Standard model of particle physics
Standard Model
Background Particle physics Quantum field theory Gauge theory Spontaneous symmetry breaking Higgs mechanism
Constituents Electroweak interaction Quantum chromodynamics CKM matrix
Limitations Strong CP problem Hierarchy problem Neutrino oscillations
Theorists Sudarshan · Marshak · Feynman · Gell-Mann · Sakata · Glashow · Zweig · Nambu · Han · Cabibbo · Weinberg · Salam · Kobayashi · Maskawa · 't Hooft · Veltman · Gross · Politzer · Wilczek · Riazuddin
v t e

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; as such, it is considered to be 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 flavour changing allows for quarks to swap their 'flavour', 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^[1]). However, 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. The theory of the weak interaction can be called Quantum Flavordynamics (QFD), in analogy with the terms QCD and QED, but in practice the term is rarely used because the weak force is best understood in terms of electro-weak theory (EWT).^[2]

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.^[3]

Properties[link]

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/c^2[4]) these carrier particles, termed the W and Z bosons, are short-lived: they have a lifetime of under 1×10⁻²⁴ seconds.^[5] 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 and the electromagnetic coupling constant of about 10^-2;^[6] consequently the weak interaction is weak in terms of strength.^[7] The weak interaction has a very short range (around 10⁻¹⁷–10⁻¹⁶ m^[7]).^[6] 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.^[8]

The weak interaction affects all the fermions of the Standard Model, as well as the hypothetical Higgs boson; neutrinos interact through gravity and the weak interaction only, and neutrinos were the original reason for the name weak force.^[7] 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.^[9]

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.^[10] 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.^[11]

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.^[12] In contrast, a free neutron (which also decays through the weak interaction) lives about 15 minutes.^[11]

Weak isospin and weak hypercharge[link]

Weak isospin (T₃) is a property (quantum number) of all particles, which governs how particles interact in the weak interaction.^{[citation needed]} Weak isospin is to the weak interaction what electric charge is to the electromagnetism, and what color charge is to strong interaction. Elementary particles that are fermions 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. Bosons have weak isospin of ±1, or 0.

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 a weak isospin of 1 normally decays into a ν
μ (+1/2) and a μ+
(as a right-handed antiparticle, +1/2).^[12]

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:

Failed to parse (Missing texvc executable; please see math/README to configure.): \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.^{[citation needed]} Weak hypercharge is the generator of the U(1) component of the electroweak gauge group.^{[citation needed]}

Violation of symmetry[link]

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.^[14] 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.^[15]

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.^[16] In 1973, Makoto Kobayashi and Toshihide Maskawa showed that CP violation in the weak interaction required more than two generations of particles,^[17] effectively predicting the existence of a then unknown third generation. This discovery earned them half of the 2008 Nobel Prize in Physics.^[18] 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.^[19]

Interaction types[link]

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[link]

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:

Failed to parse (Missing texvc executable; please see math/README to configure.): \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:

Failed to parse (Missing texvc executable; please see math/README to configure.): d \to u+ W^-

Failed to parse (Missing texvc executable; please see math/README to configure.): d+ W^+\to u

Failed to parse (Missing texvc executable; please see math/README to configure.): c\to s + W^+

Failed to parse (Missing texvc executable; please see math/README to configure.): c+ W^-\to s

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

Failed to parse (Missing texvc executable; please see math/README to configure.): W^-\to e^- + \bar\nu_e~

Failed to parse (Missing texvc executable; please see math/README to configure.): W^+\to e^+ + \nu_e~

Decay of the W boson to other products can happen, with varying probabilities.^[20]

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.^[21] At the quark level, the process can be represented as:

Failed to parse (Missing texvc executable; please see math/README to configure.): d\to u+ e^- + \bar\nu_e~

Neutral current interaction[link]

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:

Failed to parse (Missing texvc executable; please see math/README to configure.): e^-\to e^- + Z^0

Like the W boson, the Z boson also decays rapidly,^[20] for example:

Failed to parse (Missing texvc executable; please see math/README to configure.): Z^0\to b+\bar b

Electroweak theory[link]

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.^[22] 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.^[23]

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.^[23]

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.^[24]

See also[link]

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

References[link]

Citations[link]

General readers[link]

• 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[link]

• 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 978-0-521-67775-2. 
• W. N. Cottingham; D. A. Greenwood (1986, 2001). An introduction to nuclear physics (2 ed.). Cambridge University Press. p. 30. ISBN 978-0-521-65733-4. http://books.google.co.uk/books?id=0VIpJPn-qWoC&pg=PA30. 
• 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. 

A Feynman diagram of a strong proton-neutron interaction mediated by a neutral pion. Time proceeds from left to right.

The same diagram with the individual quark constituents shown, to illustrate how the fundamental strong interaction gives rise to the nuclear force. Straight lines are quarks, while multi-colored loops are gluons (the carriers of the fundamental force). Other gluons, which bind together the proton, neutron, and pion "in-flight," are not shown.

