In
particle physics
Particle physics or high-energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The field also studies combinations of elementary particles up to the s ...
, lepton number (historically also called lepton charge)
[
is a conserved ]quantum number
In quantum physics and chemistry, quantum numbers are quantities that characterize the possible states of the system.
To fully specify the state of the electron in a hydrogen atom, four quantum numbers are needed. The traditional set of quantu ...
representing the difference between the number of lepton
In particle physics, a lepton is an elementary particle of half-integer spin (Spin (physics), spin ) that does not undergo strong interactions. Two main classes of leptons exist: electric charge, charged leptons (also known as the electron-li ...
s and the number of antileptons in an elementary particle reaction.[
Lepton number is an additive ]quantum number
In quantum physics and chemistry, quantum numbers are quantities that characterize the possible states of the system.
To fully specify the state of the electron in a hydrogen atom, four quantum numbers are needed. The traditional set of quantu ...
, so its sum is preserved in interactions (as opposed to multiplicative quantum number
In quantum physics and chemistry, quantum numbers are quantities that characterize the possible states of the system.
To fully specify the state of the electron in a hydrogen atom, four quantum numbers are needed. The traditional set of quantu ...
s such as parity, where the product is preserved instead). The lepton number is defined by
where
* is the number of lepton
In particle physics, a lepton is an elementary particle of half-integer spin (Spin (physics), spin ) that does not undergo strong interactions. Two main classes of leptons exist: electric charge, charged leptons (also known as the electron-li ...
s and
* is the number of antileptons.
Lepton number was introduced in 1953 to explain the absence of reactions such as
:
in the Cowan–Reines neutrino experiment
The Cowan–Reines neutrino experiment was conducted by physicists Clyde Cowan and Frederick Reines in 1956. The experiment confirmed the existence of neutrinos. Neutrinos, subatomic particles with no electric charge and very small mass, had been ...
, which instead observed
: .[
This process, ]inverse beta decay
In nuclear and particle physics, inverse beta decay, commonly abbreviated to IBD, is a nuclear reaction involving an electron antineutrino scattering off a proton, creating a positron and a neutron. This process is commonly used in the detect ...
, conserves lepton number, as the incoming antineutrino
A neutrino ( ; denoted by the Greek letter ) is an elementary particle that interacts via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is so small ('' -ino'') that it ...
has lepton number −1, while the outgoing positron
The positron or antielectron is the particle with an electric charge of +1''elementary charge, e'', a Spin (physics), spin of 1/2 (the same as the electron), and the same Electron rest mass, mass as an electron. It is the antiparticle (antimatt ...
(antielectron) also has lepton number −1.
Lepton flavor conservation
In addition to lepton number, lepton family numbers are defined as[
: the electron number, for the ]electron
The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
and the electron neutrino
The electron neutrino () is an elementary particle which has zero electric charge and a spin of . Together with the electron, it forms the first generation of leptons, hence the name ''electron neutrino''. It was first hypothesized by Wolfga ...
;
: the muon number, for the muon
A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of ''ħ'', but with a much greater mass. It is classified as a ...
and the muon neutrino
The muon neutrino is an elementary particle which has the symbol and zero electric charge. Together with the muon it forms the second generation of leptons, hence the name muon neutrino. It was discovered in 1962 by Leon Lederman, Melvin Schwa ...
; and
: the tau number, for the tauon
The tau (), also called the tau lepton, tau particle or tauon, is an elementary particle similar to the electron, with negative electric charge and a spin of . Like the electron, the muon, and the three neutrinos, the tau is a lepton, and like ...
and the tau neutrino
The tau neutrino or tauon neutrino is an elementary particle which has the symbol and zero electric charge. Together with the tau (particle), tau (), it forms the third generation (physics), generation of leptons, hence the name tau neutrino. It ...
.
Prominent examples of lepton flavor conservation are the muon decays
:
and
: .
In these decay reactions, the creation of an electron
The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
is accompanied by the creation of an electron antineutrino
The electron neutrino () is an elementary particle which has zero electric charge and a spin of . Together with the electron, it forms the first generation of leptons, hence the name ''electron neutrino''. It was first hypothesized by Wolfgang ...
, and the creation of a positron is accompanied by the creation of an electron neutrino. Likewise, a decaying negative muon
A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of ''ħ'', but with a much greater mass. It is classified as a ...
results in the creation of a muon neutrino
The muon neutrino is an elementary particle which has the symbol and zero electric charge. Together with the muon it forms the second generation of leptons, hence the name muon neutrino. It was discovered in 1962 by Leon Lederman, Melvin Schwa ...
, while a decaying positive muon results in the creation of a muon antineutrino.[
Finally, the weak decay of a lepton into a lower-mass lepton always results in the production of a ]neutrino
A neutrino ( ; denoted by the Greek letter ) is an elementary particle that interacts via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is so small ('' -ino'') that i ...
-antineutrino
A neutrino ( ; denoted by the Greek letter ) is an elementary particle that interacts via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is so small ('' -ino'') that it ...
pair:
: .
