Lepton

For the former Greek currency unit, see Greek drachma.

A muon transmutes into a muon neutrino by emitting a W⁻ boson. The W⁻ boson subsequently decays into an electron and an electron antineutrino.

Leptons are a family of elementary particles, alongside quarks and gauge bosons (also known as force carriers). Like quarks, leptons are fermions (spin-¹⁄₂ particles) and are subject to the electromagnetic force, the gravitational force, and weak interaction. But unlike quarks, leptons do not participate in the strong interaction.

There are six flavours of leptons, forming three generations. The first generation is the electronic leptons, comprising the electrons (e⁻), and electron neutrinos (νe); the second is the muonic leptons, comprising muons (μ⁻), and muon neutrinos (νμ); and the third is the tauonic leptons, comprising tauons (τ⁻), and tauon neutrinos (ντ). Each lepton has a corresponding antiparticle – these antiparticles are known as antileptons.

Leptons are an important part of the Standard Model, especially the electrons which are one of the components of atoms, alongside protons and neutrons. Exotic atoms with muons and tauons instead of electrons can also be synthesized.

1 Etymology
2 History
3 Properties
4 Universality
5 Table of leptons
6 See also
7 References
- 7.1 Bibliography
8 External links

Etymology

Lepton nomenclature
Particle name	Antiparticle name
Electron	Antielectron Positron
Electron neutrino	Electron antineutrino
Muon Mu lepton Mu	Antimuon Antimu lepton Antimu
Muon neutrino Muonic neutrino Mu neutrino	Muon antineutrino Muonic antineutrino Mu antineutrino
Tauon Tau lepton Tau	Antitauon Antitau lepton Antitau
Tauon neutrino Tauonic neutrino Tau neutrino	Tauon antineutrino Tauoninc antineutrino Tau antineutrino

According to the Oxford English Dictionary, the name "lepton" (from Greek leptos meaning 'thin') was first used by physicist Léon Rosenfeld in 1948:^[1]

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 light. When Rosenfeld named them, the only known leptons were electrons and muons. In the mid 1970s however, the tauons were discovered. While the mass of electrons (0.511 MeV/c²)^[2] and muons (105.7 MeV/c²)^[3] are fractions of the mass of the "heavy" proton (938.3 MeV/c²),^[4] the mass of the tauons (1,777 MeV/c²)^[5] is nearly twice that of protons, and about 3,500 times that of electrons.

History

See also: Electron#Discovery, Muon#Discovery, and Tauon#Discovery

The first lepton identified was the electron, discovered by J.J. Thomson and his team of British physicists in 1897.^[6]^[7] 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.^[8] Pauli theorized that an undetected particle was carrying away the observed difference between the energy, momentum, and angular momentum of the initial and final particles. The electron neutrino was simply known as the neutrino back then, as it was not yet known that neutrinos came in different flavours.

Nearly 40 years after the discovery of the electrion, the muon was discovered by Carl D. Anderson in 1936, although it was initially identified as a meson rather than a lepton.^[9] It later became evident that the muon was not a meson, as muons did not experience the strong interaction, but rather something very similar to electrons. Electrons and muons and the (electron) neutrino were thus regrouped 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 the different flavours of neutrino already, by then, already had been theorized.^[10]

The tauon was first detected in a series of experiments between 1974 and 1977 by Martin Lewis Perl with his colleagues at the SLAC LBL group.^[11] Like the electron and the muon, it too was expected to have an associated neutrino. The first evidence for tauon neutrinos came from the observation of missing energy and momentum in tauon decay, analogous to the missing energy and momentum in beta decay leading to the discovery of the electron neutrino. The first detection of tauon 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.^[12]

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 100.8 GeV/c²,^[13] while its associated neutrino has a mass of at least 45.0 GeV/c².^[14]

Properties

Charges: electric charge, spin, weak isospin, and weak hypercharge

Leptons carry different types of charges, the most known of them being the electric charge (Q). Other charges carried by leptons include, spin (S,S_z), weak isospin (T,T_z), and weak hypercharge (Y_W = 2 ( Q − T_Z )). The electric charge relates how leptons interact with the electromagnetic force, while weak isospin relates how leptons interact with the weak interaction. The two can be combined and unified into the weak hypercharge which relates how leptons interact with the electroweak interaction (which combine and unify the electromagnetic force and the weak interaction into a single interaction). Spin relates how particles in spin-spin interactions. Physicists rarely use the word "charge" to refer to any other charges but the electric charge. "Charged leptons" therefore means "leptons that carry electrical charge" rather than "leptons that carry some type of charge", unless explicitly stated otherwise.

