Menu
Home Explore People Places Arts History Plants & Animals Science Life & Culture Technology
On this page
Lepton
Class of elementary particles that do not undergo strong interactions

In particle physics, elementary particles called leptons exist in three generations: the electron and electron neutrino (first generation); the muon and muon neutrino (second); and the tau and tau neutrino (third). Leptons have half-integer spin, no strong interaction, and possess properties like electric charge and mass. Charged leptons form atoms and particles like positronium, while neutrinos rarely interact. Electrons are stable and common, whereas muons and taus decay into electrons via particle decay. Leptons also have corresponding antiparticles called antileptons. These particles are essential in the Standard Model and fundamental to the structure of atoms.

Related Image Collections Add Image
Profiles
1 Image
We don't have any YouTube videos related to Lepton yet.
We don't have any PDF documents related to Lepton yet.
We don't have any Books related to Lepton yet.

Etymology

The name lepton comes from the Greek λεπτός leptós, "fine, small, thin" (neuter nominative/accusative singular form: λεπτόν leptón);1617 the earliest attested form of the word is the Mycenaean Greek 𐀩𐀡𐀵, re-po-to, written in Linear B syllabic script.18 Lepton was first used by physicist Léon Rosenfeld in 1948:19

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)20 and the mass of a muon (with a value of 105.7 MeV/c2)21 are fractions of the mass of the "heavy" proton (938.3 MeV/c2), and the mass of a neutrino is nearly zero.22 However, the mass of the tau (discovered in the mid-1970s) (1777 MeV/c2)23 is nearly twice that of the proton and 3477‍24 times that of the electron.

History

See also: Electron § Discovery, Muon § History, and Tau (particle) § History

Lepton nomenclature
Particle nameAntiparticle name
electronantielectronpositron
electron neutrinoelectron antineutrino
muonmu leptonmuantimuonantimu leptonantimu
muon neutrinomuonic neutrinomu neutrinomuon antineutrinomuonic antineutrinomu antineutrino
tauontau leptontauantitauonantitau leptonantitau
tauon neutrinotauonic neutrino tau neutrinotauon antineutrinotauonic antineutrinotau antineutrino

The first lepton identified was the electron, discovered by J.J. Thomson and his team of British physicists in 1897.2526 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.27 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.28 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.29

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.30 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,31 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 100.8 GeV/c2,32 while its associated neutrino would have a mass of at least 45.0 GeV/c2.33

Properties

Spin and chirality

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 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−L) and right-handed fields are denoted by a capital R subscript (e.g. a positron e+R).

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 (YW).

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 e 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 e− with a negative electric charge and the electrically neutral electron neutrino νe.

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

μ = g Q ℏ 4 m   , {\displaystyle \mu =g\,{\frac {\;Q\hbar \;}{4m}}\ ,}

where m is the mass of the lepton and g is the so-called "g factor" for the lepton. First-order quantum mechanical approximation 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.34 The results for the muon, however, are problematic, hinting at a small, persistent discrepancy between the Standard Model and experiment.

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 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 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 (W+, W−, Z0) mediating the weak interaction, and one massless vector boson, the photon (γ), responsible for the electromagnetic interaction. The electric charge Q can be calculated from the isospin projection T3 and weak hypercharge YW through the Gell-Mann–Nishijima formula,

Q = T3 + ⁠ 1 /2⁠ YW.

To recover the observed electric charges for all particles, the left-handed weak isospin doublet (νeL, e−L) must thus have YW = −1, while the right-handed isospin scalar e−R must have YW = −2. 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.35

However, it is known from indirect experiments—most prominently from observed neutrino oscillations36—that neutrinos have to have a nonzero mass, probably less than 2 eV/c2.37 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.

Lepton flavor quantum numbers

Main article: Lepton number

The members of each generation's weak isospin doublet are assigned leptonic numbers that are conserved under the Standard Model.38 Electrons and electron neutrinos have an electronic number of Le = 1, while muons and muon neutrinos have a muonic number of Lμ = 1, while tau particles and tau neutrinos have a tauonic number of Lτ = 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:

γ    →   e− + e+, Z0  →   τ− + τ+,

but none of these:

γ      →   e− + μ+, W−  →   e− + ντ, 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 with no subscript), conserved even in the case of neutrino oscillations, but even it is still violated by a tiny amount by the chiral anomaly.

