Weak interaction

In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is the mechanism of interaction between subatomic particles that is responsible for the radioactive decay of atoms. The weak interaction participates in nuclear fission, and the theory describing it in terms of both its behaviour and effects is sometimes called quantum flavourdynamics (QFD). However, the term QFD is rarely used, because the weak force is better understood in terms of electroweak theory (EWT).[1]

The effective range of the weak force is limited to subatomic distances, and is less than the diameter of a proton. It is one of the four known force-related fundamental interactions of nature, alongside the strong interaction, electromagnetism, and gravitation.

Background

The Standard Model of particle physics provides a uniform framework for understanding the electromagnetic, weak, and strong interactions. An interaction occurs when two particles (typically but not necessarily half-integer spin fermions) exchange integer-spin, force-carrying bosons. The fermions involved in such exchanges can be either elementary (e.g. electrons or quarks) or composite (e.g. protons or neutrons), although at the deepest levels, all weak interactions ultimately are between elementary particles.

In the weak interaction, fermions can exchange three types of force carriers, namely W+, W−, and Z bosons. The masses of these bosons are far greater than the mass of a proton or neutron, which is consistent with the short range of the weak force. In fact, the force is termed weak because its field strength over a given distance is typically several orders of magnitude less than that of the strong nuclear force or electromagnetic force.

Quarks, which make up composite particles like neutrons and protons, come in six "flavours" – up, down, strange, charm, top and bottom – which give those composite particles their properties. The weak interaction is unique in that it allows quarks to swap their flavour for another. The swapping of those properties is mediated by the force carrier bosons. For example, during beta minus decay, a down quark within a neutron is changed into an up quark, thus converting the neutron to a proton and resulting in the emission of an electron and an electron antineutrino.

The weak interaction is the only fundamental interaction that breaks parity-symmetry, and similarly, the only one to break charge parity symmetry.

Other important examples of phenomena involving the weak interaction include beta decay, and the fusion of hydrogen into helium that powers the Sun's thermonuclear process. Most fermions decay by a weak interaction over time. Such decay 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.[2]

During the quark epoch of the early universe, the electroweak force separated into the electromagnetic and weak forces.
History

In 1933, Enrico Fermi proposed the first theory of the weak interaction, known as Fermi's interaction. He suggested that beta decay could be explained by a four-fermion interaction, involving a contact force with no range.[3][4]

However, it is better described as a non-contact force field having a finite range, albeit very short. In 1968, Sheldon Glashow, Abdus Salam and Steven Weinberg unified the electromagnetic force and the weak interaction by showing them to be two aspects of a single force, now termed the electroweak force.[5][6]

The existence of the W and Z bosons was not directly confirmed until 1983.[7]
Properties
A diagram depicting the decay routes due to the charged weak interaction and some indication of their likelihood. The intensity of the lines is given by the CKM parameters.

The electrically charged weak interaction is unique in a number of respects:

It is the only interaction that can change the flavour of quarks (i.e., of changing one type of quark into another).
It is the only interaction that violates P or parity-symmetry. It is also the only one that violates charge-parity CP symmetry.
Both the electrically charged and the electrically neutral interactions are mediated (propagated) by force carrier particles that have significant masses, an unusual feature which is explained in the Standard Model by the Higgs mechanism.

Due to their large mass (approximately 90 GeV/c2[8]) these carrier particles, called the W and Z bosons, are short-lived with a lifetime of under 10⁻²⁴ seconds.[9] 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 1 and the electromagnetic coupling constant of about 10⁻²;[10] consequently the weak interaction is ‘weak’ in terms of strength.[11] The weak interaction has a very short effective range (around 10⁻¹⁷ to 10⁻¹⁶ m[11]).[10] At distances around 10⁻¹⁸ meters, the weak interaction has a strength of a similar magnitude to the electromagnetic force, but this starts to decrease exponentially with increasing distance. Scaled up by just one and a half orders of magnitude, at distances of around 3×10⁻¹⁷ m, the weak interaction becomes 10,000 times weaker.[12]

The weak interaction affects all the fermions of the Standard Model, as well as the Higgs boson; neutrinos interact only through gravity and the weak interaction. 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.[13]

Its most noticeable effect is due to its first unique feature: The charged weak interaction causes flavour change. For example, a neutron is heavier than a proton (its partner nucleon), and can decay into a proton by changing the flavour (type) of one of its two down quarks to an up quark. Neither the strong interaction nor electromagnetism permit flavour-changing, so this proceeds by weak decay; without weak decay, quark properties such as strangeness and charm (associated with the Strange quarks and charm quarks, respectively) would also be conserved across all interactions.

