Weak interaction

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The radioactive beta decay is due to the weak interaction, which transforms a neutron into a proton, an electron, and an electron antineutrino.

Template:Standard model of particle physics

In nuclear physics and particle physics, the weak interaction, weak force or the weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction, and gravitation. It 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 nuclear fusion. The theory describing its behaviour and effects is sometimes called quantum flavordynamics (QFD); however, the term QFD is rarely used, because the weak force is better understood by electroweak theory (EWT).<ref name="griffiths">Template:Cite book</ref>

The effective range of the weak force is limited to subatomic distances and is less than the diameter of a proton.<ref>Template:Cite journal</ref>

BackgroundEdit

The Standard Model of particle physics provides a uniform framework for understanding 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 electric (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 and Z bosons|Template:Math⁺, Template:Math⁻, and Template:Math 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.<ref name="hyperphysics">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> 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 parity symmetry, and similarly, but far more rarely, the only interaction to break charge–parity symmetry.

Quarks, which make up composite particles like neutrons and protons, come in six "flavours"Template:Snd up, down, charm, strange, top and bottomTemplate:Snd 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.

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.<ref name="hyperphysics"/>

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 luminescence, and in the related field of betavoltaics<ref>Template:Cite press release</ref> (but not similar to radium luminescence).

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

HistoryEdit

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.<ref name="Fermi's theory">Template:Cite journal</ref><ref name="Fermi's theory translation">Template:Cite journal</ref>

In the mid-1950s, Chen-Ning Yang and Tsung-Dao Lee first suggested that the handedness of the spins of particles in weak interaction might violate the conservation law or symmetry. In 1957, the Wu experiment, carried by Chien Shiung Wu and collaborators confirmed the symmetry violation.<ref> {{#invoke:citation/CS1|citation |CitationClass=web }} </ref>

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.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref><ref name="Salam">Template:Cite press release</ref>

The [[W and Z bosons#Discovery|existence of the Template:Math and Template:Math bosons]] was not directly confirmed until 1983.<ref name=Cottingham-Greenwood-1986-2001> Template:Cite book</ref>Template:Rp

PropertiesEdit

File:Weak Decay (flipped).svg

A diagram depicting the decay routes for the six quarks 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 and leptons (i.e., of changing one type of quark into another).Template:Efn
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<ref name="PDG">Template:Cite journal</ref>) these carrier particles, called the Template:Math and Template:Math bosons, are short-lived with a lifetime of under Template:10^ seconds.<ref>Template:Cite book</ref> The weak interaction has a coupling constant (an indicator of how frequently interactions occur) between Template:10^ and Template:10^, compared to the electromagnetic coupling constant of about Template:10^ and the strong interaction coupling constant of about 1;<ref name="coupling">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> consequently the weak interaction is "weak" in terms of intensity.<ref name="physnet"/> The weak interaction has a very short effective range (around Template:10^ to Template:10^ m (0.01 to 0.1 fm)).Template:Efn<ref name="physnet">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref><ref name="coupling"/> At distances around Template:10^ meters (0.001 fm), the weak interaction has an intensity 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 3Template:E m, the weak interaction becomes 10,000 times weaker.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

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 Template:Snd something that gravity does on an astronomical scale, the electromagnetic force does at the molecular and atomic levels, and the strong nuclear force does only at the subatomic level, inside of nuclei.<ref name="greiner">Template:Cite book</ref>

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 can only proceed by weak decay; without weak decay, quark properties such as strangeness and charm (associated with the strange quark and charm quark, respectively) would also be conserved across all interactions.

All mesons are unstable because of weak decay.<ref name=Cottingham-Greenwood-1986-2001/>Template:Rp Template:Efn In the process known as beta decay, a down quark in the neutron can change into an up quark by emitting a virtual Template:Math boson, which then decays into an electron and an electron antineutrino.<ref name=Cottingham-Greenwood-1986-2001/>Template:Rp Another example is electron capture Template:Snd a common variant of radioactive decay Template:Snd 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.Template:Efn For example, a neutral pion decays electromagnetically, and so has a life of only about Template:10^ seconds. In contrast, a charged pion can only decay through the weak interaction, and so lives about Template:10^ seconds, or a hundred million times longer than a neutral pion.<ref name=Cottingham-Greenwood-1986-2001/>Template:Rp A particularly extreme example is the weak-force decay of a free neutron, which takes about 15 minutes.<ref name=Cottingham-Greenwood-1986-2001/>Template:Rp