Universality

See also: LHCb experiment § Lepton flavour 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.39 This property is called lepton universality and has been tested in measurements of the muon and tau lifetimes and of Z boson partial decay widths, particularly at the Stanford Linear Collider (SLC) and Large Electron–Positron Collider (LEP) experiments.40: 241–243 41: 138 

The decay rate ( Γ {\displaystyle \Gamma } ) of muons through the process μ− → e− + νe + νμ is approximately given by an expression of the form (see muon decay for more details)42

Γ ( μ − → e − + ν e ¯ + ν μ ) ≈ K 2 G F 2 m μ 5   , {\displaystyle \Gamma \left(\mu ^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{\mu }\right)\approx K_{2}\,G_{\text{F}}^{2}\,m_{\mu }^{5}~,}

where K2 is some constant, and GF is the Fermi coupling constant. The decay rate of tau particles through the process τ− → e− + νe + ντ is given by an expression of the same form43

Γ ( τ − → e − + ν e ¯ + ν τ ) ≈ K 3 G F 2 m τ 5   , {\displaystyle \Gamma \left(\tau ^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{\tau }\right)\approx K_{3}\,G_{\text{F}}^{2}\,m_{\tau }^{5}~,}

where K3 is some other constant. Muon–tauon universality implies that K2 ≈ K3. On the other hand, electron–muon universality implies44

0.9726 × Γ ( τ − → e − + ν e ¯ + ν τ ) = Γ ( τ − → μ − + ν μ ¯ + ν τ )   . {\displaystyle 0.9726\times \Gamma \left(\tau ^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{\tau }\right)=\Gamma \left(\tau ^{-}\rightarrow \mu ^{-}+{\bar {\nu _{\mu }}}+\nu _{\tau }\right)~.}

The branching 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.45

Universality also accounts for the ratio of muon and tau lifetimes. The lifetime T ℓ {\displaystyle \mathrm {T} _{\ell }} of a lepton ℓ {\displaystyle \ell } (with ℓ {\displaystyle \ell } = "μ" or "τ") is related to the decay rate by46

T ℓ = B ( ℓ − → e − + ν e ¯ + ν ℓ ) Γ ( ℓ − → e − + ν e ¯ + ν ℓ ) {\displaystyle \mathrm {T} _{\ell }={\frac {\;{\mathcal {B}}\left(\ell ^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{\ell }\right)\;}{\Gamma \left(\ell ^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{\ell }\right)}}\,} ,

where B ( x → y ) {\displaystyle \;{\mathcal {B}}(x\rightarrow y)\;} denotes the branching ratios and Γ ( x → y ) {\displaystyle \;\Gamma (x\rightarrow y)\;} denotes the resonance width of the process x → y   , {\displaystyle \;x\rightarrow y~,} with x and y replaced by two different particles from "e" or "μ" or "τ".

The ratio of tau and muon lifetime is thus given by47

T τ T μ = B ( τ − → e − + ν e ¯ + ν τ ) B ( μ − → e − + ν e ¯ + ν μ ) ( m μ m τ ) 5   . {\displaystyle {\frac {\,\mathrm {T} _{\tau }\,}{\mathrm {T} _{\mu }}}={\frac {\;{\mathcal {B}}\left(\tau ^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{\tau }\right)\;}{{\mathcal {B}}\left(\mu ^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{\mu }\right)}}\,\left({\frac {m_{\mu }}{m_{\tau }}}\right)^{5}~.}

Using values from the 2008 Review of Particle Physics for the branching ratios of the muon48 and tau49 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 K2 and K3 not actually being constants: They depend slightly on the mass of leptons involved.