All mesons are unstable because of weak decay.[14][a] 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.[15] Another example is the electron capture, a common variant of radioactive decay, wherein a proton and an electron within an atom interact, and are changed to a neutron (an up quark is changed to a down quark) and an electron neutrino is emitted.

Due to the large masses of the W bosons, particle transformations or decays (e.g., flavour change) that depend on the weak interaction typically occur much more slowly than transformations or decays that depend only on the strong or electromagnetic forces. For example, a neutral pion decays electromagnetically, and so has a life of only about 10−16 seconds. In contrast, a charged pion can only decay through the weak interaction, and so lives about 10−8 seconds, or a hundred million times longer than a neutral pion.[16] A particularly extreme example is the weak-force decay of a free neutron, which takes about 15 minutes.[15]

Weak isospin and weak hypercharge
Main article: Weak isospin

**Left-handed fermions in the Standard Model**^[17]
Generation 1			Generation 2			Generation 3
Fermion	Symbol	Weak isospin	Fermion	Symbol	Weak isospin	Fermion	Symbol	Weak isospin
Electron neutrino	ν _e	++1/2	Muon neutrino	ν _μ	++1/2	Tau neutrino	ν _τ	++1/2
Electron	e⁻	−+1/2	Muon	μ⁻	−+1/2	Tau	τ⁻	−+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 of the above left-handed (regular) particles have corresponding right-handed anti-particles with equal and opposite weak isospin.
All right-handed (regular) particles and left-handed antiparticles have weak isospin of 0.

All particles have a property called weak isospin (symbol T3), which serves as an additive quantum number that restricts how the particle can behave in the weak interaction. Weak isospin plays the same role in the weak interaction as does electric charge in electromagnetism, and color charge in the strong interaction. All left-handed fermions have a weak isospin value of either ++1/2 or −+1/2; all right-handed fermions have 0 isospin. For example, the up quark has a T3 of ++1/2 and the down quark −+1/2. A quark never decays through the weak interaction into a quark of the same T3: Quarks with a T3 of ++1/2 only decay into quarks with a T3 of −+1/2 and vice versa.

π+ decay through the weak interaction

In any given interaction, weak isospin is conserved: The sum of the weak isospin numbers of the particles entering the interaction equals the sum of the weak isospin numbers of the particles exiting that interaction. For example, a (left-handed)
π+ , with a weak isospin of +1 normally decays into a
ν
μ (with T3 = ++1/2) and a μ+ (as a right-handed antiparticle, ++1/2).[16]

For the development of the electroweak theory, another property, weak hypercharge, was created. It depends on a particle's electrical charge and weak isospin, and is defined by:

\( {\displaystyle Y_{\text{W}}=2(Q-T_{3})} \)

where YW 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 known spin 1/2 particles have a non-zero weak hypercharge.[b] Weak hypercharge is the generator of the U(1) component of the electroweak gauge group.
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). It 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 Z0 boson. It is responsible for the (rare) deflection of neutrinos. The two types of interaction follow different selection rules.
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 ("flavour") 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:

\( {\begin{aligned}d&\to u+W^{-}\\d+W^{+}&\to u\\c&\to s+W^{+}\\c+W^{-}&\to s\end{aligned}} \)

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

\( {\begin{aligned}W^{-}&\to e^{-}+{\bar \nu }_{e}~\\W^{+}&\to e^{+}+\nu _{e}~\end{aligned}} \)

Decay of a W boson to other products can happen, with varying probabilities.[18]

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.[19] 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± bosons, the Z0 boson also decays rapidly,[18] for example:

\( Z^0\to b+\bar b \)

Unlike the charged-current interaction, whose selection rules are strictly limited by chirality, electric charge, and / or weak isospin, the neutral-current Z0
interaction can cause any two fermions in the standard model to deflect: Either particles and anti-particles of any electric charge, and both left- and right-chirality, although the strength of the interaction differs.[c]

