Lepton

From Wikipedia, the free encyclopedia

Lepton

Leptons are involved in several processes such as beta decay.
Composition	Elementary particle
Statistics	Fermionic
Generation	1st, 2nd, 3rd
Interactions	Electromagnetism, Gravitation, Weak
Symbol	l
Antiparticle	Antilepton (l)
Types	6 (electron, electron neutrino, muon, muon neutrino, tau, tau neutrino)
Electric charge	+1 e, 0 e, −1 e
Color charge	No
Spin	1⁄2

A lepton is an elementary, spin-¹⁄₂ particle that does not undergo strong interactions, but is subject to the Pauli exclusion principle.^[1] The best known of all leptons is the electron, which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons), and neutral leptons (better known as neutrinos). Charged leptons can combine with other particles to form various composite particles such as atoms and positronium, while neutrinos rarely interact with anything, and are consequently rarely observed.

There are six types of leptons, known as flavours, forming three generations.^[2] The first generation is the electronic leptons, comprising the electron (e−) and electron neutrino (ν
e); the second is the muonic leptons, comprising the muon (μ−) and muon neutrino (ν
μ); and the third is the tauonic leptons, comprising the tau (τ−) and the tau neutrino (ν
τ). Electrons have the least mass of all the charged leptons. The heavier muons and taus will rapidly change into electrons through a process of particle decay: the transformation from a higher mass state to a lower mass state. Thus electrons are stable and the most common charged lepton in the universe, whereas muons and taus can only be produced in high energy collisions (such as those involving cosmic rays and those carried out in particle accelerators).

Leptons have various intrinsic properties, including electric charge, spin, and mass. Unlike quarks however, leptons are not subject to the strong interaction, but they are subject to the other three fundamental interactions: gravitation, electromagnetism (excluding neutrinos, which are electrically neutral), and the weak interaction. For every lepton flavor there is a corresponding type of antiparticle, known as antilepton, that differs from the lepton only in that some of its properties have equal magnitude but opposite sign. However, according to certain theories, neutrinos may be their own antiparticle, but it is not currently known whether this is the case or not.

The first charged lepton, the electron, was theorized in the mid-19th century by several scientists^[3][4][5] and was discovered in 1897 by J. J. Thomson.^[6] The next lepton to be observed was the muon, discovered by Carl D. Anderson in 1936, but it was erroneously classified as a meson at the time.^[7] After investigation, it was realized that the muon did not have the expected properties of a meson, but rather behaved like an electron, only with higher mass. It took until 1947 for the concept of "leptons" as a family of particle to be proposed.^[8] The first neutrino, the electron neutrino, was proposed by Wolfgang Pauli in 1930 to explain certain characteristics of beta decay.^[8] It was first observed in the Cowan–Reines neutrino experiment conducted by Clyde Cowan and Frederick Reines in 1956.^[8][9] The muon neutrino was discovered in 1962 by Leon M. Lederman, Melvin Schwartz and Jack Steinberger,^[10] and the tau discovered between 1974 and 1977 by Martin Lewis Perl and his colleagues from the Stanford Linear Accelerator Center and Lawrence Berkeley National Laboratory.^[11] The tau neutrino remained elusive until July 2000, when the DONUT collaboration from Fermilab announced its discovery.^[12][13]

Leptons are an important part of the Standard Model. Electrons are one of the components of atoms, alongside protons and neutrons. Exotic atoms with muons and taus instead of electrons can also be synthesized, as well as lepton–antilepton particles such as positronium.

Etymology

The name lepton comes from the Greek λεπτόν (leptón), neuter of λεπτός (leptós), "fine, small, thin";^[14] the earliest attested form of the word is the Mycenaean Greek 𐀩𐀡𐀵, re-po-to, written in Linear B syllabic script.^[15] Lepton was first used by physicist Léon Rosenfeld in 1948:^[16]

Following a suggestion of Prof. C. Møller, I adopt — as a pendant to "nucleon" — the denomination "lepton" (from λεπτός, small, thin, delicate) to denote a particle of small mass.