Recent tests of lepton universality in B meson decays, performed by the LHCb, BaBar, and Belle 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 of new physics.50

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 τ / μ = B ( W → τ ν τ ) / B ( W → μ ν μ ) = 0.992 ± 0.013 {\displaystyle R_{W}^{\tau /\mu }={\mathcal {B}}(W\rightarrow \tau \nu _{\tau })/{\mathcal {B}}(W\rightarrow \mu \nu _{\mu })=0.992\pm 0.013} , which agrees with the standard-model prediction of unity.515253 In 2024 a preprint by the ATLAS collaboration has published a new value of R W μ / e = B ( W → μ ν μ ) / B ( W → e ν e ) = 0.9995 ± 0.0045 {\displaystyle R_{W}^{\mu /e}={\mathcal {B}}(W\rightarrow \mu \nu _{\mu })/{\mathcal {B}}(W\rightarrow e\nu _{e})=0.9995\pm 0.0045} the most precise ratio so far testing the lepton flavour universality.5455

Table of leptons

Properties of leptons
SpinJ [ħ]Particle or antiparticle nameSymbolChargeQ [e]Lepton flavor numberMass[MeV/c2]Lifetime[s]
LeLμLτ
⁠1/2⁠electron56e−−1+1000.510998910(13)stable
positron57e++1−1
muon58μ−−10+10105.6583668(38)2.197019(21)×10−6        
antimuon59μ++1−1
tau60τ−−100+11776.84(17)2.906(10)×10−13
antitau61τ++1−1
electron neutrino62νe0+100< 0.000002263unknown
electron antineutrinoνe−1
muon neutrino64νμ0+10< 0.1765unknown
muon antineutrino66 νμ −1
tau neutrino67 ντ 00+1< 15.568unknown
tau antineutrino69 ντ −1

See also

Notes

Bibliography

Wikimedia Commons has media related to Leptons. Look up lepton in Wiktionary, the free dictionary.

References

  1. "Lepton (physics)". Encyclopædia Britannica. Retrieved 29 September 2010. https://www.britannica.com/EBchecked/topic/336940/lepton ↩

  2. Nave, R. "Leptons". HyperPhysics. Georgia State University, Department of Physics and Astronomy. Retrieved 29 September 2010. http://hyperphysics.phy-astr.gsu.edu/hbase/Particles/lepton ↩

  3. Farrar, W. V. (1969). "Richard Laming and the Coal-Gas Industry, with His Views on the Structure of Matter". Annals of Science. 25 (3): 243–254. doi:10.1080/00033796900200141. /wiki/Annals_of_Science ↩

  4. Arabatzis, T. (2006). Representing Electrons: A Biographical Approach to Theoretical Entities. University of Chicago Press. pp. 70–74. ISBN 978-0-226-02421-9. 978-0-226-02421-9 ↩

  5. Buchwald, J. Z.; Warwick, A. (2001). Histories of the Electron: The Birth of Microphysics. MIT Press. pp. 195–203. ISBN 978-0-262-52424-7. 978-0-262-52424-7 ↩

  6. Thomson, J. J. (1897). "Cathode Rays". Philosophical Magazine. 44 (269): 293. doi:10.1080/14786449708621070. /wiki/J._J._Thomson ↩

  7. Neddermeyer & Anderson 1937 - Neddermeyer, S. H.; Anderson, C. D. (1937). "Note on the Nature of Cosmic-Ray Particles" (PDF). Physical Review. 51 (10): 884–886. Bibcode:1937PhRv...51..884N. doi:10.1103/PhysRev.51.884. https://authors.library.caltech.edu/8618/1/NEDpr37.pdf ↩

  8. "The Reines-Cowan Experiments: Detecting the Poltergeist" (PDF). Los Alamos Science. 25: 3. 1997. Retrieved 2010-02-10. http://library.lanl.gov/cgi-bin/getfile?25-02.pdf ↩

  9. "The Reines-Cowan Experiments: Detecting the Poltergeist" (PDF). Los Alamos Science. 25: 3. 1997. Retrieved 2010-02-10. http://library.lanl.gov/cgi-bin/getfile?25-02.pdf ↩

  10. "The Reines-Cowan Experiments: Detecting the Poltergeist" (PDF). Los Alamos Science. 25: 3. 1997. Retrieved 2010-02-10. http://library.lanl.gov/cgi-bin/getfile?25-02.pdf ↩

  11. Reines, F.; Cowan, C.L. Jr. (1956). "The Neutrino". Nature. 178 (4531): 446. Bibcode:1956Natur.178..446R. doi:10.1038/178446a0. S2CID 4293703. /wiki/Nature_(journal) ↩