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. This theory was developed around 1968 by Sheldon Glashow, Abdus Salam and Steven Weinberg, and they were awarded the 1979 Nobel Prize in Physics for their work.[20] The Higgs mechanism provides an explanation for the presence of three massive gauge bosons (W+,W−,Z0, the three carriers of the weak interaction) and the massless photon (γ, the carrier of the electromagnetic interaction).[21]

According to the electroweak theory, at very high energies, the universe has four components of the Higgs field whose interactions are carried by four massless gauge bosons – each similar to the photon – forming a complex scalar Higgs field doublet. However, at low energies, this gauge symmetry is spontaneously broken down to the U(1) symmetry of electromagnetism, since one of the Higgs fields acquires a vacuum expectation value. This symmetry-breaking would be expected to produce three massless bosons, but instead they become integrated by the other three fields and acquire mass through the Higgs mechanism. These three boson integrations produce the W+,W− and Z0 bosons of the weak interaction. The fourth gauge boson is the photon of electromagnetism, and remains massless.[21]

This theory has made a number of predictions, including a prediction of the masses of the Z and W-bosons before their discovery and detection in 1983.

On 4 July 2012, the CMS and the ATLAS experimental teams at the Large Hadron Collider independently announced that they had confirmed the formal discovery of a previously unknown boson of mass between 125–127 GeV/c2, whose behaviour so far was "consistent with" a Higgs boson, while adding a cautious note that further data and analysis were needed before positively identifying the new boson as being a Higgs boson of some type. By 14 March 2013, a Higgs boson was tentatively confirmed to exist.[22]

In a speculative case where the electroweak symmetry breaking scale were lowered, the unbroken SU(2) interaction would eventually become confining. Alternative models where SU(2) becomes confining above that scale appear quantitatively similar to the Standard Model at lower energies, but dramatically different above symmetry breaking.[23]
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 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.[24] 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.[25]

Although the weak interaction was once described by Fermi's theory, the discovery of parity violation and renormalization theory suggested that 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. 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.[26] In 1973, Makoto Kobayashi and Toshihide Maskawa showed that CP violation in the weak interaction required more than two generations of particles,[27] effectively predicting the existence of a then unknown third generation. This discovery earned them half of the 2008 Nobel Prize in Physics.[28]

Unlike parity violation, CP violation occurs only in limited circumstances. Despite its rarity, it is widely believed to be the reason that there is much more matter than antimatter in the universe, and thus forms one of Andrei Sakharov's three conditions for baryogenesis.[29]
See also

Weakless Universe – the postulate that weak interactions are not anthropically necessary
Gravity
Strong interaction
Electromagnetism

Footnotes

The neutral pion, however, decays electromagnetically, and several mesons mostly decay strongly, when their quantum numbers allow.
Some hypothesised fermions, such as the sterile neutrinos, would have zero weak hypercharge – in fact, no gauge charges at all. Whether such particles exist is an active area of research.

The only fermions which the Z0 does not interact with are the hypothetical "sterile" neutrinos: Left-chiral anti-neutrinos and right-chiral neutrinos. They are called "sterile" because they would not interact with any Standard Model particle, but as yet remain entirely a conjecture; no such neutrinos are known to actually exist.