While the electric charge and the weak hypercharge are scalar charges (charges that can be expressed as simple numbers), spin and weak isospin are vector charges (charges that have a length and a direction). While scalar charges can be completely determined by experiment, the length and direction of vector charges can never be completely determined,^[15] only the length (S, T) and the projection along some axis (S_z, T_z) can be known. While any axis could be chosen (x, y, or z), the z-axis usually is chosen by convention. See spin vector for more details.

The charged leptons (electrons, muons, and tauons) all carry an electric charge of Q = −1 e and have a weak isospin projection of T_z = −¹⁄₂, while all neutrinos are electrically neutral (Q = 0) and have a weak isospin projection of T_z = +¹⁄₂. This implies that all leptons carry a weak hyperchage of Y_W = −1. All known processes conserve both electric charge and weak isospin (and thus weak hypercharge). Other types of charges exists, such as the colour charge, which relates how particles interact with the strong interaction, but leptons do not carry them.

Spin and chirality

Left-handed and right-handed helicities

Leptons are spin-¹⁄₂ particles. The spin-statistics theorem thus implies that they are fermions and thus that they are subject the Pauli exclusion principle; no two leptons of the same species can be in exactly the same state a 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 that of 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 assymetrically. Only left-handed fermions participate in the weak interaction, while there are no right-handed neutrinos. This is an example of parity violation.

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 (νe_L,e⁻_L) 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 T_z 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 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 (W⁺, W⁻, Z⁰) mediating the weak interaction, and one massless vector boson, the photon, responsible for the electromagnetic interaction. The electric charge Q can be calculated form the isospin projection T_z and weak hypercharge Y_W through the following formula,

Q = T_z + Y_W/2

To recover the observed electric charges for all particles the left-handed weak isospin doublet (νe_L,e⁻_L) must thus have Y_W = −1, while the right-handed isospin scalar e⁻_R must have Y_W = −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 tauon) 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.^[16]

It is however known from experiment – most prominently from observed neutrino oscillations^[17] – that neutrinos do in fact have some very small mass, probably less than 2 eV/c².^[18] This implies that there are 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.

Leptonic numbers

$\begin{pmatrix} e^- \\ \nu_e\\ \end{pmatrix}, \begin{pmatrix} \mu^- \\ \nu_\mu\\ \end{pmatrix}, \begin{pmatrix} \tau^- \\ \nu_\tau\\ \end{pmatrix}$

Each generation forms a weak isospin doublet.

The members of each generation's weak isospin doublet are assigned leptonic numbers that are conserved under the Standard Model.^[19] 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 tauons and tauon 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:

e⁻ + e⁺ → γ + γ,

τ⁻ + τ⁺ → Z⁰ + Z⁰,

but not 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), 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).^[19] This property is called lepton universality and has been tested in measurements of the tauon and muon lifetimes and of Z boson partial decay widths, particularly at the Stanford Linear Collider (SLC) and Large Electron-Positron Collider (LEP) experiments.

The decay rate (Γ) of muons through the process μ⁻ → e⁻ + νe + νμ is given by an expression of the form^[19]

$\Gamma \left ( \mu^- \rarr e^- + \bar{\nu_e} +\nu_\mu \right ) = K_1G_F^2m_\mu^5,$

where K₁ is some constant, and G_F is the Fermi coupling constant. The decay rate of tauons through the process τ⁻ → e⁻ + νe + ντ is given by an expression of the same form^[19]

$\Gamma \left ( \tau^- \rarr e^- + \bar{\nu_e} +\nu_\mu \right ) = K_2G_F^2m_\tau^5,$

where K₂ is some constant. Electron-muon universality implies that K₁ = K₂, and thus ^[19]

$\Gamma \left ( \mu^- \rarr e^- + \bar{\nu_e} +\nu_\mu \right ) = \Gamma \left ( \tau^- \rarr \mu^- + \bar{\nu_\mu} +\nu_\tau \right ).$