The etymology incorrectly implies that all the leptons are of small mass. When Rosenfeld named them, the only known leptons were electrons and muons, which are in fact of small mass — the mass of an electron (0.511 MeV/c²)^[17] and the mass of a muon (with a value of 105.7 MeV/c²)^[18] are fractions of the mass of the "heavy" proton (938.3 MeV/c²).^[19] However, the mass of the tau (discovered in the mid 1970s) (1777 MeV/c²)^[20] is nearly twice that of the proton, and about 3,500 times that of the electron.

History

A muon transmutes into a muon neutrino by emitting a W− boson. The W− boson subsequently decays into an electron and an electron antineutrino.

The first lepton identified was the electron, discovered by J.J. Thomson and his team of British physicists in 1897.^[21][22]
Then in 1930 Wolfgang Pauli postulated the electron neutrino to preserve conservation of energy, conservation of momentum, and conservation of angular momentum in beta decay.^[23] Pauli theorized that an undetected particle was carrying away the difference between the energy, momentum, and angular momentum of the initial and observed final particles. The electron neutrino was simply called the neutrino, as it was not yet known that neutrinos came in different flavours (or different "generations").

Nearly 40 years after the discovery of the electron, the muon was discovered by Carl D. Anderson in 1936. Due to its mass, it was initially categorized as a meson rather than a lepton.^[24] It later became clear that the muon was much more similar to the electron than to mesons, as muons do not undergo the strong interaction, and thus the muon was reclassified: electrons, muons, and the (electron) neutrino were grouped into a new group of particles – the leptons. In 1962 Leon M. Lederman, Melvin Schwartz and Jack Steinberger showed that more than one type of neutrino exists by first detecting interactions of the muon neutrino, which earned them the 1988 Nobel Prize, although by then the different flavours of neutrino had already been theorized.^[25]

The tau was first detected in a series of experiments between 1974 and 1977 by Martin Lewis Perl with his colleagues at the SLAC LBL group.^[26] Like the electron and the muon, it too was expected to have an associated neutrino. The first evidence for tau neutrinos came from the observation of "missing" energy and momentum in tau decay, analogous to the "missing" energy and momentum in beta decay leading to the discovery of the electron neutrino. The first detection of tau neutrino interactions was announced in 2000 by the DONUT collaboration at Fermilab, making it the latest particle of the Standard Model to have been directly observed,^[27] apart from the Higgs boson, which probably has been discovered in 2012.

Although all present data is consistent with three generations of leptons, some particle physicists are searching for a fourth generation. The current lower limit on the mass of such a fourth charged lepton is 100.8 GeV/c²,^[28] while its associated neutrino would have a mass of at least 45.0 GeV/c².^[29]

Properties

Spin and chirality

Left-handed and right-handed helicities

Leptons are spin-¹⁄₂ particles. The spin-statistics theorem thus implies that they are fermions and thus that they are subject to the Pauli exclusion principle; no two leptons of the same species can be in exactly the same state at the same time. Furthermore, it means that a lepton can have only two possible spin states, namely up or down.

A closely related property is chirality, which in turn is closely related to a more easily visualized property called helicity. The helicity of a particle is the direction of its spin relative to its momentum; particles with spin in the same direction as their momentum are called right-handed and otherwise they are called left-handed. When a particle is mass-less, the direction of its momentum relative to its spin is frame independent, while for massive particles it is possible to 'overtake' the particle by a Lorentz transformation flipping the helicity. Chirality is a technical property (defined through the transformation behaviour under the Poincaré group) that agrees with helicity for (approximately) massless particles and is still well defined for massive particles.

In many quantum field theories—such as quantum electrodynamics and quantum chromodynamics—left and right-handed fermions are identical. However in the Standard Model left-handed and right-handed fermions are treated asymmetrically. Only left-handed fermions participate in the weak interaction, while there are no right-handed neutrinos. This is an example of parity violation. In the literature left-handed fields are often denoted by a capital L subscript (e.g. e−_L) and right-handed fields are denoted by a capital R subscript.