References
Citations

Griffiths, David (2009). Introduction to Elementary Particles. pp. 59–60. ISBN 978-3-527-40601-2.
"The Nobel Prize in Physics 1979: Press Release". NobelPrize.org. Nobel Media. Retrieved 22 March 2011.
Fermi, Enrico (1934). "Versuch einer Theorie der β-Strahlen. I". Zeitschrift für Physik A. 88 (3–4): 161–177. Bibcode:1934ZPhy...88..161F. doi:10.1007/BF01351864.
Wilson, Fred L. (December 1968). "Fermi's Theory of Beta Decay". American Journal of Physics. 36 (12): 1150–1160. Bibcode:1968AmJPh..36.1150W. doi:10.1119/1.1974382.
"Steven Weinberg, Weak Interactions, and Electromagnetic Interactions". Archived from the original on 9 August 2016.
"1979 Nobel Prize in Physics". Nobel Prize. Archived from the original on 6 July 2014.
Cottingham & Greenwood (1986, 2001), p. 8
Yao, W.-M.; et al. (Particle Data Group) (2006). "Review of Particle Physics: Quarks" (PDF). Journal of Physics G. 33 (1): 1–1232. arXiv:astro-ph/0601168. Bibcode:2006JPhG...33....1Y. doi:10.1088/0954-3899/33/1/001.
Peter Watkins (1986). Story of the W and Z. Cambridge: Cambridge University Press. p. 70. ISBN 978-0-521-31875-4.
"Coupling Constants for the Fundamental Forces". HyperPhysics. Georgia State University. Retrieved 2 March 2011.
J. Christman (2001). "The Weak Interaction" (PDF). Physnet. Michigan State University. Archived from the original (PDF) on 20 July 2011.
"Electroweak". The Particle Adventure. Particle Data Group. Retrieved 3 March 2011.
Walter Greiner; Berndt Müller (2009). Gauge Theory of Weak Interactions. Springer. p. 2. ISBN 978-3-540-87842-1.
Cottingham & Greenwood (1986, 2001), p. 29.
Cottingham & Greenwood (1986, 2001), p. 28
Cottingham & Greenwood (1986, 2001), p. 30
Baez, John C.; Huerta, John (2010). "The algebra of grand unified theories". Bulletin of the American Mathematical Society. 0904 (3): 483–552. arXiv:0904.1556. Bibcode:2009arXiv0904.1556B. doi:10.1090/s0273-0979-10-01294-2. Retrieved 15 October 2013.
K. Nakamura et al. (Particle Data Group) (2010). "Gauge and Higgs Bosons" (PDF). Journal of Physics G. 37 (7A): 075021. Bibcode:2010JPhG...37g5021N. doi:10.1088/0954-3899/37/7a/075021.
K. Nakamura et al. (Particle Data Group) (2010). "n" (PDF). Journal of Physics G. 37: 7. Bibcode:2010JPhG...37g5021N. doi:10.1088/0954-3899/37/7a/075021.
"The Nobel Prize in Physics 1979". NobelPrize.org. Nobel Media. Retrieved 26 February 2011.
C. Amsler et al. (Particle Data Group) (2008). "Review of Particle Physics – Higgs Bosons: Theory and Searches" (PDF). Physics Letters B. 667 (1): 1–6. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018.
"New results indicate that new particle is a Higgs boson | CERN". Home.web.cern.ch. Retrieved 20 September 2013.
Claudson, M.; Farhi, E.; Jaffe, R. L. (1 August 1986). "Strongly coupled standard model". Physical Review D. 34 (3): 873–887. doi:10.1103/PhysRevD.34.873. PMID 9957220.
Charles W. Carey (2006). "Lee, Tsung-Dao". American scientists. Facts on File Inc. p. 225. ISBN 9781438108070.
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"The Nobel Prize in Physics 1980". NobelPrize.org. Nobel Media. Retrieved 26 February 2011.
M. Kobayashi; T. Maskawa (1973). "CP-Violation in the Renormalizable Theory of Weak Interaction" (PDF). Progress of Theoretical Physics. 49 (2): 652–657. Bibcode:1973PThPh..49..652K. doi:10.1143/PTP.49.652. hdl:2433/66179.
"The Nobel Prize in Physics 2008". NobelPrize.org. Nobel Media. Retrieved 17 March 2011.

Paul Langacker (2001) [1989]. "Cp Violation and Cosmology". In Cecilia Jarlskog (ed.). CP violation. London, River Edge: World Scientific Publishing Co. p. 552. ISBN 9789971505615.

General readers

R. Oerter (2006). The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics. Plume. ISBN 978-0-13-236678-6.
B.A. Schumm (2004). Deep Down Things: The Breathtaking Beauty of Particle Physics. Johns Hopkins University Press. ISBN 0-8018-7971-X.

Texts
Walter Greiner; B. Müller (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 978-0-521-67775-2.
W.N. Cottingham; D.A. Greenwood (2001) [1986]. An introduction to nuclear physics (2nd ed.). Cambridge University Press. p. 30. ISBN 978-0-521-65733-4.
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.

Standard Model
Background

Particle physics
Fermions Gauge boson Higgs boson Quantum field theory Gauge theory Strong interaction
Color charge Quantum chromodynamics Quark model Electroweak interaction
Weak interaction Quantum electrodynamics Fermi's interaction Weak hypercharge Weak isospin