Weak isospin and weak hyperchargeEdit

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Left-handed fermions in the Standard Model<ref name="baez"> Template:Cite journal </ref>
Generation 1			Generation 2			Generation 3
Fermion	Symbol	Weak isospin	Fermion	Symbol	Weak isospin	Fermion	Symbol	Weak isospin
electron neutrino	Template:Math	Template:Sfrac	muon neutrino	Template:Math	Template:Sfrac	tau neutrino	Template:Math	Template:Sfrac
electron	Template:Math	Template:Sfrac	muon	Template:Math	Template:Sfrac	tau	Template:Math	Template:Sfrac
up quark	Template:Math	Template:Sfrac	charm quark	Template:Math	Template:Sfrac	top quark	Template:Math	Template:Sfrac
down quark	Template:Math	Template:Sfrac	strange quark	Template:Math	Template:Sfrac	bottom quark	Template:Math	Template:Sfrac
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 Template:Mvar₃), which serves as an additive quantum number that restricts how the particle can interact with the Template:Math of the weak force. Weak isospin plays the same role in the weak interaction with Template:Math as electric charge does in electromagnetism, and color charge in the strong interaction; a different number with a similar name, weak charge, discussed below, is used for interactions with the Template:Math. All left-handed fermions have a weak isospin value of either Template:Sfrac or Template:Sfrac; all right-handed fermions have 0 isospin. For example, the up quark has Template:Nowrap and the down quark has Template:Nowrap. A quark never decays through the weak interaction into a quark of the same Template:Mvar₃: Quarks with a Template:Mvar₃ of Template:Sfrac only decay into quarks with a Template:Mvar₃ of Template:Sfrac and conversely.

File:PiPlus muon decay.svg

Template:SubatomicParticle decay through the weak interaction

In any given strong, electromagnetic, or weak interaction, weak isospin is conserved:Template:Efn 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) Template:Math with a weak isospin of +1 normally decays into a Template:Math (with Template:Nowrap) and a Template:Math (as a right-handed antiparticle, Template:Sfrac).<ref name=Cottingham-Greenwood-1986-2001/>Template:Rp

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

where Template:Mvar_W is the weak hypercharge of a particle with electrical charge Template:Mvar (in elementary charge units) and weak isospin Template:Mvar₃. Weak hypercharge is the generator of the U(1) component of the electroweak gauge group; whereas some particles have a weak isospin of zero, all known [[fermions|spin-Template:Sfrac particles]] have a non-zero weak hypercharge.Template:Efn

Interaction typesEdit

There are two types of weak interaction (called vertices). The first type is called the "charged-current interaction" because the weakly interacting fermions form a current with total electric charge that is nonzero. The second type is called the "neutral-current interaction" because the weakly interacting fermions form a current with total electric charge of zero. It is responsible for the (rare) deflection of neutrinos. The two types of interaction follow different selection rules. This naming convention is often misunderstood to label the electric charge of the [[W and Z boson|Template:Math and Template:Math boson]]s, 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.Template:Efn

Charged-current interactionEdit

{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}}

File:Beta Negative Decay.svg

The Feynman diagram for beta-minus decay of a neutron (Template:Math) into a proton (Template:Math), electron (Template:Math), and electron anti-neutrino Template:Math, via a charged vector boson (Template:Math).

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|Template:Math 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 Template:Math, muon Template:Math, or tau Template:Math) is the same as the type of lepton in the interaction, for example:

<math> \mu^- + \mathrm{W}^+ \to \nu_\mu </math>

Similarly, a down-type quark (Template:Math, Template:Math, or Template:Math, with a charge of Template:Sfrac) can be converted into an up-type quark (Template:Math, Template:Math, or Template:Math, with a charge of Template:Sfrac), by emitting a Template:SubatomicParticle boson or by absorbing a Template:Math 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 Template:Math boson, or absorb a Template:Math boson, and thereby be converted into a down-type quark, for example:

<math>\begin{align}

                \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{align}</math>

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

<math>\begin{align}

 \mathrm{W}^- &\to \mathrm{e}^- + \bar\nu_\mathrm{e} ~ \\
 \mathrm{W}^+ &\to \mathrm{e}^+ + \nu_\mathrm{e} ~