Electromagnetic interaction

Lepton-photon interaction

One of the most prominent properties of leptons is their electric charge, Q. The electric charge determines the strength of their electromagnetic interactions. It determines the strength of the electric field generated by the particle (see Coulomb's law) and how strongly the particle reacts to an external electric or magnetic field (see Lorentz force). Each generation contains one lepton with Q = −1 (conventionally the charge of a particle is expressed in units of the elementary charge) and one lepton with zero electric charge. The lepton with electric charge is commonly simply referred to as a 'charged positive lepton' while the neutral lepton is called a neutrino. For example the first generation consists of the electron e− with a negative electric charge and the electrically neutral electron neutrino ν
e.

In the language of quantum field theory the electromagnetic interaction of the charged leptons is expressed by the fact that the particles interact with the quantum of the electromagnetic field, the photon. The Feynman diagram of the electron-photon interaction is shown on the right.

Because leptons possess an intrinsic rotation in the form of their spin, charged leptons generate a magnetic field. The size of their magnetic dipole moment μ is given by,

where m is the mass of the lepton and g is the so-called g-factor for the lepton. First order approximation quantum mechanics predicts that the g-factor is 2 for all leptons. However, higher order quantum effects caused by loops in Feynman diagrams introduce corrections to this value. These corrections, referred to as the anomalous magnetic dipole moment, are very sensitive to the details of a quantum field theory model and thus provide the opportunity for precision tests of the standard model. The theoretical and measured values for the electron anomalous magnetic dipole moment are within agreement within eight significant figures.^[30]

Weak Interaction

The weak interactions of the first generation leptons.

In the Standard Model the left-handed charged lepton and the left-handed neutrino are arranged in doublet (ν
e_L, e−_L) that transforms in the spinor representation (T = ¹⁄₂) of the weak isospin SU(2) gauge symmetry. This means that these particles are eigenstates of the isospin projection T₃ with eigenvalues ¹⁄₂ and −¹⁄₂ respectively. In the meantime, the right-handed charged lepton transforms as a weak isospin scalar (T = 0) and thus does not participate in the weak interaction, while there is no right-handed neutrino at all.

The Higgs mechanism recombines the gauge fields of the weak isospin SU(2) and the weak hypercharge U(1) symmetries to three massive vector bosons (W+, W−, Z0) mediating the weak interaction, and one massless vector boson, the photon, responsible for the electromagnetic interaction. The electric charge Q can be calculated from the isospin projection T₃ and weak hypercharge Y_W through the Gell-Mann–Nishijima formula,

Q = T₃ + Y_W/2

To recover the observed electric charges for all particles the left-handed weak isospin doublet (ν
e_L, e−_L) must thus have Y_W = −1, while the right-handed isospin scalar e−
R must have Y_W = −2. The interaction of the leptons with the massive weak interaction vector bosons is shown in the figure on the left.

Mass

In the Standard Model each lepton starts out with no intrinsic mass. The charged leptons (i.e. the electron, muon, and tau) obtain an effective mass through interaction with the Higgs field, but the neutrinos remain massless. For technical reasons the masslessness of the neutrinos implies that there is no mixing of the different generations of charged leptons as there is for quarks. This is in close agreement with current experimental observations.^[31]

However, it is known from experiments – most prominently from observed neutrino oscillations^[32] – that neutrinos do in fact have some very small mass, probably less than 2 eV/c².^[33] This implies the existence of physics beyond the Standard Model. The currently most favoured extension is the so-called seesaw mechanism, which would explain both why the left-handed neutrinos are so light compared to the corresponding charged leptons, and why we have not yet seen any right-handed neutrinos.

Leptonic numbers

The members of each generation's weak isospin doublet are assigned leptonic numbers that are conserved under the Standard Model.^[34] Electrons and electron neutrinos have an electronic number of L_e = 1, while muons and muon neutrinos have a muonic number of L_μ = 1, while tau particles and tau neutrinos have a tauonic number of L_τ = 1. The antileptons have their respective generation's leptonic numbers of −1.
Conservation of the leptonic numbers means that the number of leptons of the same type remains the same, when particles interact. This implies that leptons and antileptons must be created in pairs of a single generation. For example, the following processes are allowed under conservation of leptonic numbers:

Each generation forms a weak isospin doublet.

e− + e+ → γ + γ,

τ− + τ+ → Z0 + Z0,

but not these:

γ → e− + μ+,

W− → e− + ν
τ,

Z0 → μ− + τ+.

