There are six types of leptons, known asflavours, grouped in threegenerations.[2] Thefirst-generation leptons, also calledelectronic leptons, comprise theelectron (e− ) and theelectron neutrino (ν e); the second are themuonic leptons, comprising themuon (μ− ) and themuon neutrino (ν μ); and the third are thetauonic leptons, comprising thetau (τ− ) and thetau neutrino (ν τ). Electrons have the least mass of all the charged leptons. The heavier muons and taus will rapidly change into electrons and neutrinos through a process ofparticle decay: the transformation from a higher mass state to a lower mass state. Thus electrons are stable and the most common charged lepton in theuniverse, whereas muons and taus can only be produced inhigh-energy collisions (such as those involvingcosmic rays and those carried out inparticle accelerators).
For every lepton flavor, there is a corresponding type ofantiparticle, known as an antilepton, that differs from the lepton only in that some of its properties haveequal magnitude but opposite sign. According to certain theories, neutrinos may betheir own antiparticle. It is not currently known whether this is the case.
Leptons are an important part of theStandard Model. Electrons are one of the components ofatoms, alongsideprotons andneutrons.Exotic atoms with muons and taus instead of electrons can also be synthesized, as well as lepton–antilepton particles such aspositronium.
The namelepton comes from theGreekλεπτόςleptós, "fine, small, thin" (neuter nominative/accusative singular form: λεπτόνleptón);[14][15] the earliest attested form of the word is theMycenaean Greek𐀩𐀡𐀵,re-po-to, written inLinear B syllabic script.[16]Lepton was first used by physicistLéon Rosenfeld in 1948:[17]
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 (0.511 MeV/c2)[18] and the mass of a muon (with a value of105.7 MeV/c2)[19] are fractions of the mass of the "heavy" proton (938.3 MeV/c2), and the mass of a neutrino is nearly zero.[20] However, the mass of the tau (discovered in the mid-1970s) (1777 MeV/c2)[21] is nearly twice that of the proton and3477[22] times that of the electron.
Nearly 40 years after the discovery of the electron, themuon was discovered byCarl D. Anderson in 1936. Due to its mass, it was initially categorized as ameson rather than a lepton.[26] It later became clear that the muon was much more similar to the electron than to mesons, as muons do not undergo thestrong 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, andJack Steinberger showed that more than one type of neutrino exists by first detecting interactions of themuon neutrino, which earned them the1988 Nobel Prize, although by then the different flavours of neutrino had already been theorized.[27]
Thetau was first detected in a series of experiments between 1974 and 1977 byMartin Lewis Perl with his colleagues at theSLACLBL group.[28] 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 theDONUT collaboration atFermilab, making it the second-to-latest particle of theStandard Model to have been directly observed,[29] withHiggs 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 is100.8 GeV/c2,[30] while its associated neutrino would have a mass of at least45.0 GeV/c2.[31]
Leptons arespin1/2 particles. Thespin-statistics theorem thus implies that they arefermions and thus that they are subject to thePauli 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 ischirality, which in turn is closely related to a more easily visualized property calledhelicity. The helicity of a particle is the direction of its spin relative to itsmomentum; particles with spin in the same direction as their momentum are calledright-handed and they are otherwise calledleft-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-movingreference frame; in the faster frame, the helicity is reversed. Chirality is a technical property, defined through transformation behaviour under thePoincaré 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 manyquantum field theories, such asquantum electrodynamics andquantum chromodynamics, left- and right-handed fermions are identical. However, the Standard Model'sweak 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 ofparity violation explicitly written into the model. In the literature, left-handed fields are often denoted by a capitalL subscript (e.g. the normal electron e− L) and right-handed fields are denoted by a capitalR subscript (e.g. a positron e+ R).
Right-handed neutrinos and left-handed anti-neutrinos have no possible interaction with other particles (seeSterile 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 thecombined electroweak force, although with different strengths (YW).
One of the most prominent properties of leptons is theirelectric charge,Q. The electric charge determines the strength of theirelectromagnetic interactions. It determines the strength of theelectric field generated by the particle (seeCoulomb's law) and how strongly the particle reacts to an external electric or magnetic field (seeLorentz force). Each generation contains one lepton withQ = −1e and one lepton with zero electric charge. The lepton with electric charge is commonly simply referred to as acharged lepton while a neutral lepton is called aneutrino. For example, the first generation consists of the electrone− with a negative electric charge and the electrically neutral electron neutrinoν 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, thephoton. TheFeynman 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 theirmagnetic dipole momentμ is given by
wherem is the mass of the lepton andg is the so-called"g factor" for the lepton. First-order quantum mechanical approximation predicts that the magnitude of theg 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 theanomalous 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 theelectron anomalous magnetic dipole moment are within agreement within eight significant figures.[32] The results for themuon, however,are problematic, hinting at a small, persistent discrepancy between the Standard Model and experiment.