\end{align}</math>

Decay of a W boson to other products can happen, with varying probabilities.<ref name="PDG2">Template:Cite journal</ref>

In the so-called beta decay of a neutron (see picture, above), a down quark within the neutron emits a virtual Template:Math 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 Template:Math boson can only carry sufficient energy to produce an electron and an electron-antineutrino – the two lowest-possible masses among its prospective decay products.<ref name=PDG3> Template:Cite journal </ref> At the quark level, the process can be represented as:

<math> \mathrm{d} \to \mathrm{u} + \mathrm{e}^- + \bar\nu_\mathrm{e} ~</math>

Neutral-current interactionEdit

{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}} In neutral current interactions, a quark or a lepton (e.g., an electron or a muon) emits or absorbs a neutral [[Z boson|Template:Math boson]]. For example:

<math> \mathrm{e}^- \to \mathrm{e}^- + \mathrm{Z}^0</math>

Like the Template:Math bosons, the Template:Math boson also decays rapidly,<ref name="PDG2"/> for example:

<math> \mathrm{Z}^0 \to \mathrm{b} + \bar \mathrm{b} </math>

Unlike the charged-current interaction, whose selection rules are strictly limited by chirality, electric charge, Template:Nowrap weak isospin, the neutral-current Template:Math 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.Template:Efn

Template:AnchorThe quantum number weak charge (Template:Mvar_Template:Sc) serves the same role in the neutral current interaction with the Template:Math that electric charge (Template:Mvar, with no subscript) does in the electromagnetic interaction: It quantifies the vector part of the interaction. Its value is given by:<ref name=dzuba> Template:Cite journal </ref>

<math> 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 ~.</math>

Since the weak mixing angle Template:Tmath, the parenthetic expression Template:Tmath, with its value varying slightly with the momentum difference (called "running") between the particles involved. Hence

<math>\ Q_\mathsf{w} \approx 2 \ T_3 - Q = \sgn(Q)\ \big(1 - |Q|\big)\ ,</math>

since by convention Template:Tmath, and for all fermions involved in the weak interaction Template:Tmath. The weak charge of charged leptons is then close to zero, so these mostly interact with the Template:Math boson through the axial coupling.

Electroweak theoryEdit

Template:Main article 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.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> The Higgs mechanism provides an explanation for the presence of three massive gauge bosons (Template:Math, Template:Math, Template:Math, the three carriers of the weak interaction), and the photon (Template:Math, the massless gauge boson that carries the electromagnetic interaction).<ref name="PDGHiggs"> Template:Cite journal </ref>

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 scalar bosons forming a complex scalar Higgs field doublet. Likewise, there are four massless electroweak vector bosons, each similar to the photon. However, at low energies, this gauge symmetry is spontaneously broken down to the Template:Math 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 Template:Math, Template:Math, and Template:Math bosons actually observed in the weak interaction. The fourth electroweak gauge boson is the photon (Template:Mvar) of electromagnetism, which does not couple to any of the Higgs fields and so remains massless.<ref name="PDGHiggs"/>

This theory has made a number of predictions, including a prediction of the masses of the Template:Math and Template:Math 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 Template:Val, 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.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

In a speculative case where the electroweak symmetry breaking scale were lowered, the unbroken Template:Math interaction would eventually become confining. Alternative models where Template:Math becomes confining above that scale appear quantitatively similar to the Standard Model at lower energies, but dramatically different above symmetry breaking.<ref>Template:Cite journal</ref>

Violation of symmetryEdit

File:Right left helicity.svg

Left- and right-handed particles: Template:Mvar is the particle's momentum and Template:Mvar 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 separately constructed, mirror-reflected copy of the experimental apparatus watched through the mirror. 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.<ref> Template:Cite book </ref> 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.<ref> {{#invoke:citation/CS1|citation |CitationClass=web }} </ref>

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.<ref> {{#invoke:citation/CS1|citation |CitationClass=web }} </ref> In 1973, Makoto Kobayashi and Toshihide Maskawa showed that CP violation in the weak interaction required more than two generations of particles,<ref name="KM"> Template:Cite journal </ref> effectively predicting the existence of a then unknown third generation. This discovery earned them half of the 2008 Nobel Prize in Physics.<ref> {{#invoke:citation/CS1|citation |CitationClass=web }} </ref>

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.<ref> Template:Cite book </ref>