Weak interaction

Standard Model of particle physics
Elementary particles of the Standard Model
Background Particle physics Standard Model Quantum field theory Gauge theory Spontaneous symmetry breaking Higgs mechanism
Constituents Electroweak interaction Quantum chromodynamics CKM matrix Standard Model mathematics
Limitations Strong CP problem Hierarchy problem Neutrino oscillations Physics beyond the Standard Model
Scientists Rutherford Thomson Chadwick Bose Sudarshan Davis Jr Anderson Fermi Dirac Feynman Rubbia Gell-Mann Kendall Taylor Friedman Powell Anderson Glashow Iliopoulos Lederman Maiani Meer Cowan Nambu Chamberlain Cabibbo Schwartz Perl Majorana Weinberg Lee Ward Salam Kobayashi Maskawa Mills Yang Yukawa 't Hooft Veltman Gross Pais Pauli Politzer Reines Schwinger Wilczek Cronin Fitch Vleck Higgs Englert Brout Hagen Guralnik Kibble de Mayolo Lattes Zweig
v t e

In

The effective range of the weak force is limited to subatomic distances and is less than the diameter of a proton.[2]

Background

The

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.^[3] In fact, the force is termed weak because its field strength over any set distance is typically several orders of magnitude less than that of the electromagnetic force, which itself is further orders of magnitude less than the strong nuclear force.

The weak interaction is the only fundamental interaction that breaks

Weak interaction is important in the fusion of hydrogen into helium in a star. This is because it can convert a proton (hydrogen) into a neutron to form deuterium which is important for the continuation of nuclear fusion to form helium. The accumulation of neutrons facilitates the buildup of heavy nuclei in a star.^[3]

Most fermions decay by a weak interaction over time. Such decay makes

The electroweak force is believed to have separated into the electromagnetic and weak forces during the quark epoch of the early universe.

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.^[5][6]

In the mid-1950s,

In the 1960s, 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.^[8][9]

The existence of the W and Z bosons was not directly confirmed until 1983.^[10](p8)

Properties

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

• It is the only interaction that can change the flavour of quarks and leptons (i.e., of changing one type of quark into another).^[a]
• It is the only interaction 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

All mesons are unstable because of weak decay.^[10](p29)[c] In the process known as

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.[d] 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.^[10](p30) A particularly extreme example is the weak-force decay of a free neutron, which takes about 15 minutes.^[10](p28)

Weak isospin and weak hypercharge

All particles have a property called

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 T₃ = ++1/2 and the down quark has T₃ = −+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 conversely.

In any given strong, electromagnetic, or weak interaction, weak isospin is

conserved:^[e] 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).^[10]

^(p30)

For the development of the electroweak theory, another property, weak hypercharge, was invented, defined as

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

where Y_W is the weak hypercharge of a particle with electrical charge Q (in

spin-1/2 particles have a non-zero weak hypercharge.^[f]

Interaction types

There are two types of weak interaction (called

W and Z bosons, however the naming convention predates the concept of the mediator bosons, and clearly (at least in name) labels the charge of the current (formed from the fermions), not necessarily the bosons.^[g]

Charged-current interaction

Main article: Charged current

In one type of charged current interaction, a charged

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 ν_e, muon ν_μ, or tau ν_τ) is the same as the type of lepton in the interaction, for example:

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

Similarly, a down-type

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:

${\displaystyle {\begin{aligned}\mathrm {d} &\to \mathrm {u} +\mathrm {W} ^{-}\\\mathrm {d} +\mathrm {W} ^{+}&\to \mathrm {u} \\\mathrm {c} &\to \mathrm {s} +\mathrm {W} ^{+}\\\mathrm {c} +\mathrm {W} ^{-}&\to \mathrm {s} \end{aligned}}}$

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

${\displaystyle {\begin{aligned}\mathrm {W} ^{-}&\to \mathrm {e} ^{-}+{\bar {\nu }}_{\mathrm {e} }~\\\mathrm {W} ^{+}&\to \mathrm {e} ^{+}+\nu _{\mathrm {e} }~\end{aligned}}}$