However, neutrino oscillations are known to violate the conservation of the individual leptonic numbers. Such a violation is considered to be smoking gun evidence for physics beyond the Standard Model. A much stronger conservation law is the conservation of the total number of leptons (L), conserved even in the case of neutrino oscillations, but even it is still violated by a tiny amount by the chiral anomaly.

Universality

The coupling of the leptons to gauge bosons are flavour-independent (i.e., the interactions between leptons and gauge bosons are the same for all leptons).^[34] This property is called lepton universality and has been tested in measurements of the tau and muon lifetimes and of Z boson partial decay widths, particularly at the Stanford Linear Collider (SLC) and Large Electron-Positron Collider (LEP) experiments.^{[35]:241–243[36]:138}

The decay rate (Γ) of muons through the process μ− → e− + ν
e + ν
μ is approximately given by an expression of the form (see muon decay for more details)^[34]

where K₁ is some constant, and G_F is the Fermi coupling constant. The decay rate of tau particles through the process τ− → e− + ν
e + ν
τ is given by an expression of the same form^[34]

where K₂ is some constant. Muon–Tauon universality implies that K₁ = K₂. On the other hand, electron–muon universality implies^[34]

This explains why the branching ratios for the electronic mode (17.85%) and muonic (17.36%) mode of tau decay are equal (within error).^[20]

Universality also accounts for the ratio of muon and tau lifetimes. The lifetime of a lepton (τ_l) is related to the decay rate by^[34]

where B(x → y) and Γ(x → y) denotes the branching ratios and the resonance width of the process x → y.

The ratio of tau and muon lifetime is thus given by^[34]

Using the values of the 2008 Review of Particle Physics for the branching ratios of muons^[18] and tau^[20] yields a lifetime ratio of ~1.29×10⁻⁷, comparable to the measured lifetime ratio of ~1.32×10⁻⁷. The difference is due to K₁ and K₂ not actually being constants; they depend on the mass of leptons.

Table of leptons

Properties of leptons

Particle/Antiparticle Name	Symbol	Q (e)	S	Le	Lμ	Lτ	Mass (MeV/c2)	Lifetime (s)	Common decay
Electron / Positron[17]	e−/e+	−1/+1	1⁄2	+1/−1	0	0	0.510998910(13)	Stable	Stable
Muon / Antimuon[18]	μ−/μ+	−1/+1	1⁄2	0	+1/−1	0	105.6583668(38)	2.197019(21)×10−6	e− + ν e + ν μ
Tau / Antitau[20]	τ−/τ+	−1/+1	1⁄2	0	0	+1/−1	1776.84(17)	2.906(10)×10−13	See τ− decay modes
Electron neutrino / Electron antineutrino[33]	ν e/ν e	0	1⁄2	+1/−1	0	0	< 2.2×10−6[37]	Unknown
Muon neutrino / Muon antineutrino[33]	ν μ/ν μ	0	1⁄2	0	+1/−1	0	< 0.17[37]	Unknown
Tau neutrino / Tau antineutrino[33]	ν τ/ν τ	0	1⁄2	0	0	+1/−1	< 15.5[37]	Unknown

Hadron

From Wikipedia, the free encyclopedia

 

In particle physics, a hadron ⁱ/ˈhædrɒn/ (Greek: ἁδρός, hadrós, "stout, thick") is a composite particle made of quarks held together by the strong force (in a similar way as molecules are held together by the electromagnetic force).

Hadrons are categorized into two families: baryons (such as protons and neutrons, made of three quarks) and mesons (such as pions, made of one quark and one antiquark). A tetraquark state (an exotic meson), named the Z(4430)^– was discovered in 2014 by the LHCb collaboration.^[1] Other types of exotic hadrons may exist, such as pentaquarks (exotic baryons), but no current evidence conclusively suggests their existence.^[2][3]

Of the hadrons, protons are stable, and neutrons bound within atomic nuclei are stable, whereas other hadrons are unstable under ordinary conditions; free neutrons decay with a half life of about 880 seconds. Experimentally, hadron physics is studied by colliding protons or nuclei of heavy elements such as lead, and detecting the debris in the produced particle showers.