This explains why the branching ratios for the electronic mode (17.85%) and muonic (17.36%) mode of tauon decay are equal (within error).^[5]

Universality also account for the ratio of muon and tauon lifetimes. The lifetime of a lepton (τ_l) is related to the decay rate by^[19]

$\tau_l=\frac{B \left ( l^- \rarr e^- + \bar{\nu_e} +\nu_l \right )}{\Gamma \left ( l^- \rarr e^- + \bar{\nu_e} +\nu_l \right )},$

where B(x → y) and Γ(x → y) denotes the branching ratios and the resonance width of the process x → y.

The ratio of tauon and muon lifetime is thus given by^[19]

$\frac{\tau_\tau}{\tau_\mu} = \frac{B \left ( \tau^- \rarr e^- + \bar{\nu_e} +\nu_\tau \right )}{B \left ( \mu^- \rarr e^- + \bar{\nu_e} +\nu_\mu \right )}\left (\frac{m_\mu}{m_\tau}\right )^5.$

Using the values of the 2008 Review of Particle Physics for the branching ratios of muons^[3] and tauon^[5] yields a lifetime ratio of ~1.29×10⁻⁷, comparable to the measured lifetime ratio of ~1.32×10⁷.

Table of leptons

Properties of leptons
Particle/Antiparticle Name	Symbol	Q (e)	S_z	T_z	Y_W	L_e	L_μ	L_τ	Mass (MeV/c²)	Lifetime (s)	Common decay
Electron / Antielectron^[2]	e⁻/e⁺	−1	±¹⁄₂	+¹⁄₂	1	1	0	0	0.510998910(13)	Stable	Stable
Muon / Antimuon^[3]	μ⁻/μ⁺	−1	±¹⁄₂	+¹⁄₂	1	0	1	0	105.6583668(38)	2.197019(21) × 10⁻⁶	e⁻ + νe + νμ
Tauon / Antitauon^[5]	τ⁻/τ⁺	−1	±¹⁄₂	+¹⁄₂	1	0	0	1	1,776.84(17)	290.6(10) × 10⁻¹⁵	See τ⁻ decay modes
Electron neutrino / Electron antineutrino^[20]	νe/νe	0	±¹⁄₂	−¹⁄₂	0	1	0	0	< 0.0000022 ^[21]	Unknown
Muon neutrino / Muon antineutrino^[20]	νμ/νμ	0	±¹⁄₂	−¹⁄₂	0	0	1	0	< 0.17 ^[21]	Unknown
Tauon neutrino / Tauon antineutrino^[20]	ντ/ντ	0	±¹⁄₂	−¹⁄₂	0	0	0	1	< 15.5 ^[21]	Unknown

References

↑ L. Rosenfeld (1948)
↑ ^2.0 ^2.1 C.Amsler et al. (2008): Particle listings – e⁻
↑ ^3.0 ^3.1 ^3.2 C.Amsler et al. (2008): Particle listings – μ⁻
↑ C.Amsler et al. (2008): Particle listings – p⁺
↑ ^5.0 ^5.1 ^5.2 ^5.3 C.Amsler et al. (2008): Particle listings – τ⁻
↑ S. Weinberg (2003)
↑ R. Wilson (1997)
↑ K. Riesselmann (2007)
↑ S.H. Neddermeyer, C.D. Anderson (1937)
↑ I.V. Anicin (2005)
↑ M.L. Perl et al. (1975)
↑ K. Kodama (2001)
↑ C.Amsler et al. Heavy Charged Leptons Searches
↑ C.Amsler et al. Searches for Heavy Neutral Leptons
↑ The technical reason for this is that spin projection operators S_x and S_z (or T_x and T_z in the case of weak isospin projection operators) do not commute. See R. Shankar (1994)
↑ Peskin and Schroeder (1995)
↑ Y. Fukuda et al. (1998)
↑ C. Amsler et al. (2008)
↑ ^19.0 ^19.1 ^19.2 ^19.3 ^19.4 ^19.5 ^19.6 B.R Martin, G. Shaw (1992)
↑ ^20.0 ^20.1 ^20.2 C.Amsler et al. (2008): Particle listings – Neutrino properties
↑ ^21.0 ^21.1 ^21.2 J. Peltoniemi, J. Sarkamo (2005)