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 limited energy involved in the process (i.e., the mass difference between the down quark and the up quark), the virtual
W⁻
boson can only carry sufficient energy to produce an electron and an electron-antineutrino – the two lowest-possible masses among its prospective decay products.^[19] At the quark level, the process can be represented as:

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

Neutral-current interaction

Main article: Neutral current

In

Z boson

. For example:

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

Like the
W^±
 bosons, the
Z⁰
 boson also decays rapidly,^[18] for example:

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

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 or anti-particles, with any electric charge, and both left- and right-chirality, although the strength of the interaction differs.^[h]

The quantum number

electromagnetic interaction: It quantifies the vector part of the interaction. Its value is given by:^[21]

${\displaystyle Q_{\mathsf {w}}=2\,T_{3}-4\,Q\,\sin ^{2}\theta _{\mathsf {w}}=2\,T_{3}-Q+(1-4\,\sin ^{2}\theta _{\mathsf {w}})\,Q~.}$

Since the

weak mixing angle

${\displaystyle \theta _{\mathsf {w}}\approx 29^{\circ }}$, the parenthetic expression ${\displaystyle (1-4\,\sin ^{2}\theta _{\mathsf {w}})\approx 0.060}$, with its value varying slightly with the momentum difference (called "running") between the particles involved. Hence

${\displaystyle \ Q_{\mathsf {w}}\approx 2\ T_{3}-Q=\operatorname {sgn}(Q)\ {\big (}1-|Q|{\big )}\ ,}$

since by convention ${\displaystyle \operatorname {sgn} T_{3}\equiv \operatorname {sgn} Q}$, and for all fermions involved in the weak interaction ${\displaystyle T_{3}=\pm {\tfrac {1}{2}}}$. The weak charge of charged leptons is then close to zero, so these mostly interact with the Z boson through the axial coupling.

Electroweak theory

Main article: Electroweak interaction

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.^[22] 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 photon (γ, the massless gauge boson that carries the electromagnetic interaction).^[23]

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. Likewise, there are four massless electroweak bosons. 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. Naïvely, the symmetry-breaking would be expected to produce three massless bosons, but instead those "extra" three Higgs bosons become incorporated into the three weak bosons, which then acquire mass through the Higgs mechanism. These three composite bosons are the
W⁺
,
W⁻
, and
Z⁰
 bosons actually observed in the weak interaction. The fourth electroweak gauge boson is the photon (γ) of electromagnetism, which does not couple to any of the Higgs fields and so remains massless.^[23]

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 and 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.^[24]

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.^[25]

Violation of symmetry

The

Chien Shiung Wu and collaborators in 1957 discovered that the weak interaction violates parity, earning Yang and Lee the 1957 Nobel Prize in Physics.^[27]

Although the weak interaction was once described by

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

Makoto Kobayashi and Toshihide Maskawa showed that CP violation in the weak interaction required more than two generations of particles,^[29] effectively predicting the existence of a then unknown third generation. This discovery earned them half of the 2008 Nobel Prize in Physics.^[30]

Unlike parity violation, CP violation occurs only in rare circumstances. Despite its limited occurrence under present conditions, 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.^[31]

See also

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

Footnotes

1. ^ Because of its unique ability to change particle flavour, analysis of the weak interaction is occasionally called quantum flavour dynamics, in analogy to the name quantum chromodynamics sometimes used for the strong force.
2. proton charge radius
   of 8.3×10⁻¹⁶ m ~ 0.83 fm.
3. ^ The neutral pion (
   π⁰
   ), however, decays electromagnetically, and several other mesons (when their quantum numbers permit) mostly decay via a strong interaction.
4. ^ The prominent and possibly unique exception to this rule is the decay of the
   color force
   ") can bind it to other quarks.
5. ^ Only interactions with the Higgs boson violate conservation of weak isospin, and appear to always do so maximally: ${\displaystyle {\bigl |}\Delta T_{3}{\bigr |}={\tfrac {1}{2}}\ .}$
6. ^ Some hypothesised fermions, such as the sterile neutrinos, would have zero weak hypercharge – in fact, no gauge charges of any known kind. Whether any such particles actually exist is an active area of research.
7. ^ The exchange of a virtual W boson can be equally well thought of as (say) the emission of a W⁺ or the absorption of a W⁻; that is, for time on the vertical co‑ordinate axis, as a W⁺ from left to right, or equivalently as a W⁻ from right to left.
8. ^ The only fermions which the
   Z⁰
   does not interact with at all 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, except perhaps the Higgs boson. So far they remain entirely a conjecture: As of October 2021, no such neutrinos are known to actually exist.