Etymology

The term "hadron" was introduced by Lev B. Okun in a plenary talk at the 1962 International Conference on High Energy Physics.^[4] In this talk he said:

Not withstanding the fact that this report deals with weak interactions, we shall frequently have to speak of strongly interacting particles. These particles pose not only numerous scientific problems, but also a terminological problem. The point is that "strongly interacting particles" is a very clumsy term which does not yield itself to the formation of an adjective. For this reason, to take but one instance, decays into strongly interacting particles are called non-leptonic. This definition is not exact because "non-leptonic" may also signify "photonic". In this report I shall call strongly interacting particles "hadrons", and the corresponding decays "hadronic" (the Greek ἁδρός signifies "large", "massive", in contrast to λεπτός which means "small", "light"). I hope that this terminology will prove to be convenient. — Lev B. Okun, 1962

Properties

All types of hadrons have zero total color charge. (three examples shown)

According to the quark model,^[5] the properties of hadrons are primarily determined by their so-called valence quarks. For example, a proton is composed of two up quarks (each with electric charge +²⁄₃, for a total of +⁴⁄₃ together) and one down quark (with electric charge −¹⁄₃). Adding these together yields the proton charge of +1. Although quarks also carry color charge, hadrons must have zero total color charge because of a phenomenon called color confinement. That is, hadrons must be "colorless" or "white". These are the simplest of the two ways: three quarks of different colors, or a quark of one color and an antiquark carrying the corresponding anticolor. Hadrons with the first arrangement are called baryons, and those with the second arrangement are mesons.

Hadrons, however, are not composed of just three or two quarks, because of the strength of the strong force. More accurately, strong force gluons have enough energy (E) to have resonances composed of massive (m) quarks (E > mc²) . Thus, virtual quarks and antiquarks, in a 1:1 ratio, form the majority of massive particles inside a hadron. The two or three quarks are the excess of quarks vs. antiquarks in hadrons, and vice versa in anti-hadrons. Because the virtual quarks are not stable wave packets (quanta), but irregular and transient phenomena, it is not meaningful to ask which quark is real and which virtual; only the excess is apparent from the outside. Massless virtual gluons compose the numerical majority of particles inside hadrons.

Like all subatomic particles, hadrons are assigned quantum numbers corresponding to the representations of the Poincaré group: J^PC(m), where J is the spin quantum number, P the intrinsic parity (or P-parity), and C, the charge conjugation (or C-parity), and the particle's mass, m. Note that the mass of a hadron has very little to do with the mass of its valence quarks; rather, due to mass–energy equivalence, most of the mass comes from the large amount of energy associated with the strong interaction. Hadrons may also carry flavor quantum numbers such as isospin (or G parity), and strangeness. All quarks carry an additive, conserved quantum number called a baryon number (B), which is +¹⁄₃ for quarks and −¹⁄₃ for antiquarks. This means that baryons (groups of three quarks) have B = 1 whereas mesons have B = 0.

Hadrons have excited states known as resonances. Each ground state hadron may have several excited states; several hundreds of resonances have been observed in particle physics experiments. Resonances decay extremely quickly (within about 10⁻²⁴ seconds) via the strong nuclear force.

In other phases of matter the hadrons may disappear. For example, at very high temperature and high pressure, unless there are sufficiently many flavors of quarks, the theory of quantum chromodynamics (QCD) predicts that quarks and gluons will no longer be confined within hadrons, "because the strength of the strong interaction diminishes with energy". This property, which is known as asymptotic freedom, has been experimentally confirmed in the energy range between 1 GeV (gigaelectronvolt) and 1 TeV (teraelectronvolt).^[6]

All free hadrons except the proton (and antiproton) are unstable.

