Lepton

Name	Lepton
Caption	Leptons are involved in several processes such as beta decay.
Num types	6 (electron, electron neutrino, muon, muon neutrino, tau, tau neutrino)
Composition	Elementary particle
Statistics	Fermionic
Generation	1st, 2nd, 3rd
Interaction	Electromagnetism, Gravitation, Weak
Antiparticle	Antilepton ()
Symbol
Baryon number	0
Electric charge	+1 e, 0 e, −1 e
Color charge	No
Spin

A lepton is an elementary particle and a fundamental constituent of matter. 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. The first generation is the electronic leptons, comprising the electrons () and electron neutrinos (); the second is the muonic leptons, comprising muons () and muon neutrinos (); and the third is the tauonic leptons, comprising taus () and tau neutrinos (). 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 and was discovered in 1897 by J. J. Thomson. 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. 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. The muon neutrino was discovered in 1962 by Leon M. Lederman, Melvin Schwartz and Jack Steinberger, 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. The tau neutrino remained elusive until July 2000, when the DONUT collaboration from Fermilab announced its discovery.

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" (lepton), neuter of "λεπτός" (leptos), "fine, small, thin" and the earliest attested form of the word is the Mycenaean Greek re-po-to, written in Linear B syllabic script. Lepton was first used by physicist Léon Rosenfeld in 1948:

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 () and the mass of a muon (with a value of ) are fractions of the mass of the "heavy" proton (). However, the mass of the tau (discovered in the mid 1970s) () is nearly twice that of the proton, and about 3,500 times that of the electron.

History

by emitting a boson. The 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. 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. 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. 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.

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. 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.

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 the fourth charged lepton is , while its associated neutrino has a mass of at least .

Properties

Spin and chirality

Leptons are spin- 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 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 massless 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 Poincare 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. _L) and right-handed fields are denoted by a capital R subscript.

Electromagnetic 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 with a negative electric charge and the electrically neutral electron neutrino .

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.

Since leptons have 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, :$\backslash mu\; =\; g\; \backslash frac\{\; Q\; e\; \backslash hbar\}\{4\; m\}$, where m is the mass of the lepton and g is the so called g-factor for the lepton. To 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 agree up to eight significant figures.

Weak Interaction

{| style="float:left; width:160px;" |- | {|class=wikitable style="font-size:90%;" | |- | |- | |- |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 _L, _L)}} that transforms in the spinor representation (T = ) of the weak isospin SU(2) gauge symmetry. This means that these particles are eigenstates of the isospin projection T₃ with eigenvalues and − 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 (, , ) 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 _L, _L)}} must thus have Y_W = −1, while the right-handed isospin scalar e 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.

It is however known from experiment – most prominently from observed neutrino oscillations – that neutrinos do in fact have some very small mass, probably less than . 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: doublet.]] : + → + , : + → + ,

but not these:

: → + , : → + , : → + .

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). | / | 0 | | +1/−1 | 0 | 0 | < | Unknown | |- |style="text-align:left"| Muon neutrino / Muon antineutrino | / | 0 | | 0 | +1/−1 | 0 | < 0.17 | Unknown | |- |style="text-align:left"| Tau neutrino / Tau antineutrino | / | 0 | | 0 | 0 | +1/−1 | < 15.5 | Unknown | |}

See also

Koide formula

List of particles

Quark

Weak interaction

Notes

References

External links

Particle Data Group homepage. The PDG compiles authoritative information on particle properties.

Leptons, a summary of leptons from Hyperphysics.

Category:Fundamental physics concepts