   "MicroBooNE has made a very comprehensive exploration through multiple types of interactions, and multiple analysis and reconstruction techniques", says co-spokesperson Bonnie Fleming of Yale. "They all tell us the same thing, and that gives us very high confidence in our results that we are not seeing a hint of a sterile neutrino."^[20]

   ... "eV-scale sterile neutrinos no longer appear to be experimentally motivated, and never solved any outstanding problems in the Standard Model", says theorist Mikhail Shaposhnikov of EPFL. "But GeV-to-keV-scale sterile neutrinos – so-called Majorana fermions – are well motivated theoretically and do not contradict any existing experiment."^[20]

References

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2. ISSN 0003-4916
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3. ^ ^{a b} Nave, CR. "Fundamental Forces - The Weak Force". Georgia State University. Archived from the original on 2 April 2023. Retrieved 12 July 2023.
4. ^ "The Nobel Prize in Physics 1979". NobelPrize.org (Press release). Nobel Media. Retrieved 22 March 2011.
5. S2CID 125763380
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15. ^ "Electroweak". The Particle Adventure. Particle Data Group. Retrieved 3 March 2011.
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    S2CID 2941843
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    doi:10.1088/0954-3899/37/7a/075021
    .
20. ^ ^{a b} Rayner, Mark (28 October 2021). "MicroBooNE sees no hint of a sterile neutrino". CERN Courier. Retrieved 9 November 2021.
21. ^ Dzuba, V. A.; Berengut, J. C.; Flambaum, V. V.; Roberts, B. (2012). "Revisiting parity non-conservation in Cesium". Physical Review Letters. 109 (20): 203003.
    S2CID 27741778
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22. ^ "The Nobel Prize in Physics 1979". NobelPrize.org. Nobel Media. Retrieved 26 February 2011.
23. ^ ^{a b} C. Amsler et al. (
    S2CID 227119789
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24. ^ "New results indicate that new particle is a Higgs boson". home.web.cern.ch. CERN. March 2013. Retrieved 20 September 2013.
25. PMID 9957220
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26. ^ Carey, Charles W. (2006). "Lee, Tsung-Dao". American scientists. Facts on File Inc. p. 225.
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27. ^ "The Nobel Prize in Physics". NobelPrize.org. Nobel Media. 1957. Retrieved 26 February 2011.
28. ^ "The Nobel Prize in Physics". NobelPrize.org. Nobel Media. 1980. Retrieved 26 February 2011.
29. ^ Kobayashi, M.; Maskawa, T. (1973). "CP-Violation in the Renormalizable Theory of Weak Interaction" (PDF).
    hdl:2433/66179
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    ISBN 9789971505615
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• ISBN 3-540-67672-4
  .
• Coughlan, G. D.; Dodd, J. E.; Gripaios, B. M. (2006). The Ideas of Particle Physics: An introduction for scientists (3rd ed.). Cambridge University Press.
  ISBN 978-0-521-67775-2
  .
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  ISBN 978-0-521-65733-4
  .
• Griffiths, D. J. (1987). Introduction to Elementary Particles. John Wiley & Sons.
  ISBN 0-471-60386-4
  .

• Kane, G. L. (1987). Modern Elementary Particle Physics.
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  .
• Perkins, D. H. (2000). Introduction to High Energy Physics. Cambridge University Press.
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For general readers

• Oerter, R. (2006). The Theory of Almost Everything: The Standard Model, the unsung triumph of modern physics.
  ISBN 978-0-13-236678-6
  .
• Schumm, B. A. (2004). Deep Down Things: The breathtaking beauty of particle physics.
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External links

Wikiquote has quotations related to Weak interaction.

• Harry Cheung, The Weak Force @Fermilab
• Fundamental Forces @Hyperphysics, Georgia State University.
• Brian Koberlein, What is the weak force?