Baryons

All known baryons are made of three valence quarks, so they are fermions, i.e., they have odd half-integral spin, because they have an odd number of quarks. As quarks possess baryon number B = ¹⁄₃, baryons have baryon number B = 1. The best-known baryons are the proton and the neutron.
One can hypothesise baryons with further quark-antiquark pairs in addition to their three quarks. Hypothetical baryons with one extra quark-antiquark pair (5 quarks in all) are called pentaquarks.^[7] Several pentaquark candidates were found in the early 2000s, but upon further review these states have now been established as nonexistent.^[8] (This does not rule against pentaquarks in general, only the candidates put forward).

Each type of baryon has a corresponding antiparticle (antibaryon) in which quarks are replaced by their corresponding antiquarks. For example, just as a proton is made of two up-quarks and one down-quark, its corresponding antiparticle, the antiproton, is made of two up-antiquarks and one down-antiquark.

Mesons

Mesons are hadrons composed of a quark-antiquark pair. They are bosons, meaning they have integral spin, i.e., 0, 1, or −1, as they have an even number of quarks. They have baryon number B = 0. Examples of mesons commonly produced in particle physics experiments include pions and kaons. Pions also play a role in holding atomic nuclei together via the residual strong force.
In principle, mesons with more than one quark-antiquark pair may exist; a hypothetical meson with two pairs is called a tetraquark. Several tetraquark candidates were found in the 2000s, but their status is under debate.^[9] Several other hypothetical "exotic" mesons lie outside the quark model of classification. These include glueballs and hybrid mesons (mesons bound by excited gluons).

Boson

From Wikipedia, the free encyclopedia

Satyendra Nath Bose

In quantum mechanics, bosons (/ˈboʊsɒn/,^[1] /ˈboʊzɒn/^[2]) make up one of the two classes of particles, the other being fermions.^[3] The name boson was coined by Paul Dirac^[4] to commemorate the contribution of the Indian physicist Satyendra Nath Bose^[5][6] in developing, with Einstein, Bose–Einstein statistics—which theorizes the characteristics of elementary particles.^[7] Examples of bosons include fundamental particles such as photons, gluons, and W and Z bosons (the four force-carrying gauge bosons of the Standard Model), the Higgs boson, and the still-theoretical graviton of quantum gravity; composite particles (e.g. mesons and stable nuclei of even mass number such as deuterium (with one proton and one neutron, mass number = 2), helium-4, or lead-208^{[Note 1]}); and some quasiparticles (e.g. Cooper pairs, plasmons, and phonons).^[8]:130

An important characteristic of bosons is that their statistics do not restrict the number that can occupy the same quantum state. This property is exemplified in helium-4 when it is cooled to become a superfluid.^[9] In contrast, two fermions cannot occupy the same quantum space. Whereas the elementary particles that make up matter (i.e. leptons and quarks) are fermions, the elementary bosons are force carriers that function as the 'glue' holding matter together.^[10] This property holds for all particles with integer spin (s = 0, 1, 2 etc.) as an immediate consequence of the spin–statistics theorem.

Properties

Bosons contrast with fermions, which obey Fermi–Dirac statistics. Two or more fermions cannot occupy the same quantum state (see Pauli exclusion principle).

Since bosons with the same energy can occupy the same place in space, bosons are often force carrier particles. In contrast, fermions are usually associated with matter (although in quantum physics the distinction between the two concepts is not clear cut).

Bosons may be either elementary, like photons, or composite, like mesons.

While most bosons are composite particles, in the Standard Model, there are five bosons which are elementary:

• the four gauge bosons (γ · g · Z · W±)
• the only scalar boson (the Higgs boson (H0))

Additionally, the graviton (G) is a hypothetical elementary particle not incorporated in the Standard Model. If it exists, a graviton must be a boson, and could conceivably be a gauge boson.
Composite bosons are important in superfluidity and other applications of Bose–Einstein condensates.

Definition and basic properties

Symmetric wavefunction for a (bosonic) 2-particle state in an infinite square well potential.