In the Standard Model, the left-handed charged lepton and the left-handed neutrino are arranged indoublet that transforms in thespinor representation (T = 1 /2) of theweak isospinSU(2) gauge symmetry. This means that these particles are eigenstates of the isospin projectionT3 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 theweak interaction, while there is no evidence that a right-handed neutrino exists at all.
TheHiggs mechanism recombines the gauge fields of the weak isospin SU(2) and theweak hypercharge U(1) symmetries to three massive vector bosons (W+ ,W− ,Z0 ) mediating theweak interaction, and one massless vector boson, the photon (γ), responsible for the electromagnetic interaction. The electric chargeQ can be calculated from the isospin projectionT3 and weak hyperchargeYW through theGell-Mann–Nishijima formula,
Q =T3 + 1 /2YW.
To recover the observed electric charges for all particles, the left-handed weak isospin doublet(νeL, e− L) must thus haveYW = −1, while the right-handed isospin scalare− R must haveYW = −2. The interaction of the leptons with the massive weak interaction vector bosons is shown in the figure on the right.
In theStandard 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 theHiggs 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 asthere is for quarks. The zero mass of neutrino is in close agreement with current direct experimental observations of the mass.[33]
However, it is known from indirect experiments—most prominently from observedneutrino oscillations[34]—that neutrinos have to have a nonzero mass, probably less than2 eV/c2.[35] This implies the existence of physicsbeyond the Standard Model. The currently most favoured extension is the so-calledseesaw 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.
The members of each generation'sweak isospindoublet are assignedleptonic numbers that are conserved under the Standard Model.[36] Electrons and electron neutrinos have anelectronic number ofLe = 1, while muons and muon neutrinos have amuonic number ofLμ = 1, while tau particles and tau neutrinos have atauonic number ofLτ = 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:
However,neutrino oscillations are known to violate the conservation of the individual leptonic numbers. Such a violation is considered to be smoking gun evidence forphysics beyond the Standard Model. A much stronger conservation law is the conservation of the total number of leptons (Lwithno subscript), conserved even in the case of neutrino oscillations, but even it is still violated by a tiny amount by thechiral anomaly.
The coupling of leptons to all types ofgauge boson are flavour-independent: The interaction between leptons and a gauge boson measures the same for each lepton.[36] This property is calledlepton universality and has been tested in measurements of themuon andtaulifetimes and ofZ boson partialdecay widths, particularly at theStanford Linear Collider (SLC) andLarge Electron–Positron Collider (LEP) experiments.[37]: 241–243 [38]: 138
The decay rate () of muons through the processμ− →e− +ν e +ν μ is approximately given by an expression of the form (seemuon decay for more details)[36]
whereK2 is some constant, andGF is theFermi coupling constant. The decay rate of tau particles through the processτ− →e− +ν e +ν τ is given by an expression of the same form[36]
whereK3 is some other constant. Muon–tauon universality implies thatK2 ≈K3. On the other hand, electron–muon universality implies[36]
Thebranching ratios for the electronic mode (17.82%) and muonic (17.39%) mode of tau decay are not equal due to the mass difference of the final state leptons.[21]
Universality also accounts for the ratio of muon and tau lifetimes. The lifetime of a lepton (with = "μ" or "τ") is related to the decay rate by[36]
,
where denotes the branching ratios and denotes theresonance width of the process withx andy replaced by two different particles from "e" or "μ" or "τ".
The ratio of tau and muon lifetime is thus given by[36]
Using values from the 2008Review of Particle Physics for the branching ratios of the muon[19] and tau[21] yields a lifetime ratio of ~ 1.29×10−7, comparable to the measured lifetime ratio of ~ 1.32×10−7. The difference is due toK2 andK3 notactually being constants: They depend slightly on the mass of leptons involved.
Recent tests of lepton universality inB meson decays, performed by theLHCb,BaBar, andBelle experiments, have shown consistent deviations from the Standard Model predictions. However the combined statistical and systematic significance is not yet high enough to claim an observation ofnew physics.[39]
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 theATLAS collaboration have twice the precision and give a ratio of, which agrees with the standard-model prediction of unity.[40][41][42] In 2024 a preprint by the ATLAS collaboration has published a new value of the most precise ratio so far testing the lepton flavour universality.[43][44]
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