A lepton is an elementary, half-integer
spin particle that does not undergo
strong interactions, but is subject to
the Pauli exclusion principle. The best
known of all leptons is the electron,
which is directly tied to all chemical
properties. Two main classes of leptons
exist: charged leptons, and neutral
leptons. Charged leptons can combine
with other particles to form various
composite particles such as atoms and
positronium, while neutrinos rarely
interact with anything, and are
consequently rarely observed.
There are six types of leptons, known as
flavours, forming three generations. The
first generation is the electronic
leptons, comprising the electron and
electron neutrino (ν
e); the second is the muonic leptons,
comprising the muon and muon neutrino (ν
μ); and the third is the tauonic
leptons, comprising the tau and the tau
neutrino (ν
τ). Electrons have the least mass of all
the charged leptons. The heavier muons
and taus will rapidly change into
electrons through a process of particle
decay: the transformation from a higher
mass state to a lower mass state. Thus
electrons are stable and the most common
charged lepton in the universe, whereas
muons and taus can only be produced in
high energy collisions.
Leptons have various intrinsic
properties, including electric charge,
spin, and mass. Unlike quarks however,
leptons are not subject to the strong
interaction, but they are subject to the
other three fundamental interactions:
gravitation, electromagnetism, and the
weak interaction. For every lepton
flavor there is a corresponding type of
antiparticle, known as antilepton, that
differs from the lepton only in that
some of its properties have equal
magnitude but opposite sign. However,
according to certain theories, neutrinos
may be their own antiparticle, but it is
not currently known whether this is the
case or not.
The first charged lepton, the electron,
was theorized in the mid-19th century by
several scientists and was discovered in
1897 by J. J. Thomson. The next lepton
to be observed was the muon, discovered
by Carl D. Anderson in 1936, which was
classified as a meson at the time. After
investigation, it was realized that the
muon did not have the expected
properties of a meson, but rather
behaved like an electron, only with
higher mass. It took until 1947 for the
concept of "leptons" as a family of
particle to be proposed. The first
neutrino, the electron neutrino, was
proposed by Wolfgang Pauli in 1930 to
explain certain characteristics of beta
decay. It was first observed in the
Cowan–Reines neutrino experiment
conducted by Clyde Cowan and Frederick
Reines in 1956. The muon neutrino was
discovered in 1962 by Leon M. Lederman,
Melvin Schwartz and Jack Steinberger,
and the tau discovered between 1974 and
1977 by Martin Lewis Perl and his
colleagues from the Stanford Linear
Accelerator Center and Lawrence Berkeley
National Laboratory. The tau neutrino
remained elusive until July 2000, when
the DONUT collaboration from Fermilab
announced its discovery.
Leptons are an important part of the
Standard Model. Electrons are one of the
components of atoms, alongside protons
and neutrons. Exotic atoms with muons
and taus instead of electrons can also
be synthesized, as well as
lepton–antilepton particles such as
positronium.
Etymology 
The name lepton comes from the Greek
λεπτός leptós, "fine, small, thin"; the
earliest attested form of the word is
the Mycenaean Greek 𐀩𐀡𐀵, re-po-to,
written in Linear B syllabic script.
Lepton was first used by physicist Léon
Rosenfeld in 1948:
Following a suggestion of Prof. C.
Møller, I adopt — as a pendant to
"nucleon" — the denomination "lepton" to
denote a particle of small mass.
The etymology incorrectly implies that
all the leptons are of small mass. When
Rosenfeld named them, the only known
leptons were electrons and muons, which
are in fact of small mass — the mass of
an electron and the mass of a muon are
fractions of the mass of the "heavy"
proton. However, the mass of the tau is
nearly twice that of the proton, and
about 3,500 times that of the electron.
History 
The first lepton identified was the
electron, discovered by J.J. Thomson and
his team of British physicists in 1897.
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. 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.
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. 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
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.
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. 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
latest particle of the Standard Model to
have been directly observed, apart from
the Higgs boson, which probably has been
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
7002100800000000000♠100.8 GeV/c2, while
its associated neutrino would have a
mass of at least
7001450000000000000♠45.0 GeV/c2.
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 exactly 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 otherwise they
are called left-handed. When a particle
is mass-less, 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 that agrees with
helicity for 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
asymmetrically. Only left-handed
fermions participate in the weak
interaction, while there are no
right-handed neutrinos. This is an
example of parity violation. In the
literature left-handed fields are often
denoted by a capital L subscript and
right-handed fields are denoted by a
capital R subscript.
= 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
and how strongly the particle reacts to
an external electric or magnetic field.
Each generation contains one lepton with
Q = −e and one lepton with zero electric
charge. The lepton with electric charge
is commonly simply referred to as a
'charged lepton' while the 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 ν
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,
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,
where m is the mass of the lepton and g
is the so-called g-factor for the
lepton. First order approximation
quantum mechanics 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.
= Weak Interaction =
In the Standard Model the left-handed
charged lepton and the left-handed
neutrino are arranged in doublet (ν
eL, e−L) that transforms in the spinor
representation 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 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 mediating
the weak interaction, and one massless
vector boson, the photon, 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 + YW/2
To recover the observed electric charges
for all particles the left-handed weak
isospin doublet (ν
eL, 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 left.
= Mass =
In the Standard Model each lepton starts
out with no intrinsic mass. The charged
leptons 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.
However, it is known from experiments –
most prominently from observed neutrino
oscillations – that neutrinos do in fact
have some very small mass, probably less
than 7000200000000000000♠2 eV/c2. 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.