By definition, bosons are particles which obey Bose–Einstein statistics: when one swaps two bosons (of the same species), the wavefunction of the system is unchanged.^[11] Fermions, on the other hand, obey Fermi–Dirac statistics and the Pauli exclusion principle: two fermions cannot occupy the same quantum state, resulting in a "rigidity" or "stiffness" of matter which includes fermions. Thus fermions are sometimes said to be the constituents of matter, while bosons are said to be the particles that transmit interactions (force carriers), or the constituents of radiation. The quantum fields of bosons are bosonic fields, obeying canonical commutation relations.

The properties of lasers and masers, superfluid helium-4 and Bose–Einstein condensates are all consequences of statistics of bosons. Another result is that the spectrum of a photon gas in thermal equilibrium is a Planck spectrum, one example of which is black-body radiation; another is the thermal radiation of the opaque early Universe seen today as microwave background radiation. Interactions between elementary particles are called fundamental interactions. The fundamental interactions of virtual bosons with real particles result in all forces we know.

All known elementary and composite particles are bosons or fermions, depending on their spin: particles with half-integer spin are fermions; particles with integer spin are bosons. In the framework of nonrelativistic quantum mechanics, this is a purely empirical observation. However, in relativistic quantum field theory, the spin–statistics theorem shows that half-integer spin particles cannot be bosons and integer spin particles cannot be fermions.^[12]

In large systems, the difference between bosonic and fermionic statistics is only apparent at large densities—when their wave functions overlap. At low densities, both types of statistics are well approximated by Maxwell–Boltzmann statistics, which is described by classical mechanics.

Elementary bosons

All observed elementary particles are either fermions or bosons. The observed elementary bosons are all gauge bosons: photons, W and Z bosons, gluons, and the Higgs boson.

• Photons are the force carriers of the electromagnetic field.
• W and Z bosons are the force carriers which mediate the weak force.
• Gluons are the fundamental force carriers underlying the strong force.
• Higgs Bosons give other particles mass via the Higgs mechanism. Their existence was confirmed by CERN on 14 March 2013.

Finally, many approaches to quantum gravity postulate a force carrier for gravity, the graviton, which is a boson of spin plus or minus two.

Composite bosons

Composite particles (such as hadrons, nuclei, and atoms) can be bosons or fermions depending on their constituents. More precisely, because of the relation between spin and statistics, a particle containing an even number of fermions is a boson, since it has integer spin.
Examples include the following:

• Any meson, since mesons contain one quark and one antiquark.
• The nucleus of a carbon-12 atom, which contains 6 protons and 6 neutrons.
• The helium-4 atom, consisting of 2 protons, 2 neutrons and 2 electrons.

The number of bosons within a composite particle made up of simple particles bound with a potential has no effect on whether it is a boson or a fermion.

To which states can bosons crowd?

Bose–Einstein statistics encourages identical bosons to crowd into one quantum state, but not any state is necessarily convenient for it. Aside of statistics, bosons can interact – for example, helium-4 atoms are repulsed by intermolecular force on a very close approach, and if one hypothesize their condensation in a spatially-localized state, then gains from the statistics cannot overcome a prohibitive force potential. A spatially-delocalized state (i.e. with low |ψ(x)|) is preferable: if the number density of the condensate is about the same as in ordinary liquid or solid state, then the repulsive potential for the N-particle condensate in such state can be not higher than for a liquid or a crystalline lattice of the same N particles described without quantum statistics. Thus, Bose–Einstein statistics for a material particle is not a mechanism to bypass physical restrictions on the density of the corresponding substance, and superfluid liquid helium has the density comparable to the density of ordinary liquid matter. Spatially-delocalized states also permit for a low momentum according to uncertainty principle, hence for low kinetic energy; that's why superfluidity and superconductivity are usually observed in low temperatures.

Photons do not interact with themselves and hence do not experience this difference in states where to crowd (see squeezed coherent state).

Fermion

From Wikipedia, the free encyclopedia

Enrico Fermi

Antisymmetric wavefunction for a (fermionic) 2-particle state in an infinite square well potential.

In particle physics, a fermion (a name coined by Paul Dirac^[1] from the surname of Enrico Fermi) is any particle characterized by Fermi–Dirac statistics and following the Pauli exclusion principle; fermions include all quarks and leptons, as well as any composite particle made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions contrast with bosons, which obey Bose–Einstein statistics.