An animation of the interaction. The colored double circles are gluons. Anticolors are shown as per this diagram. For a larger version, click here

The nuclear force (or nucleon-nucleon interaction or residual strong force) is the force between two or more nucleons. It is responsible for binding of protons and neutrons into atomic nuclei. The energy released causes the masses of nuclei to be less than the total mass of the protons and neutrons which form them. The force is powerfully attractive between nucleons at distances of about 1 femtometer (fm) between their centers, but rapidly decreases to insignificance at distances beyond about 2.5 fm. At very short distances less than 0.7 fm, it becomes repulsive, and is responsible for the physical size of nuclei, since the nucleons can come no closer than the force allows.

The nuclear force is now understood as a residual effect of the even more powerful strong force, or strong interaction, which is the attractive force that binds particles called quarks together, to form the nucleons themselves. This more powerful force is mediated by particles called gluons. Gluons hold quarks together with a force like that of electric charge, but of far greater power.

The concept of a nuclear force was first quantitatively constructed in 1934, shortly after the discovery of the neutron revealed that atomic nuclei were made of protons and neutrons, held together by an attractive force. The nuclear force at that time was conceived to be transmitted by particles called mesons, which were predicted in theory before being discovered in 1947. In the 1970’s, further understanding revealed these mesons to be combinations of quarks and gluons, transmitted between nucleons that themselves were made of quarks and gluons. This new model allowed the strong forces that held nucleons together, to be felt in neighboring nucleons, as residual strong forces.

The nuclear forces arising between nucleons are now seen to be analogous to the forces in chemistry between neutral atoms called van der Waals forces. Such forces between atoms are much weaker than the electrical forces that hold the atoms themselves together, and their range is shorter, because they arise from spontaneous separation of charges inside the atom. Similarly, even though nucleons are made of quarks and gluons that are in combinations which cancel most gluon forces, some combinations of quarks and gluons nevertheless leak away from nucleons, in the form of short-range nuclear force fields that extend from one nucleon to another close by. These nuclear forces are very weak compared to direct gluon forces inside nucleons, and they extend only over a few nuclear diameters, falling exponentially with distance. Nevertheless, they are strong enough to bind neutrons and protons over short distances, and overcome the electrical repulsion between protons in the nucleus.

History[link]

The nuclear force has been at the heart of nuclear physics ever since the field was born in 1932 with the discovery of the neutron by James Chadwick. The traditional goal of nuclear physics is to understand the properties of atomic nuclei in terms of the 'bare' interaction between pairs of nucleons, or nucleon-nucleon forces (NN forces).

In 1934, Hideki Yukawa made the earliest attempt to explain the nature of the nuclear force. According to his theory, massive bosons (mesons) mediate the interaction between two nucleons. Although, in light of QCD, meson theory is no longer perceived as fundamental, the meson-exchange concept (where hadrons are treated as elementary particles) continues to represent the best working model for a quantitative NN potential.

Historically, it was a formidable task to describe the nuclear force phenomenologically, and the first semi-empirical quantitative models came in the mid-1950s. There has been substantial progress in experiment and theory related to the nuclear force. Most basic questions were settled in the 1960s and 1970s. In recent years, experimenters have concentrated on the subtleties of the nuclear force, such as its charge dependence, the precise value of the πNN coupling constant, improved phase shift analysis, high-precision NN data, high-precision NN potentials, NN scattering at intermediate and high energies, and attempts to derive the nuclear force from QCD.

To a large extent, the nuclear force can be understood in terms of the exchange of virtual light mesons, such as the pions. Sometimes the nuclear force is called the residual strong force, in contrast to the strong interactions which are now understood to arise from quantum chromodynamics (QCD). This phrasing arose during the 1970s when QCD was being established. Before that time, the strong nuclear force referred to the inter-nucleon potential. After the verification of the quark model, strong interaction has come to mean QCD.

Basic properties of the nuclear force[link]

The nuclear force is only felt among hadrons. At small separations between nucleons (less than ~ 0.7 femtometer (fm) between their centers, depending upon spin alignment) the force becomes repulsive, which keeps the nucleons at a certain average separation, even if they are of different types. This repulsion is to be understood in terms of the Pauli exclusion force for identical nucleons (such as two neutrons or two protons), and also a Pauli exclusion between quarks of the same type within nucleons, when the nucleons are different (a proton and a neutron, for example). As will be discussed, the nuclear force also has a "tensor" component which depends on whether or not the spins of the nucleons are aligned or anti-aligned. A graph of internuclear forces and potentials is presented in the reference:^[1]

At distances larger than 0.7 fm the force becomes attractive between spin-aligned nucleons, becoming maximal at a center-center distance of about 0.9 fm. Beyond this distance the force drops essentially exponentially, until beyond about 2.0 fm separation, the force drops to negligibly small values.

