# Lepton number

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 Flavour in particle physics Flavour quantum numbers: Isospin: I or I3 Charm: C Strangeness: S Topness: T Bottomness: B′ Related quantum numbers: Baryon number: B Lepton number: L Weak isospin: T or T3 Electric charge: Q X-charge: X Combinations: Hypercharge: Y Y = (B + S + C + B′ + T) Y = 2 (Q − I3) Weak hypercharge: YW YW = 2 (Q − T3) X + 2YW = 5 (B − L) Flavour mixing This box:

In particle physics, the lepton number is the number of leptons minus the number of antileptons.

In equation form,

$L = n_{\ell} - n_{\overline{\ell}}$

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).

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

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.

## Violations of the lepton number conservation laws

In the Standard Model, leptonic family numbers (LF numbers) would be preserved if neutrinos were massless. Since neutrino oscillations have been observed, neutrinos do have a tiny nonzero mass and conservation laws for LF numbers 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 (total) lepton number conservation law must still hold (under the Standard Model). Thus, it is possible to see rare muon decays such as:

 μ− → e− + ν e + ν μ L: 1 = 1 + 1 − 1 Le : 0 ≠ 1 + 1 + 0 Lμ : 1 ≠ 0 + 0 − 1

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 BL is much more likely to work and is seen in different models such as the Pati–Salam model.

## 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.