  12. Danby, G.; et al. (1962). "Observation of high-energy neutrino reactions and the existence of two kinds of neutrinos". Physical Review Letters. 9 (1): 36. Bibcode:1962PhRvL...9...36D. doi:10.1103/PhysRevLett.9.36. http://inspirehep.net/search?p=PRLTA,9,36 ↩

  13. Perl 1975 - Perl, M. L.; et al. (1975). "Evidence for Anomalous Lepton Production in e+–e− Annihilation". Physical Review Letters. 35 (22): 1489–1492. Bibcode:1975PhRvL..35.1489P. doi:10.1103/PhysRevLett.35.1489. https://ui.adsabs.harvard.edu/abs/1975PhRvL..35.1489P ↩

  14. "Physicists find first direct evidence for tau neutrino at Fermilab" (Press release). Fermilab. 20 July 2000. http://www.fnal.gov/pub/presspass/press_releases/donut.html ↩

  15. Kodama 2001 - Kodama, K.; et al. (2001). "Observation of tau neutrino interactions". Physics Letters B. 504 (3): 218–224. arXiv:hep-ex/0012035. Bibcode:2001PhLB..504..218D. doi:10.1016/S0370-2693(01)00307-0. S2CID 119335798. https://arxiv.org/abs/hep-ex/0012035 ↩

  16. "lepton". Online Etymology Dictionary. http://www.etymonline.com/index.php?term=lepton ↩

  17. λεπτός. Liddell, Henry George; Scott, Robert; A Greek–English Lexicon at the Perseus Project. https://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.04.0057:entry=lepto/s ↩

  18. Found on the KN L 693 and PY Un 1322 tablets. "The Linear B word re-po-to". Palaeolexicon. Word study tool of ancient languages. Raymoure, K.A. "re-po-to". Minoan Linear A & Mycenaean Linear B. Deaditerranean. Archived from the original on 2016-01-16. Retrieved 2014-03-22. "KN 693 L (103)". "PY 1322 Un + fr. (Cii)". DĀMOS: Database of Mycenaean at Oslo. University of Oslo. /wiki/Knossos ↩

  19. Rosenfeld 1948 - Rosenfeld, L. (1948). Nuclear Forces. Interscience Publishers. p. xvii. ↩

  20. Amsler 2008: Particle listings—e− - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩

  21. Amsler 2008: Particle listings—μ− - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩

  22. Amsler 2008: Particle listings—p+ - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩

  23. Amsler 2008: Particle listings—τ− - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩

  24. "2022 CODATA Value: tau-electron mass ratio". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 2024-05-18. https://physics.nist.gov/cgi-bin/cuu/Value?mtausme ↩

  25. Weinberg 2003 - Weinberg, S. (2003). The Discovery of Subatomic Particles. Cambridge University Press. ISBN 978-0-521-82351-7. https://archive.org/details/discoveryofsubat00wein_0 ↩

  26. Wilson 1997 - Wilson, R. (1997). Astronomy Through the Ages: The Story of the Human Attempt to Understand the Universe. CRC Press. p. 138. ISBN 978-0-7484-0748-4. ↩

  27. Riesselmann 2007 - Riesselmann, K. (2007). "Logbook: Neutrino Invention". Symmetry Magazine. 4 (2). Archived from the original on 31 May 2009. https://web.archive.org/web/20090531073123/http://www.symmetrymagazine.org/cms/?pid=1000450 ↩

  28. Neddermeyer & Anderson 1937 - Neddermeyer, S. H.; Anderson, C. D. (1937). "Note on the Nature of Cosmic-Ray Particles" (PDF). Physical Review. 51 (10): 884–886. Bibcode:1937PhRv...51..884N. doi:10.1103/PhysRev.51.884. https://authors.library.caltech.edu/8618/1/NEDpr37.pdf ↩

  29. Anicin 2005 - Anicin, I. V. (2005). "The Neutrino: Its Past, Present and Future". arXiv:physics/0503172. https://arxiv.org/abs/physics/0503172 ↩