At short distances (less than 1.7 fm or so), the nuclear force is stronger than the Coulomb force between protons; it thus overcomes the repulsion of protons inside the nucleus. However, the Coulomb force between protons has a much larger range due to its decay as the inverse square of charge separation, and Coulomb repulsion thus becomes the only significant force between protons when their separation exceeds about 2 to 2.5 fm.

To disassemble a nucleus into unbound protons and neutrons would require doing work against the nuclear force. Conversely, energy is released when a nucleus is created from other nucleons or nuclei: the nuclear binding energy. Because of mass–energy equivalence (i.e. Einstein's famous formula E = mc²), releasing this energy causes the mass of the nucleus to be lower than the total mass of the individual nucleons, leading to the so-called "mass deficit".^[2]

The nuclear force is nearly independent of whether the nucleons are neutrons or protons. This property is called charge independence. It depends on whether the spins of the nucleons are parallel or antiparallel, and has a noncentral or tensor component. This part of the force does not conserve orbital angular momentum, which is a constant of motion under central forces.

Since nucleons have no color charge, the nuclear force does not directly involve the force carriers of quantum chromodynamics, the gluons. However, just as electrically neutral atoms (each composed of cancelling charges) attract each other via the second-order effects of electrical polarization, via the van der Waals forces (London forces), so by analogy, "color-neutral" nucleons may attract each other by a type of polarization which allows some basically gluon-mediated effects to be carried from one color-neutral nucleon to another, via the virtual mesons which transmit the forces, and which themselves are held together by virtual gluons. It is this van der Waals-like nature which is responsible for the term "residual" in the term "residual strong force." The basic idea is that while the nucleons are "color-neutral," just as atoms are "charge-neutral," in both cases, polarization effects acting between near-by neutral particles allow a "residual" charge effect to cause net charge-mediated attraction between uncharged species, although it is necessarily of a much weaker and less direct nature than the basic forces which act internally within the particles.^[3]

Nucleon-nucleon potentials[link]

Two-nucleon systems such as the deuteron, the nucleus of a deuterium atom, as well as proton-proton or neutron-proton scattering are ideal for studying the NN force. Such systems can be described by attributing a potential (such as the Yukawa potential) to the nucleons and using the potentials in a Schrödinger equation. The form of the potential is derived phenomenologically, although for the long-range interaction, meson-exchange theories help to construct the potential. The parameters of the potential are determined by fitting to experimental data such as the deuteron binding energy or NN elastic scattering cross sections (or, equivalently in this context, so-called NN phase shifts).

The most widely used NN potentials are the Paris potential, the Argonne AV18 potential ^[4], the CD-Bonn potential and the Nijmegen potentials.

A more recent approach is to develop effective field theories for a consistent description of nucleon-nucleon and three-nucleon forces. In particular, chiral symmetry breaking can be analysed in terms of an effective field theory (called chiral perturbation theory) which allows perturbative calculations of the interactions between nucleons with pions as exchange particles.

From nucleons to nuclei[link]

The ultimate goal of nuclear physics would be to describe all nuclear interactions from the basic interactions between nucleons. This is called the microscopic or ab initio approach of nuclear physics. There are two major obstacles to overcome before this dream can become reality:

• Calculations in many-body systems are difficult and require advanced computation techniques.
• There is evidence that three-nucleon forces (and possibly higher multi-particle interactions) play a significant role. This means that three-nucleon potentials must be included into the model.

This is an active area of research with ongoing advances in computational techniques leading to better first-principles calculations of the nuclear shell structure. Two- and three-nucleon potentials have been implemented for nuclear masses up to A=12.

Nuclear potentials[link]

A successful way of describing nuclear interactions is to construct one potential for the whole nucleus instead of considering all its nucleon components. This is called the macroscopic approach. For example, scattering of neutrons from nuclei can be described by considering a plane wave in the potential of the nucleus, which comprises a real part and an imaginary part. This model is often called the optical model since it resembles the case of light scattered by an opaque glass sphere.

Nuclear potentials can be local or global: local potentials are limited to a narrow energy range and/or a narrow nuclear mass range, while global potentials, which have more parameters and are usually less accurate, are functions of the energy and the nuclear mass and can therefore be used in a wider range of applications.

References[link]

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (October 2007)

• Gerald Edward Brown and A. D. Jackson, The Nucleon-Nucleon Interaction, (1976) North-Holland Publishing, Amsterdam ISBN 0-7204-0335-9
• R. Machleidt and I. Slaus, "The nucleon-nucleon interaction", J. Phys. G 27 (2001) R69 (topical review).
• Kenneth S. Krane, "Introductory Nuclear Physics", (1988) Wiley & Sons ISBN 0-471-80553-X
• P. Navrátil and W.E. Ormand, "Ab initio shell model with a genuine three-nucleon force for the p-shell nuclei", Phys. Rev. C 68, 034305 (2003).