Lepton.html

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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 one of the Standard Model's family of elementary particles, alongside quarks and gauge bosons (also known as force carriers). Like quarks, leptons are fermions – spin-¹⁄₂ particles, but unlike quark do not experience the strong interaction. There are three generations of leptons. The first generation is the electronic leptons comprised of the electrons (e⁻), and electron neutrinos (νe); the second is the muonic leptons, comprised of muons (μ⁻), muon neutrinos (νμ); and the third is the tauonic leptons, comprised of tauons (τ⁻), tauon neutrinos (ντ). Each lepton has a corresponding antiparticle – these antiparticles are known as antileptons.

1 Etymology
2 Properties of leptons
3 Lepton universality
4 Table of leptons
5 See also
6 References
- 6.1 References
7 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.

Properties of leptons

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 doublet are assigned leptonic numbers that are conserved under the Standard Model.⁶ 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. However neutrino oscillations are an example of a violation of the conservation of the individual leptonic numbers. A much stronger conservation law is the total number of leptons (conserved even in the case of neutrino oscillations), but it is still violated by a tiny amount by the chiral anomaly.

Nonetheless, the leptonic numbers are conserved in most particle interactions, and 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,

μ⁻ + νμ → e⁻ + e⁺,

τ⁻ + τ⁺ → Z⁰ + Z⁰,

but not these:

γ → e⁻ + μ⁺,

W⁻ → e⁻ + ντ,

Z⁰ → μ⁻ + τ⁺.

Charge, hypercharge, and weak isospin

The charged leptons (electrons, muons, and tauons) all carry an electric charge (Q) of −1 e and have a weak isospin projection (T_z) of ¹⁄₂. The neutrinos on the other hand, do not carry any electric charge, and their weak isospin projection is of −¹⁄₂. All known processes conserve both electric charge and weak isospin.

The weak hypercharge(Y_W) of leptons is given by Y_W = 2 ( Q − T_Z ). This implies that the charged leptons have a weak hypercharge of 1, while the neutrinos have a weak hypercharge of 0.

Mass

According to the Standard Model, each weak isospin doublet comprises one charged massive particle (sometimes called "electron-like lepton") and one massless particle (neutrino). The masses of the charged leptons obey the Koide formula

$Q = \frac{m_e + m_{\mu} + m_{\tau}}{(\sqrt{m_e}+\sqrt{m_{\mu}}+\sqrt{m_{\tau}})^2},$

but at present this relationship cannot be explained. Also in reality, neutrinos are not massless as evidenced by neutrino oscillations. This is considered to be an indication of "physics beyond the standard model".

Spin, helicity, and parity

Left-handed and right-handed helicities

Since leptons are spin-¹⁄₂ particles, they have two possible helicities. When their spin point in the same direction as their momentum, they are said to be right-handed, otherwise they are said to be left-handed. However, all leptons are observed to be left-handed, while all antileptons are observed to be right-handed. This is an example of parity violation.

Lepton universality

The couplings of the leptons to gauge bosons are flavor-independent.⁶ 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.^{citation needed}

The decay rate (Γ) of muons through the process μ⁻ → e⁻ + νe + νμ is given by an expression of the form⁶

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

while the decay rate of tauons through the process τ⁻ → e⁻ + νe + ντ is given by an expression of the form⁶

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

Electron-muon universality implies that⁶

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

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 by⁶

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

The ratio of tauon and muon lifetime is thus given by⁶

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

Using the values of the 2008 Review of Particle Physics for the branching ratios of muons³ and tauon⁵ 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 / Antielectron²	e⁻/e⁺	−1	±¹⁄₂	+¹⁄₂	1	1	0	0	0.510998910(13)	Stable	Stable
Muon / Antimuon³	μ⁻/μ⁺	−1	±¹⁄₂	+¹⁄₂	1	0	1	0	105.6583668(38)	2.197019(21) × 10⁻⁶	e⁻ + νe + νμ
Tauon / Antitauon⁵	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 antineutrino⁷	νe/νe	0	±¹⁄₂	−¹⁄₂	0	1	0	0	< 0.0000022 ⁸	Unknown
Muon neutrino / Muon antineutrino⁷	νμ/νμ	0	±¹⁄₂	−¹⁄₂	0	0	1	0	< 0.17 ⁸	Unknown
Tauon neutrino / Tauon antineutrino⁷	ντ/ντ	0	±¹⁄₂	−¹⁄₂	0	0	0	1	< 15.5 ⁸	Unknown

Note that the neutrino masses are known to be non-zero because of neutrino oscillation, but their masses are sufficiently light that they have not been measured directly as of 2008. However, the differences of the mass squares between the neutrinos have been measured (indirectly based on the oscillation periods), which are estimated to be $\Delta m^2_{12} = 80\mbox{ meV}^2$ and $\Delta m^2_{23} \approx \Delta m^2_{13} = 2400\mbox{ meV}^2$ .^clarify^{citation needed} This leads to the following conclusions:

νμ and ντ are lighter than 2.2 eV (as νe is and the mass differences between the neutrinos are of order of millielectronvolts)^clarify
one (or more) of the neutrinos is heavier than 0.040 eV^clarify
two (or three) of the neutrinos are heavier than 0.008 eV^clarify

References

^ L. Rosenfeld (1948)
^ ^a ^b C.Amsler et al. (2008): Particle listings – e⁻
^ ^a ^b ^c C.Amsler et al. (2008): Particle listings – μ⁻
^ C.Amsler et al. (2008): Particle listings – p⁺
^ ^a ^b ^c ^d C.Amsler et al. (2008): Particle listings – τ⁻
^ ^a ^b ^c ^d ^e ^f ^g B.R Martin, G. Shaw (1992)
^ ^a ^b ^c C.Amsler et al. (2008): Particle listings – Neutrino properties
^ ^a ^b ^c J. Peltoniemi, J. Sarkamo(2005)

References

C.Amsler et al. (2008). "Review of Particle Physics". Physics Letters (Particle Data Group) B667 (1).
J. Peltoniemi, J. Sarkamo (2005). "Laboratory measurements and limits for neutrino properties". The Ultimate Neutrino Page. Retrieved on 2008-11-07.
B.R. Martin, G. Shaw (1992). "Chapter 2 – Leptons, quarks and hadrons", Particle physics. Chichester (England): John Wiley & Sons, 23–47. ISBN 0-471-92358-3.
L. Rosenfeld (1948). Nuclear Forces. New York (NY, USA): Interscience Publishers, xvii.

External links

Wikimedia Commons has media related to:

Leptons

Look up lepton in
Wiktionary, the free dictionary.

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

v • d • e 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

Lists	List of particles · List of quasiparticles · List of baryons · List of mesons · Timeline of particle discoveries

Lepton.html

Contents

Etymology

Properties of leptons

Leptonic numbers

Charge, hypercharge, and weak isospin

Mass

Spin, helicity, and parity

Lepton universality

Table of leptons

See also

References

References

External links