In particle physics, a lepton is an elementary
particle of half-integer spin (spin ​1⁄2)
that does not undergo strong interactions.
Two main classes of leptons exist: charged
leptons (also known as the electron-like leptons),
and neutral leptons (better known as neutrinos).
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. The best known of all leptons
is the electron.
There are six types of leptons, known as flavours,
grouped in three generations. The first-generation
leptons, also called electronic leptons, comprise
the electron (e−) and the electron neutrino
(νe); the second are the muonic leptons,
comprising the muon (μ−) and the muon neutrino
(νμ); and the third are the tauonic leptons,
comprising the tau (τ−) and the tau neutrino
(ντ). Electrons have the least mass of all
the charged leptons. The heavier muons and
taus will rapidly change into electrons and
neutrinos 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
(such as those involving cosmic rays and those
carried out in particle accelerators).
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, the weak interaction, and to
electromagnetism, of which the latter is proportional
to charge, and is thus zero for the electrically
neutral neutrinos.
For every lepton flavor there is a corresponding
type of antiparticle, known as an antilepton,
that differs from the lepton only in that
some of its properties have equal magnitude
but opposite sign. According to certain theories,
neutrinos may be their own antiparticle. It
is not currently known whether this is the
case.
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" (neuter nominative/accusative
singular form: λεπτόν leptón); 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" (from λεπτός,
small, thin, delicate) 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, whose masses are indeed small compared
to nucleons—the mass of an electron (0.511
MeV/c2) and the mass of a muon (with a value
of 105.7 MeV/c2) are fractions of the mass
of the "heavy" proton (938.3 MeV/c2). However,
the mass of the tau (discovered in the mid
1970s) (1777 MeV/c2) 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
(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. 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.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 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 100.8 GeV/c2, while
its associated neutrino would have a mass
of at least 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 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 Poincaré 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, the Standard Model's Weak interaction,
treats left-handed and right-handed fermions
are asymmetrically: 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: eL−) and right-handed
fields are denoted by a capital R subscript
(e.g. a positron eR+).
Right-handed neutrinos and left-handed anti-neutrinos
have no possible interaction with other particles
(see sterile neutrinos) 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 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 electro-weak
force, although with a 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 = −e (conventionally
the charge of a particle is expressed in units
of the elementary charge) 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 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 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 (νeL, 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 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,
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 + ½ YWTo 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
left.
=== 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. 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 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− + 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). 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 (SLC) and
Large Electron-Positron Collider (LEP) experiments.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)
Γ
(
μ
−
→
e
−
+
ν
e
¯
+
ν
μ
)
=
K
1
G
F
2
m
μ
5
,
{\displaystyle \Gamma \left(\mu ^{-}\rightarrow
e^{-}+{\bar {\nu _{e}}}+\nu _{\mu }\right)=K_{1}G_{F}^{2}m_{\mu
}^{5},}
where K1 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
form
Γ
(
τ
−
→
e
−
+
ν
e
¯
+
ν
τ
)
=
K
2
G
F
2
m
τ
5
,
{\displaystyle \Gamma \left(\tau ^{-}\rightarrow
e^{-}+{\bar {\nu _{e}}}+\nu _{\tau }\right)=K_{2}G_{F}^{2}m_{\tau
}^{5},}
where K2 is some constant. Muon–Tauon universality
implies that K1 = K2. On the other hand, electron–muon
universality implies
Γ
(
τ
−
→
e
−
+
ν
e
¯
+
ν
τ
)
=
Γ
(
τ
−
→
μ
−
+
ν
μ
¯
+
ν
τ
)
.
{\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 (17.85%) and muonic (17.36%)
mode of tau decay are equal (within error).Universality
also accounts for the ratio of muon and tau
lifetimes. The lifetime of a lepton (τℓ)
is related to the decay rate by
τ
ℓ
=
B
(
ℓ
−
→
e
−
+
ν
e
¯
+
ν
ℓ
)
Γ
(
ℓ
−
→
e
−
+
ν
e
¯
+
ν
ℓ
)
,
{\displaystyle \tau _{\ell }={\frac {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) and
Γ
{\displaystyle \Gamma }
(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
τ
τ
τ
μ
=
B
(
τ
−
→
e
−
+
ν
e
¯
+
ν
τ
)
B
(
μ
−
→
e
−
+
ν
e
¯
+
ν
μ
)
(
m
μ
m
τ
)
5
.
{\displaystyle {\frac {\tau _{\tau }}{\tau
_{\mu }}}={\frac {B\left(\tau ^{-}\rightarrow
e^{-}+{\bar {\nu _{e}}}+\nu _{\tau }\right)}{B\left(\mu
^{-}\rightarrow 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
and tau 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
K1 and K2 not actually being constants: They
depend on the mass of leptons.
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 statitical and systematic significance
is not yet high enough to claim an observation
of new physics.
== Table of leptons ==
== 
See also ==
Koide formula
List of particles
Preons—hypothetical particles which were
once postulated to be subcomponents of quarks
and leptons
