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particle physics Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
, lepton number (historically also called lepton charge) is a conserved
quantum number In quantum physics and chemistry, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can ...
representing the difference between the number of
lepton In particle physics, a lepton is an elementary particle of half-integer spin (spin ) that does not undergo strong interactions. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neutr ...
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 describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can ...
, so its sum is preserved in interactions (as opposed to multiplicative
quantum number In quantum physics and chemistry, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can ...
s such as parity, where the product is preserved instead). Mathematically, the lepton number ~ L ~ is defined by :~ L = n_\ell - n_ ~, where *~ n_\ell \quad is the number of
lepton In particle physics, a lepton is an elementary particle of half-integer spin (spin ) that does not undergo strong interactions. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neutr ...
s and *~ n_ \quad 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, which instead observed : This process, inverse beta decay, conserves lepton number, as the incoming antineutrino has lepton number −1, while the outgoing
positron The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. It has an electric charge of +1 '' e'', a spin of 1/2 (the same as the electron), and the same mass as an electron. When a positron collide ...
(antielectron) also has lepton number −1.


Lepton flavor conservation

In addition to lepton number, lepton family numbers are defined as : ~ L_\mathrm ~~ the electron number, for the
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...
and the electron neutrino; : ~ L_\mathrm ~~ 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 , but with a much greater mass. It is classified as a lepton. As w ...
and the muon neutrino; and : ~ L_\mathrm ~~ the tau number, for the
tauon The tau (), also called the tau lepton, tau particle, tauon or tau electron, 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 l ...
and the tau neutrino. Prominent examples of lepton flavor conservation are the muon decays : and : In these decay reactions, the creation of an
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...
is accompanied by the creation of an electron antineutrino, 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 , but with a much greater mass. It is classified as a lepton. As w ...
results in the creation of a muon neutrino, while a decaying positive muon results in the creation of a muon antineutrino. Finally, the
weak decay In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interacti ...
of a lepton into a lower-mass lepton always results in the production of a
neutrino A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...
- antineutrino pair: : One neutrino carries through the lepton number of the decaying heavy lepton, (a
tauon The tau (), also called the tau lepton, tau particle, tauon or tau electron, 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 l ...
in this example, whose faint residue is a tau neutrino) and an antineutrino that cancels the lepton number of the newly created, lighter lepton that replaced the original. (In this example, an muon antineutrino with ~ L_\mathrm = -1~ that cancels the muon's ~ L_\mathrm = +1~.)


Violations of the lepton number conservation laws

Lepton flavor is only approximately conserved, and is notably not conserved in neutrino oscillation. However, total lepton number is still conserved in the Standard Model. Numerous searches for physics beyond the Standard Model 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 Meg is a feminine given name, often a short form of Megatron, Megan, Megumi (Japanese), etc. It may refer to: People * Meg (singer), a Japanese singer *Meg Cabot (born 1967), American author of romantic and paranormal fiction * Meg Burton Cahill ...
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 In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories ...
, 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 models. If neutrinos turn out to be
Majorana fermions A Majorana fermion (, uploaded 19 April 2013, retrieved 5 October 2014; and also based on the pronunciation of physicist's name.), also referred to as a Majorana particle, is a fermion that is its own antiparticle. They were hypothesised by E ...
, neither individual lepton numbers, nor the total lepton number : ~ L \equiv L_\mathrm + L_\mathrm + L_\mathrm ~, 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 clos ...
, 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 and the sign of
strangeness In particle physics, strangeness ("''S''") is a property of particles, expressed as a quantum number, for describing decay of particles in strong and electromagnetic interactions which occur in a short period of time. The strangeness of a parti ...
quantum number ( for quarks), both of which conventionally have the otherwise arbitrary sign of the
quantum number In quantum physics and chemistry, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can ...
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 ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...
,
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 , but with a much greater mass. It is classified as a lepton. As w ...
,
tauon The tau (), also called the tau lepton, tau particle, tauon or tau electron, 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 l ...
, and any
neutrino A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...
counts as ~ \bar = -1 ~; the lepton number of the
positron The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. It has an electric charge of +1 '' e'', a spin of 1/2 (the same as the electron), and the same mass as an electron. When a positron collide ...
, antimuon, antitauon, and any antineutrino counts as ~ \bar = +1 ~. When this reversed-sign convention is observed, the baryon number is left unchanged, but the difference is replaced with a sum: whose number value remains unchanged, since : and :


See also

* Baryon number


Footnotes


References

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