  30. Perl 1975 - Perl, M. L.; et al. (1975). "Evidence for Anomalous Lepton Production in e+–e− Annihilation". Physical Review Letters. 35 (22): 1489–1492. Bibcode:1975PhRvL..35.1489P. doi:10.1103/PhysRevLett.35.1489. https://ui.adsabs.harvard.edu/abs/1975PhRvL..35.1489P ↩

  31. Kodama 2001 - Kodama, K.; et al. (2001). "Observation of tau neutrino interactions". Physics Letters B. 504 (3): 218–224. arXiv:hep-ex/0012035. Bibcode:2001PhLB..504..218D. doi:10.1016/S0370-2693(01)00307-0. S2CID 119335798. https://arxiv.org/abs/hep-ex/0012035 ↩

  32. Amsler 2008 Heavy Charged Leptons Searches - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩

  33. Amsler 2008 Searches for Heavy Neutral Leptons - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩

  34. Peskin & Schroeder 1995, p. 197 - Peskin, M. E.; Schroeder, D. V. (1995). Introduction to Quantum Field Theory. Westview Press. ISBN 978-0-201-50397-5. https://archive.org/details/introductiontoqu0000pesk ↩

  35. Peskin & Schroeder 1995, p. 27 - Peskin, M. E.; Schroeder, D. V. (1995). Introduction to Quantum Field Theory. Westview Press. ISBN 978-0-201-50397-5. https://archive.org/details/introductiontoqu0000pesk ↩

  36. Fukuda 1998 - Fukuda, Y.; et al. (1998). "Evidence for Oscillation of Atmospheric Neutrinos". Physical Review Letters. 81 (8): 1562–1567. arXiv:hep-ex/9807003. Bibcode:1998PhRvL..81.1562F. doi:10.1103/PhysRevLett.81.1562. S2CID 7102535. https://arxiv.org/abs/hep-ex/9807003 ↩

  37. Amsler 2008: Particle listings — Neutrino properties - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩

  38. Martin & Shaw 1992 - Martin, B. R.; Shaw, G. (1992). "Chapter 2: Leptons, quarks and hadrons". Particle Physics. John Wiley & Sons. pp. 23–47. ISBN 978-0-471-92358-9. https://archive.org/details/particlephysics0000mart/page/23 ↩

  39. Martin & Shaw 1992 - Martin, B. R.; Shaw, G. (1992). "Chapter 2: Leptons, quarks and hadrons". Particle Physics. John Wiley & Sons. pp. 23–47. ISBN 978-0-471-92358-9. https://archive.org/details/particlephysics0000mart/page/23 ↩

  40. Cumalat, J.P. (1993). Physics in Collision. Vol. 12. Atlantica Séguier Frontières. ISBN 978-2-86332-129-4. 978-2-86332-129-4 ↩

  41. Fraser, G. (1 January 1998). The Particle Century. CRC Press. ISBN 978-1-4200-5033-2 – via Google Books. 978-1-4200-5033-2 ↩

  42. Martin & Shaw 1992 - Martin, B. R.; Shaw, G. (1992). "Chapter 2: Leptons, quarks and hadrons". Particle Physics. John Wiley & Sons. pp. 23–47. ISBN 978-0-471-92358-9. https://archive.org/details/particlephysics0000mart/page/23 ↩

  43. Martin & Shaw 1992 - Martin, B. R.; Shaw, G. (1992). "Chapter 2: Leptons, quarks and hadrons". Particle Physics. John Wiley & Sons. pp. 23–47. ISBN 978-0-471-92358-9. https://archive.org/details/particlephysics0000mart/page/23 ↩

  44. Martin & Shaw 1992 - Martin, B. R.; Shaw, G. (1992). "Chapter 2: Leptons, quarks and hadrons". Particle Physics. John Wiley & Sons. pp. 23–47. ISBN 978-0-471-92358-9. https://archive.org/details/particlephysics0000mart/page/23 ↩

  45. Amsler 2008: Particle listings—τ− - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩

  46. Martin & Shaw 1992 - Martin, B. R.; Shaw, G. (1992). "Chapter 2: Leptons, quarks and hadrons". Particle Physics. John Wiley & Sons. pp. 23–47. ISBN 978-0-471-92358-9. https://archive.org/details/particlephysics0000mart/page/23 ↩

