Lepton number

In particle physics, lepton number (historically also called lepton charge)

is a conserved quantum number representing the difference between the number of leptons and the number of antileptons in an elementary particle reaction.

Lepton number is an additive quantum number, so its sum is preserved in interactions (as opposed to multiplicative quantum numbers such as parity, where the product is preserved instead). The lepton number

L

{\displaystyle L}

is defined by

L

=

n

ℓ

−

n

ℓ

¯

,

{\displaystyle L=n_{\ell }-n_{\overline {\ell }},}

where

n

ℓ

{\displaystyle n_{\ell }\quad }

is the number of leptons and

n

ℓ

¯

{\displaystyle n_{\overline {\ell }}\quad }

is the number of antileptons.

Lepton number was introduced in 1953 to explain the absence of reactions such as

ν + n → p + e−

in the Cowan–Reines neutrino experiment, which instead observed

ν + p → n + e+ .

This process, inverse beta decay, conserves lepton number, as the incoming antineutrino has lepton number −1, while the outgoing positron (antielectron) also has lepton number −1.

Lepton flavor conservation

In addition to lepton number, lepton family numbers are defined as

L

e

{\displaystyle L_{\mathrm {e} }}

the electron number, for the electron and the electron neutrino;

L

μ

{\displaystyle L_{\mathrm {\mu } }}

the muon number, for the muon and the muon neutrino; and

L

τ

{\displaystyle L_{\mathrm {\tau } }}

the tau number, for the tauon and the tau neutrino.

Prominent examples of lepton flavor conservation are the muon decays

μ− → e− + νe + νμ

and

μ+ → e+ + νe + νμ .

In these decay reactions, the creation of an electron 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 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 of a lepton into a lower-mass lepton always results in the production of a neutrino-antineutrino pair:

τ− → μ− + νμ + ντ .