Lepton

The name lepton comes from the Greek λεπτός leptós, "fine, small, thin" (neuter nominative/accusative singular form: λεπτόν leptón);[14][15] the earliest attested form of the word is the Mycenaean Greek 𐀩𐀡𐀵, re-po-to, written in Linear B syllabic script.[16] Lepton was first used by physicist Léon 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 because the only known leptons at the time were electrons and muons, whose masses are small compared to nucleons—the mass of an electron (0.511 MeV/c²)[18] and the mass of a muon (with a value of 105.7 MeV/c²)[19] are fractions of the mass of the "heavy" proton (938.3 MeV/c²).[20] However, the mass of the tau (discovered in the mid-1970s) (1777 MeV/c²)[21] is nearly twice that of the proton and about 3,500 times that of the electron.

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.[22][23] 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.[24] 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.[25] 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.[26]

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.[27] 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,[28] 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,[29] while its associated neutrino would have a mass of at least 45.0 GeV/c².[30]

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.[35] 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.[36]^{: 241–243}[37]^: 138

The decay rate (${\displaystyle \Gamma }$) 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)[35]

${\displaystyle \Gamma \left(\mu ^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{\mu }\right)\approx K_{2}\,G_{\text{F}}^{2}\,m_{\mu }^{5}~,}$

where K₂ is some constant, and 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[35]

${\displaystyle \Gamma \left(\tau ^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{\tau }\right)\approx K_{3}\,G_{\text{F}}^{2}\,m_{\tau }^{5}~,}$

where K₃ is some other constant. Muon–tauon universality implies that K₂ ≈ K₃ . On the other hand, electron–muon universality implies[35]

${\displaystyle \Gamma \left(\tau ^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{\tau }\right)=\Gamma \left(\tau ^{-}\rightarrow \mu ^{-}+{\bar {\nu _{\mu }}}+\nu _{\tau }\right)~.}$

This explains why the branching ratios for the electronic mode (17.82%) and muonic (17.39%) mode of tau decay are equal (within error).[21]

Universality also accounts for the ratio of muon and tau lifetimes. The lifetime ${\displaystyle \mathrm {T} _{\ell }}$ of a lepton ${\displaystyle \ell }$ (with ${\displaystyle \ell }$ = "μ" or "τ") is related to the decay rate by[35]

${\displaystyle \mathrm {T} _{\ell }={\frac {\;{\mathcal {B}}\left(\ell ^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{\ell }\right)\;}{\Gamma \left(\ell ^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{\ell }\right)}}\,}$,

where ${\displaystyle \;{\mathcal {B}}(x\rightarrow y)\;}$ denotes the branching ratios and ${\displaystyle \;\Gamma (x\rightarrow y)\;}$ denotes the resonance width of the process ${\displaystyle \;x\rightarrow y~,}$ 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 by[35]

${\displaystyle {\frac {\,\mathrm {T} _{\tau }\,}{\mathrm {T} _{\mu }}}={\frac {\;{\mathcal {B}}\left(\tau ^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{\tau }\right)\;}{{\mathcal {B}}\left(\mu ^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{\mu }\right)}}\,\left({\frac {m_{\mu }}{m_{\tau }}}\right)^{5}~.}$

Using values from the 2008 Review of Particle Physics for the branching ratios of the 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 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.[38]

In July 2021 results on lepton 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 ${\displaystyle {\mathcal {B}}(W\rightarrow \tau ^{-}+\nu _{\tau })/{\mathcal {B}}(W\rightarrow \mu ^{-}+\nu _{\mu })=0.992\pm 0.013}$ which agrees with the standard-model prediction of unity[39][40][41]

Properties of leptons

Spin J	Particle or Antiparticle name	Symbol	Charge Q (e)[lower-alpha 1]	Lepton flavor number			Mass (MeV/c2)	Lifetime (seconds)
				Le	Lμ	Lτ
1 /2	Electron[18]	e−	−1	+1	0	0	0.510998910  (±13)	Stable
	Positron[18]	e+	+1	−1
	Muon[19]	μ−	−1	0	+1	0	105.6583668  (±38)	2.197019×10−6 (±21)
	Antimuon[19]	μ+	+1		−1
	Tau[21]	τ−	−1	0	0	+1	1776.84  (±.17)	2.906×10−13 (±.010)
	Antitau[21]	τ+	+1			−1
	Electron neutrino[34]	ν e	0	+1	0	0	<0.0000022[42]	Unknown
	Electron antineutrino	ν e		−1
	Muon neutrino[34]	ν μ	0	0	+1	0	< 0.17[42]	Unknown
	Muon antineutrino[34]	ν μ			−1
	Tau neutrino[34]	ν τ	0	0	0	+1	< 15.5[42]	Unknown
	Tau antineutrino[34]	ν τ				−1

• Koide formula
• List of particles
• Preons—hypothetical particles which were once postulated to be subcomponents of quarks and 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.
• Anicin, I. V. (2005). "The Neutrino: Its Past, Present and Future". arXiv:physics/0503172.
• 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.
• 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.
• B. R. Martin; G. Shaw (1992). "Chapter 2: Leptons, quarks and hadrons". Particle Physics. John Wiley & Sons. pp. 23–47. ISBN 978-0-471-92358-9.
• 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.
• 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.
• Peskin, M. E.; Schroeder, D. V. (1995). Introduction to Quantum Field Theory. Westview Press. ISBN 978-0-201-50397-5.
• Riesselmann, K. (2007). "Logbook: Neutrino Invention". Symmetry Magazine. 4 (2). Archived from the original on 31 May 2009.
• Rosenfeld, L. (1948). Nuclear Forces. Interscience Publishers. p. xvii.
• Shankar, R. (1994). "Chapter 2: Rotational Invariance and Angular Momentum". Principles of Quantum Mechanics (2nd ed.). Springer. pp. 305–352. ISBN 978-0-306-44790-7.
• Weinberg, S. (2003). The Discovery of Subatomic Particles. Cambridge University Press. ISBN 978-0-521-82351-7.
• 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.

Wikimedia Commons has media related to Leptons.

Look up lepton in Wiktionary, the free dictionary.

• "Particle Data Group homepage". – The PDG compiles authoritative information on particle properties.
• "Leptons". Physics & Astronomy. Georgia State University. Hyperphysics. – a summary of leptons.