val Fitch provided clear evidence in kaon decays that CP symmetry could be broken too, winning them the 1980 Nobel Prize in Physics. In 1973, Makoto Kobayashi and Toshihide Maskawa showed that CP violation in the weak interaction required more than two generations of particles, effectively predicting the existence of a then unknown third generation. This discovery earned them half of the 2008 Nobel Prize in Physics. Unlike parity violation, CP violation occurs in only a small number of instances, but remains widely held as an answer to the difference between the amount of matter and antimatter in the universe; it thus forms one of Andrei Sakharov's three conditions for baryogenesis.

Interaction types

There are two types of weak interaction (called vertices). The first type is called the "charged current interaction" because it is mediated by particles that carry an electric charge (the
W⁺
or
W⁻
bosons), and is responsible for the beta decay phenomenon. The second type is called the "neutral current interaction" because it is mediated by a neutral particle, the Z boson.

Charged current interaction

The Feynman diagram for beta-minus decay of a neutron into a proton, electron and electron anti-neutrino, via an intermediate heavy
W⁻
boson

In one type of charged current interaction, a charged lepton (such as an electron or a muon, having a charge of -1) can absorb a
W⁺
boson (a particle with a charge of +1) and be thereby converted into a corresponding neutrino (with a charge of 0), where the type ("family") of neutrino (electron, muon or tau) is the same as the type of lepton in the interaction, for example:

$\mu ^{-}+W^{+}\to \nu _{\mu }$

Similarly, a down-type quark (d with a charge of −1⁄3) can be converted into an up-type quark (u, with a charge of +2⁄3), by emitting a
W⁻
boson or by absorbing a
W⁺
boson. More precisely, the down-type quark becomes a quantum superposition of up-type quarks: that is to say, it has a possibility of becoming any one of the three up-type quarks, with the probabilities given in the CKM matrix tables. Conversely, an up-type quark can emit a
W⁺
boson – or absorb a
W⁻
boson – and thereby be converted into a down-type quark, for example:

$d\to u+W^{-}$

$d+W^{+}\to u$

$c\to s+W^{+}$

$c+W^{-}\to s$

The W boson is unstable so will rapidly decay, with a very short lifetime. For example:

$W^{-}\to e^{-}+{\bar {\nu }}_{e}~$

$W^{+}\to e^{+}+\nu _{e}~$

Decay of the W boson to other products can happen, with varying probabilities.

In the so-called beta decay of a neutron (see picture, above), a down quark within the neutron emits a virtual
W⁻
boson and is thereby converted into an up quark, converting the neutron into a proton. Because of the energy involved in the process (i.e., the mass difference between the down quark and the up quark), the
W⁻
boson can only be converted into an electron and an electron-antineutrino. At the quark level, the process can be represented as:

$d\to u+e^{-}+{\bar {\nu }}_{e}~$

Neutral current interaction

In neutral current interactions, a quark or a lepton (e.g. an electron or a muon) emits or absorbs a neutral Z boson. For example:

$e^{-}\to e^{-}+Z^{0}$

Like the W boson, the Z boson also decays rapidly, for example:

$Z^{0}\to b+{\bar {b}}$

Electroweak theory

Main article: Electroweak interaction

The Standard Model of particle physics describes the electromagnetic interaction and the weak interaction as two different aspects of a single electroweak interaction, the theory of which was developed around 1968 by Sheldon Glashow, Abdus Salam and Steven Weinberg. They were awarded the 1979 Nobel Prize in Physics for their work. The Higgs mechanism provides an explanation for the presence of three massive gauge bosons (the three carriers of the weak interaction) and the massless photon of the electromagnetic interaction.

According to the electroweak theory, at very high energies, the universe has four massless gauge boson fields similar to the photon and a complex scalar Higgs field doublet. However, at low energies, gauge symmetry is spontaneously broken down to the U(1) symmetry of electromagnetism (one of the Higgs fields acquires a vacuum expectation value). This symmetry breaking would produce three massless bosons, but they become integrated by three photon-like fields (through the Higgs mechanism) giving them mass. These three fields become the
W⁺
,
W⁻
and Z bosons of the weak interaction, while the fourth gauge field which remains massless is the photon of electromagnetism.

Although this theory has made a number of predictions, including a prediction of the masses of the Z and W bosons before their discovery, the Higgs boson itself has never been observed. Producing Higgs bosons is a major goal of the Large Hadron Collider at CERN.

See also

• Weakless Universe – the postulate that weak interactions are not anthropically necessary

References

General readers

• R. Oerter (2006). The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics. Plume. ISBN 9780132366786.
• B.A. Schumm (2004). Deep Down Things: The Breathtaking Beauty of Particle Physics. Johns Hopkins University Press. ISBN 0-8018-7971-X.

Texts

• D.A. Bromley (2000). Gauge Theory of Weak Interactions. Springer. ISBN 3-540-67672-4.
• G.D. Coughlan, J.E. Dodd, B.M. Gripaios (2006). The Ideas of Particle Physics: An Introduction for Scientists (3rd ed.). Cambridge University Press. ISBN 978-0521677752.{{cite book}}: CS1 maint: multiple names: authors list (link)
• W. N. Cottingham; D. A. Greenwood (1986, 2001). An introduction to nuclear physics (2 ed.). Cambridge University Press. p. 30. ISBN 9780521657334. {{cite book}}: Check date values in: |year= (help)CS1 maint: year (link)
• D.J. Griffiths (1987). Introduction to Elementary Particles. John Wiley & Sons. ISBN 0-471-60386-4.
• G.L. Kane (1987). Modern Elementary Particle Physics. Perseus Books. ISBN 0-201-11749-5.
• D.H. Perkins (2000). Introduction to High Energy Physics. Cambridge University Press. ISBN 0-521-62196-8.