Bibliography

C.Amsler et al. (2008). "Review of Particle Physics". Physics Letters (Particle Data Group) B667 (1).
I.V. Anicin (2005). "The Neutrino - Its Past, Present and Future". arΧiv: physics/0503172v1 [physics] Retrieved on 2008-06-09.
Y.Fukuda et al. (1998). "Evidence for Oscillation of Atmospheric Neutrinos". Physical Review Letters 81: 1562–1567. arΧiv:hep-ex/9807003v2. http://prola.aps.org/pdf/PRL/v81/i8/p1562_1.
K. Kodama (2001). "Observation of tau neutrino interactions". Physics Letters B 504: 218. doi:10.1016/S0370-2693(01)00307-0.
B.R. Martin, G. Shaw (1992). "Chapter 2 – Leptons, quarks and hadrons". Particle physics. Chichester (England): John Wiley & Sons. pp. 23–47. ISBN 0-471-92358-3.
S.H. Neddermeyer, C.D. Anderson (1937). "Note on the Nature of Cosmic-Ray Particles". Physical Review 51: 884–886. doi:10.1103/PhysRev.51.884. http://prola.aps.org/pdf/PR/v51/i10/p884_1.
J. Peltoniemi, J. Sarkamo (2005). "Laboratory measurements and limits for neutrino properties". The Ultimate Neutrino Page. Retrieved on 2008-11-07.
M.L. Perl et al. (1975). "Evidence for Anomalous Lepton Production in e⁺–e⁻ Annihilation". Physical Review Letters 35 (22): 1489–1492. doi:10.1103/PhysRevLett.35.1489. http://prola.aps.org/pdf/PRL/v35/i22/p1489_1.
M.E. Peskin, D.V. Schroeder (1995). Introduction to Quantum Field Theory. Westview Press. p. 27. ISBN 0-201-50397-2.
K. Riesselmann (2007). "Logbook: Neutrino Invention". Symmetry 4 (2). http://www.symmetrymagazine.org/cms/?pid=1000450.
L. Rosenfeld (1948). Nuclear Forces. New York (NY, USA): Interscience Publishers. p. xvii.
R. Shankar (1994). "Chapter 2 – Rotational Invariance and Angular Momentum". Principles of Quantum Mechanics (2nd Edition ed.). New York (NY): Springer. pp. 305–352. ISBN 978-0-306-44790-7.
S. Weinberg (2003). The Discovery of Subatomic Particles. Cambridge University Press. ISBN 052182351X.
R. Wilson (1997). Astronomy Through the Ages: The Story of the Human Attempt to Understand the Universe. CRC Press. pp. 138. ISBN 0748407480.

External links

The Particle Data Group who compile authoritative information on particle properties.
Leptons a small summary of leptons from the Georgia State University.

Particles in physics

Elementary particles	Fermions: Quarks: u · d · c · s · t · b • Leptons: e⁻ · e⁺ · μ⁻ · μ⁺ · τ⁻ · τ⁺ · νe · νμ · ντ · νe · νμ · ντ Bosons: Gauge bosons: γ · g · W^± · Z Other: Ghosts

Composite particles	Hadrons: Baryons/Hyperons/Nucleons: p · n · Δ · Λ · Σ · Ξ · Ω • Mesons/Quarkonia: π · K · ρ · J/ψ · ϒ · B · D · η · η′ · φ Other: Atomic nuclei • Atoms • Exotic atoms: Positronium · Muonium · Onia • Molecules

Hypothetical elementary particles	Superpartners: Axino · Chargino · Gaugino · Gluino · Gravitino · Higgsino · Neutralino · Sfermion Other: A⁰ · Dilaton · G · H⁰ · J · Tachyon · X · Y · W' · Z' · Sterile neutrino

Hypothetical composite particles	Exotic hadrons: Exotic baryons: Dibaryon · Pentaquark • Exotic mesons: Glueball · Tetraquark Other: Mesonic molecule · Pomeron

Quasiparticles	Davydov soliton · Exciton · Magnon · Phonon · Plasmon · Polariton · Polaron · Roton

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