  47. Martin & Shaw 1992 - Martin, B. R.; Shaw, G. (1992). "Chapter 2: Leptons, quarks and hadrons". Particle Physics. John Wiley & Sons. pp. 23–47. ISBN 978-0-471-92358-9. https://archive.org/details/particlephysics0000mart/page/23 ↩

  48. Amsler 2008: Particle listings—μ− - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩

  49. Amsler 2008: Particle listings—τ− - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩

  50. Ciezarek G, Franco Sevilla M, Hamilton B, Kowalewski R, Kuhr T, Lüth V, Sato Y (2017). "A challenge to lepton universality in B meson decays". Nature. 546 (7657): 227–233. arXiv:1703.01766. Bibcode:2017Natur.546..227C. doi:10.1038/nature22346. PMID 28593973. S2CID 4385808. /wiki/ArXiv_(identifier) ↩

  51. Aad, G.; Abbott, B.; Abbott, D. C.; Abud, A. Abed; Abeling, K.; Abhayasinghe, D. K.; Abidi, S. H.; AbouZeid, O. S.; Abraham, N. L.; Abramowicz, H.; Abreu, H. (5 July 2021). "Test of the universality of τ and μ lepton couplings in W-boson decays with the ATLAS detector". Nature Physics. 17 (7): 813–818. arXiv:2007.14040. Bibcode:2021NatPh..17..813A. doi:10.1038/s41567-021-01236-w. ISSN 1745-2481. S2CID 220831347. https://www.nature.com/articles/s41567-021-01236-w ↩

  52. Middleton, Christine (2021-07-09). "ATLAS measurement supports lepton universality". Physics Today. 2021 (1): 0709a. Bibcode:2021PhT..2021a.709.. doi:10.1063/PT.6.1.20210709a. S2CID 242888088. https://physicstoday.scitation.org/do/10.1063/PT.6.1.20210709a/abs/ ↩

  53. "New ATLAS result addresses long-standing tension in the Standard Model". ATLAS. Retrieved 2021-07-12. https://atlas.cern/updates/briefing/addressing-long-standing-tension-standard-model ↩

  54. ATLAS Collaboration (2024-03-04). "Precise test of lepton flavour universality in W-boson decays into muons and electrons in pp collisions at √s = 13 TeV with the ATLAS detector". arXiv:2403.02133 [hep-ex]. /wiki/ArXiv_(identifier) ↩

  55. "The delicate balance of lepton flavours". CERN. 2024-09-18. Retrieved 2024-09-20. https://home.cern/news/news/physics/delicate-balance-lepton-flavours ↩

  56. Amsler 2008: Particle listings—e− - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩

  57. Amsler 2008: Particle listings—e− - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩

  58. Amsler 2008: Particle listings—μ− - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩

  59. Amsler 2008: Particle listings—μ− - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩

  60. Amsler 2008: Particle listings—τ− - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩

  61. Amsler 2008: Particle listings—τ− - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩

  62. Amsler 2008: Particle listings — Neutrino properties - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩

  63. Peltoniemi, J.; Sarkamo, J. (2005). "Laboratory measurements and limits for neutrino properties". The Ultimate Neutrino Page. Retrieved 7 November 2008. http://cupp.oulu.fi/neutrino/nd-mass.html ↩

  64. Amsler 2008: Particle listings — Neutrino properties - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩

  65. Peltoniemi, J.; Sarkamo, J. (2005). "Laboratory measurements and limits for neutrino properties". The Ultimate Neutrino Page. Retrieved 7 November 2008. http://cupp.oulu.fi/neutrino/nd-mass.html ↩

  66. Amsler 2008: Particle listings — Neutrino properties - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩

  67. Amsler 2008: Particle listings — Neutrino properties - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩

  68. Peltoniemi, J.; Sarkamo, J. (2005). "Laboratory measurements and limits for neutrino properties". The Ultimate Neutrino Page. Retrieved 7 November 2008. http://cupp.oulu.fi/neutrino/nd-mass.html ↩

  69. Amsler 2008: Particle listings — Neutrino properties - Amsler, C.; et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. http://scipp.ucsc.edu/%7Ehaber/pubs/Review_of_Particle_Physics_2014.pdf ↩