In high energy physics, the lepton number is the number of leptons minus the number of antileptons. CPT-symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity and time simultaneously. ... In the standard model of particle physics the Cabibbo Kobayashi Maskawa matrix (CKM matrix, sometimes earlier called KM matrix) is a unitary matrix which contains information on the strength of flavour changing weak decays. ... CP is the product of two symmetries: C for charge conjugation, which transforms a particle into its antiparticle, and P for parity, which creates the mirror image of a physical system. ... A phenomenon is said to be chiral if it is not identical to its mirror image (see Chirality (mathematics)). The spin of a particle may be used to define a handedness for that particle. ... Particle physics is a branch of physics that studies the elementary constituents of matter and radiation, and the interactions between them. ... In physics, a particle is a lepton if it has a spin of 1/2 and does not experience the strong nuclear force. ...

In equation form,

so all leptons have assigned a value of +1, antileptons −1, and non-leptonic particles 0. Lepton number (sometimes also called lepton charge) is an additive quantum number, which means that its sum is preserved in interactions (as opposed to multiplicative quantum numbers such as parity, where the product is preserved instead). A quantum number describes the energies of electrons in atoms. ... A quantum number describes the energies of electrons in atoms. ...

Beside the leptonic number, leptonic family numbers are also defined:

• the electronic number L_e for the electron and the electronic neutrino;
• the muonic number L_μ for the muon and the muonic neutrino;
• the tauonic number L_τ for the tauon and the tauonic neutrino;

with the same assigning scheme as the leptonic number: +1 for particles of the corresponding family, −1 for the antiparticles, and 0 for leptons of other families or non-leptonic particles.

Conservation laws for leptonic numbers

Many models, including the Standard Model of particle physics rely on lepton number conservation: the lepton number stays the same through an interaction. For example, in the beta decay: The Standard Model of Fundamental Particles and Interactions The Standard Model of particle physics is a theory which describes the strong, weak, and electromagnetic fundamental forces, as well as the fundamental particles that make up all matter. ... In nuclear physics, beta decay (sometimes called neutron decay) is a type of radioactive decay in which a beta particle (an electron or a positron) is emitted. ...

The lepton number before the reaction is 0 (the neutron, n, is a baryon and therefore there are no leptons before), while the lepton number after the reaction is 0 for the proton +1 for the electron (a lepton) −1 for the antineutrino (an antilepton). Thus the lepton number is zero after the decay, and so is conserved.

The lepton family numbers arise from the fact that lepton number is usually conserved in each leptonic family. For example, almost 100% of the times the muon decays as:

thus preserving the electronic and muonic numbers. This means that a lepton family number conservation law exist for each one of L_e, L_μ and L_τ.

Violations of the lepton number conservation laws

In the Standard Model, leptonic family number (LF) would be preserved if neutrinos were massless. Since neutrinos do have a tiny nonzero mass, neutrino oscillation has been observed, and conservation laws for LF are therefore only approximate. This means the conservation laws are violated, although because of the smallness of the neutrino mass they still hold to a very large degree for interactions containing charged leptons. However, the lepton number conservation law must still hold (under the Standard Model). Thus, it is possible to see rare muon decays such as: The Standard Model of Fundamental Particles and Interactions The Standard Model of particle physics is a theory which describes the strong, weak, and electromagnetic fundamental forces, as well as the fundamental particles that make up all matter. ... Neutrino oscillation is a quantum mechanical phenomenon whereby a neutrino created with a specific lepton flavor (electron, muon, or tau) can later be measured to have a different flavor. ...

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 B−L is much more likely to work and is seen in different models such as the Pati-Salam model. A chiral anomaly is the anomalous nonconservation of a chiral current. ... In high energy physics, B−L (pronounced bee minus ell) is the baryon number minus the lepton number. ...

See also

• leptons
• baryon number
• B−L

In physics, a particle is a lepton if it has a spin of 1/2 and does not experience the strong nuclear force. ... In particle physics, the baryon number is an approximate conserved quantum number. ... In high energy physics, B−L (pronounced bee minus ell) is the baryon number minus the lepton number. ...

References

• Griffiths, David J. (1987). Introduction to Elementary Particles. Wiley, John & Sons, Inc. ISBN 0-471-60386-4.
• Tipler, Paul; Llewellyn, Ralph (2002). Modern Physics (4th ed.). W. H. Freeman. ISBN 0-7167-4345-0.