Lepton

The name lepton comes from the Greek leptós, "fine, small, thin" (neuter nominative/accusative singular form: λεπτόν leptón); 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. Rosenfeld chose the name as the common name for electrons and (then hypothesized) neutrinos. Additionally, the muon, initially classified as a meson, was reclassified as a lepton in the 1950s. The masses of those particles are small compared to nucleons—the mass of an electron () and the mass of a muon (with a value of ) are fractions of the mass of the "heavy" proton (), and the mass of a neutrino is nearly zero. However, the mass of the tau (discovered in the mid-1970s) () is nearly twice that of the proton and 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 second-to-latest particle of the Standard Model to have been directly observed, with Higgs boson being 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 , while its associated neutrino would have 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 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 they are otherwise called left-handed. When a particle is massless, the direction of its momentum relative to its spin is the same in every reference frame, whereas for massive particles it is possible to 'overtake' the particle by choosing a faster-moving reference frame; in the faster frame, the helicity is reversed. Chirality is a technical property, defined through transformation behaviour under the Poincaré group, that does not change with reference frame. It is contrived to agree with helicity for massless particles, and is still well defined for particles with mass. In many quantum field theories, such as quantum electrodynamics and quantum chromodynamics, left- and right-handed fermions are identical. However, the Standard Model's weak interaction treats left-handed and right-handed fermions differently: only left-handed fermions (and right-handed anti-fermions) participate in the weak interaction. This is an example of parity violation explicitly written into the model. In the literature, left-handed fields are often denoted by a capital L subscript (e.g. the normal electron e) and right-handed fields are denoted by a capital R subscript (e.g. a positron e). Right-handed neutrinos and left-handed anti-neutrinos have no possible interaction with other particles (see Sterile neutrino) and so are not a functional part of the Standard Model, although their exclusion is not a strict requirement; they are sometimes listed in particle tables to emphasize that they would have no active role if included in the model. Even though electrically charged right-handed particles (electron, muon, or tau) do not engage in the weak interaction specifically, they can still interact electrically, and hence still participate in the combined electroweak force, although with different strengths (W). Electromagnetic interaction One of the most prominent properties of leptons is their electric charge, . 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 and one lepton with zero electric charge. The lepton with electric charge is commonly simply referred to as a charged lepton while a 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. 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 is given by : \mu = g\, \frac{\; Q \hbar \;}{4 m} \ , where is the mass of the lepton and is the so-called " factor" for the lepton. First-order quantum mechanical approximation predicts that the magnitude of the  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. The results for the muon, however, are problematic, hinting at a small, persistent discrepancy between the Standard Model and experiment. Weak interaction In the Standard Model, the left-handed charged lepton and the left-handed neutrino are arranged in doublet that transforms in the spinor representation () of the weak isospin SU(2) gauge symmetry. This means that these particles are eigenstates of the isospin projection with eigenvalues and respectively. In the meantime, the right-handed charged lepton transforms as a weak isospin scalar () and thus does not participate in the weak interaction, while there is no evidence that a right-handed neutrino exists 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 (γ), responsible for the electromagnetic interaction. The electric charge can be calculated from the isospin projection and weak hypercharge through the Gell-Mann–Nishijima formula, : To recover the observed electric charges for all particles, the left-handed weak isospin doublet must thus have , while the right-handed isospin scalar must have . The interaction of the leptons with the massive weak interaction vector bosons is shown in the figure on the right. 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. The zero mass of neutrino is in close agreement with current direct experimental observations of the mass. However, it is known from indirect experiments—most prominently from observed neutrino oscillations—that neutrinos have to have a nonzero mass, probably less than . Electrons and electron neutrinos have an electronic number of , while muons and muon neutrinos have a muonic number of , while tau particles and tau neutrinos have a tauonic number of . 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 none of 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 ( ), 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 leptons to all types of gauge boson are flavour-independent: The interaction between leptons and a gauge boson measures the same for each lepton. The decay rate (\Gamma) of muons through the process is approximately given by an expression of the form (see muon decay for more details) In July 2021 results on lepton flavour universality have been published testing W decays, previous measurements by the LEP had given a slight imbalance but the new measurement by the ATLAS collaboration have twice the precision and give a ratio of R_W^{\tau/\mu}=\mathcal{B} (W\rarr \tau\nu_\tau)/\mathcal{B}( W\rarr \mu\nu_\mu)=0.992\pm0.013, which agrees with the standard-model prediction of unity. In 2024 a preprint by the ATLAS collaboration has published a new value of R_W^{\mu/e}=\mathcal{B} (W\rarr \mu\nu_\mu)/\mathcal{B}( W\rarr e\nu_e)=0.9995\pm0.0045 the most precise ratio so far testing the lepton flavour universality. == Table of leptons ==