= Leptonic numbers =
The members of each generation's weak
isospin doublet are assigned leptonic
numbers that are conserved under the
Standard Model. 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:
e− + e+ → γ + γ,
τ− + τ+ → Z0 + Z0,
but not these:
γ → e− + μ+,
W− → e− + ν
τ,
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, 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. This
property is called lepton universality
and has been tested in measurements of
the tau and muon lifetimes and of Z
boson partial decay widths, particularly
at the Stanford Linear Collider and
Large Electron-Positron Collider
experiments.
The decay rate of muons through the
process μ− → e− + ν
e + ν
μ is approximately given by an
expression of the form
where K1 is some constant, and GF 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
where K2 is some constant. Muon–Tauon
universality implies that K1 = K2. On
the other hand, electron–muon
universality implies
This explains why the branching ratios
for the electronic mode and muonic mode
of tau decay are equal.
Universality also accounts for the ratio
of muon and tau lifetimes. The lifetime
of a lepton is related to the decay rate
by
where B(x → y) and Γ(x → y) denotes the
branching ratios and the resonance width
of the process x → y.
The ratio of tau and muon lifetime is
thus given by
Using the values of the 2008 Review of
Particle Physics for the branching
ratios of muons and tau yields a
lifetime ratio of
~6993129000000000000♠1.29×10−7,
comparable to the measured lifetime
ratio of ~6993131999999999999♠1.32×10−7.
The difference is due to K1 and K2 not
actually being constants; they depend on
the mass of leptons.
Table of leptons 
See also 
Koide formula
List of particles
Preons – hypothetical particles which
were once postulated to be subcomponents
of quarks and leptons
Notes 
References 
C. Amsler et al.; Amsler; Doser;
Antonelli; Asner; Babu; Baer; Band;
Barnett; Bergren; Beringer; Bernardi;
Bertl; Bichsel; Biebel; Bloch; Blucher;
Blusk; Cahn; Carena; Caso; Ceccucci;
Chakraborty; Chen; Chivukula; Cowan;
Dahl; d'Ambrosio; Damour et al.. "Review
of Particle Physics". Physics Letters B
667: 1. Bibcode:2008PhLB..667....1P.
doi:10.1016/j.physletb.2008.07.018. 
I.V. Anicin. "The Neutrino – Its Past,
Present and Future". SFIN year XV,
Series A: Conferences, No. A2 3–59:
3172. arXiv:physics/0503172.
Bibcode:2005physics...3172A. 
Y.Fukuda; Hayakawa, T.; Ichihara, E.;
Inoue, K.; Ishihara, K.; Ishino, H.;
Itow, Y.; Kajita, T. et al.. "Evidence
for Oscillation of Atmospheric
Neutrinos". Physical Review Letters 81:
1562–1567. arXiv:hep-ex/9807003.
Bibcode:1998PhRvL..81.1562F.
doi:10.1103/PhysRevLett.81.1562.  CS1
maint: Explicit use of et al.
K. Kodama; Ushida, N.; Andreopoulos, C.;
Saoulidou, N.; Tzanakos, G.; Yager, P.;
Baller, B.; Boehnlein, D.; Freeman, W.;
Lundberg, B.; Morfin, J.; Rameika, R.;
Yun, J.C.; Song, J.S.; Yoon, C.S.;
Chung, S.H.; Berghaus, P.; Kubantsev,
M.; Reay, N.W.; Sidwell, R.; Stanton,
N.; Yoshida, S.; Aoki, S.; Hara, T.;
Rhee, J.T.; Ciampa, D.; Erickson, C.;
Graham, M.; Heller, K. et al..
"Observation of tau neutrino
interactions". Physics Letters B 504:
218. arXiv:hep-ex/0012035.
Bibcode:2001PhLB..504..218D.
doi:10.1016/S0370-2693(01)00307-0. 
B.R. Martin, G. Shaw. "Chapter 2 –
Leptons, quarks and hadrons". Particle
Physics. John Wiley & Sons. pp. 23–47.
ISBN 0-471-92358-3. 
S.H. Neddermeyer, C.D. Anderson;
Anderson. "Note on the Nature of
Cosmic-Ray Particles". Physical Review
51: 884–886.
Bibcode:1937PhRv...51..884N.
doi:10.1103/PhysRev.51.884. 
J. Peltoniemi, J. Sarkamo. "Laboratory
measurements and limits for neutrino
properties". The Ultimate Neutrino Page.
Retrieved 2008-11-07. 
M.L. Perl; Abrams, G.; Boyarski, A.;
Breidenbach, M.; Briggs, D.; Bulos, F.;
Chinowsky, W.; Dakin, J. et al..
"Evidence for Anomalous Lepton
Production in e+–e− Annihilation".
Physical Review Letters 35: 1489–1492.
Bibcode:1975PhRvL..35.1489P.
doi:10.1103/PhysRevLett.35.1489.  CS1
maint: Explicit use of et al.
M.E. Peskin, D.V. Schroeder.
Introduction to Quantum Field Theory.
Westview Press. ISBN 0-201-50397-2. 
K. Riesselmann. "Logbook: Neutrino
Invention". Symmetry Magazine 4. 
L. Rosenfeld. Nuclear Forces.
Interscience Publishers. p. xvii. 
R. Shankar. "Chapter 2 – Rotational
Invariance and Angular Momentum".
Principles of Quantum Mechanics.
Springer. pp. 305–352. ISBN
978-0-306-44790-7. 
S. Weinberg. The Discovery of Subatomic
Particles. Cambridge University Press.
ISBN 0-521-82351-X. 
R. Wilson. Astronomy Through the Ages:
The Story of the Human Attempt to
Understand the Universe. CRC Press. p.
138. ISBN 0-7484-0748-0. 
External links 
Particle Data Group homepage. The PDG
compiles authoritative information on
particle properties.
Leptons, a summary of leptons from
Hyperphysics.