A fermion can be an elementary particle, such as the electron; or it can be a composite particle, such as the proton. According to the spin-statistics theorem in any reasonable relativistic quantum field theory, particles with integer spin are bosons, while particles with half-integer spin are fermions.

Besides this spin characteristic fermions have another specific property: they possess conserved baryon or lepton quantum numbers. Therefore what is usually referred as the spin-statistics relation is in fact a spin-statistics-quantum number relation.^[2]

In contrast to bosons, as a consequence of the Pauli principle only one fermion can occupy a particular quantum state at any given time. If multiple fermions have the same spatial probability distribution, then at least one property of each fermion, such as its spin, must be different. Fermions are usually associated with matter, whereas bosons are generally force carrier particles; although in the current state of particle physics the distinction between the two concepts is unclear.

Composite fermions, such as protons and neutrons, are key building blocks of everyday matter. Weakly interacting^{[clarification needed]} fermions can also display bosonic behavior under extreme conditions, such as in superconductivity.

Elementary fermions

The Standard Model recognizes two types of elementary fermions: quarks and leptons. In all, the model distinguishes 24 different fermions: six quarks: the up quark, down quark, strange quark, charm quark, bottom quark, and top quark; and six leptons (electron, electron neutrino, muon, muon neutrino, tau particle, tau neutrino), each with a corresponding antiparticle.

Mathematically, fermions come in three types - Weyl fermions (massless), Dirac fermions (massive), and Majorana fermions (each its own antiparticle). Most Standard Model fermions are believed to be Dirac fermions, although it is unknown at this time whether the neutrino is a Dirac or a Majorana fermion. Dirac fermions can be treated as a combination of two Weyl fermions.^[3]:106

Composite fermions

Composite particles (such as hadrons, nuclei, and atoms) can be bosons or fermions depending on their constituents. More precisely, because of the relation between spin and statistics, a particle containing an odd number of fermions is itself a fermion: it will have half-integer spin.
Examples include the following:

• A baryon, such as the proton or neutron, contains three fermionic quarks and thus it is a fermion;
• The nucleus of a carbon-13 atom contains six protons and seven neutrons and is therefore a fermion;
• The atom helium-3 (³He) is made of two protons, one neutron, and two electrons, and therefore it is a fermion.

The number of bosons within a composite particle made up of simple particles bound with a potential has no effect on whether it is a boson or a fermion.

Fermionic or bosonic behavior of a composite particle (or system) is only seen at large (compared to size of the system) distances. At proximity, where spatial structure begins to be important, a composite particle (or system) behaves according to its constituent makeup.

Fermions can exhibit bosonic behavior when they become loosely bound in pairs. This is the origin of superconductivity and the superfluidity of helium-3: in superconducting materials, electrons interact through the exchange of phonons, forming Cooper pairs, while in helium-3, Cooper pairs are formed via spin fluctuations.

The quasiparticles of the fractional quantum Hall effect are also known as composite fermions, which are electrons with an even number of quantized vortices attached to them.

Skyrmions

In a quantum field theory, there can be field configurations of bosons which are topologically twisted. These are coherent states (or solitons) which behave like a particle, and they can be fermionic even if all the constituent particles are bosons. This was discovered by Tony Skyrme in the early 1960s, so fermions made of bosons are named Skyrmions after him.
Skyrme's original example involved fields which take values on a three-dimensional sphere, the original nonlinear sigma model which describes the large distance behavior of pions. In Skyrme's model, reproduced in the large N or string approximation to quantum chromodynamics (QCD), the proton and neutron are fermionic topological solitons of the pion field.^{[citation needed]}

Whereas Skyrme's example involved pion physics, there is a much more familiar example in quantum electrodynamics with a magnetic monopole. A bosonic monopole with the smallest possible magnetic charge and a bosonic version of the electron will form a fermionic dyon.

The analogy between the Skyrme field and the Higgs field of the electroweak sector has been used ^[4] to postulate that all fermions are skyrmions. This could explain why all known fermions have baryon or lepton quantum numbers and provide a physical mechanism for the Pauli exclusion principle.