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.

In the Standard Model of particle physics the weak interaction is theorised as being caused by the exchange (i.e. emission or absorbtion) of W and Z bosons; and because it is a consequence of the emission (or absorbtion) of bosons it is a non-contact force. The best known effect of this emission is beta decay, a form of radioactivity. Unlike the other fundamental forces, it is not a form of binding energy, hence it does not produce bound states.

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. Consequently it has only a very short range. This is a consequence of the extremely short lifetime (hence, short range) of the W and Z bosons. It has one unique property – namely quark flavor changing – that does not occur in any other interaction. In addition, it also breaks parity-symmetry and CP-symmetry.

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.

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⁺
. More precisely, the down-type quark becomes a quantum superposition of up-type quarks, with probabilities as given by 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, e.g.:

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

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

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

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

The W boson is unstable so will rapidly decay, for example by:

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

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

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

In the so-called beta decay of a neutron (see picture on the right), a down quark within the neutron emits a
W⁻
boson (losing negative charge and mass), and is thereby converted into an up quark. As a result, the neutron is converted in a proton. Because of the energy involved in the process, the
W⁻
boson emitted by the down quark 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, either a lepton or a quark can emit or absorb a neutral Z boson, e.g.:

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

Z bosons also decay, for example:

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

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 particles; 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. A down quark in the neutron can change into an up quark by emitting a
W⁻
boson which decays into a high-energy electron and an electron antineutrino through beta decay.

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

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.

π⁺
decay through the weak interaction

Weak isospin (T₃) is to the weak interaction what color charge is to the strong interaction, and what mass is to gravity. Weak isospin is a quantum number; particles not involved in the weak interactions have a value of 0. 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. 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).

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. 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.

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)
• 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.