One neutrino carries through the lepton number of the decaying heavy lepton, (a tauon
The tau (), also called the tau lepton, tau particle or tauon, is an elementary particle similar to the electron, with negative electric charge and a spin of . Like the electron, the muon, and the three neutrinos, the tau is a lepton, and like ...
in this example, whose faint residue is a tau neutrino
The tau neutrino or tauon neutrino is an elementary particle which has the symbol and zero electric charge. Together with the tau (particle), tau (), it forms the third generation (physics), generation of leptons, hence the name tau neutrino. It ...
) and an antineutrino that cancels the lepton number of the newly created, lighter lepton that replaced the original. (In this example, a muon antineutrino with that cancels the muon's .
Violations of the lepton number conservation laws
Lepton flavor is only approximately conserved, and is notably not conserved in neutrino oscillation
Neutrino oscillation is a quantum mechanics, quantum mechanical phenomenon in which a neutrino created with a specific lepton lepton number, family number ("lepton flavor": electron, muon, or tau lepton, tau) can later be Quantum measurement, mea ...
.[
However, both the total lepton number and lepton flavor are still conserved in the Standard Model.
Numerous searches for ]physics beyond the Standard Model
Physics beyond the Standard Model (BSM) refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the inability to explain the fundamental parameters of the standard model, the strong CP problem, neut ...
incorporate searches for lepton number or lepton flavor violation, such as the hypothetical decay[
: .
Experiments such as MEGA and SINDRUM have searched for lepton number violation in muon decays to electrons; MEG set the current branching limit of order and plans to lower to limit to after 2016.][
Some theories beyond the Standard Model, such as ]supersymmetry
Supersymmetry is a Theory, theoretical framework in physics that suggests the existence of a symmetry between Particle physics, particles with integer Spin (physics), spin (''bosons'') and particles with half-integer spin (''fermions''). It propo ...
, predict branching ratios of order to .[ The Mu2e experiment, in construction as of 2017, has a planned sensitivity of order .][
Because the lepton number conservation law in fact is violated by chiral anomalies, there are problems applying this symmetry universally over all energy scales. However, the quantum number is commonly conserved in ]Grand Unified Theory
A Grand Unified Theory (GUT) is any Mathematical model, model in particle physics that merges the electromagnetism, electromagnetic, weak interaction, weak, and strong interaction, strong fundamental interaction, forces (the three gauge theory, ...
models.
If neutrinos turn out to be Majorana fermions, neither individual lepton numbers, nor the total lepton number
nor
:
would be conserved, e.g. in neutrinoless double beta decay
In nuclear physics, double beta decay is a type of radioactive decay in which two neutrons are simultaneously transformed into two protons, or vice versa, inside an atomic nucleus. As in single beta decay, this process allows the atom to move cl ...
, where two neutrinos colliding head-on might actually annihilate, similar to the (never observed) collision of a neutrino and antineutrino.
Reversed signs convention
Some authors prefer to use lepton numbers that match the signs of the charges of the leptons involved, following the convention in use for the sign of weak isospin
In particle physics, weak isospin is a quantum number relating to the electrically charged part of the weak interaction: Particles with half-integer weak isospin can interact with the bosons; particles with zero weak isospin do not.
Weak isospin ...
and the sign of strangeness
In particle physics, strangeness (symbol ''S'') is a property of particles, expressed as a quantum number, for describing decay of particles in strong and electromagnetic interactions that occur in a short period of time. The strangeness of a ...
quantum number ( for quarks), both of which conventionally have the otherwise arbitrary sign of the quantum number
In quantum physics and chemistry, quantum numbers are quantities that characterize the possible states of the system.
To fully specify the state of the electron in a hydrogen atom, four quantum numbers are needed. The traditional set of quantu ...
match the sign of the particles' electric charges.
When following the electric-charge-sign convention, the lepton number (shown with an over-bar here, to reduce confusion) of an electron
The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
, muon
A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of ''ħ'', but with a much greater mass. It is classified as a ...
, tauon
The tau (), also called the tau lepton, tau particle or tauon, is an elementary particle similar to the electron, with negative electric charge and a spin of . Like the electron, the muon, and the three neutrinos, the tau is a lepton, and like ...
, and any neutrino
A neutrino ( ; denoted by the Greek letter ) is an elementary particle that interacts via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is so small ('' -ino'') that i ...
counts as the lepton number of the positron
The positron or antielectron is the particle with an electric charge of +1''elementary charge, e'', a Spin (physics), spin of 1/2 (the same as the electron), and the same Electron rest mass, mass as an electron. It is the antiparticle (antimatt ...
, antimuon, antitauon, and any antineutrino
A neutrino ( ; denoted by the Greek letter ) is an elementary particle that interacts via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is so small ('' -ino'') that it ...
counts as When this reversed-sign convention is observed, the baryon number
In particle physics, the baryon number (B) is an additive quantum number of a system. It is defined as
B = \frac(n_\text - n_),
where is the number of quarks, and is the number of antiquarks. Baryons (three quarks) have B = +1, mesons (one q ...
is left unchanged, but the difference is replaced with a sum: , whose number value remains unchanged, since
:
and
:
See also
* Baryon number
In particle physics, the baryon number (B) is an additive quantum number of a system. It is defined as
B = \frac(n_\text - n_),
where is the number of quarks, and is the number of antiquarks. Baryons (three quarks) have B = +1, mesons (one q ...
References
{{Authority control
Conservation laws
Particle physics
Leptons
Flavour (particle physics)
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