Lepton number

In particle physics, lepton number (historically also called lepton charge)^[1] is a conserved quantum number representing the difference between the number of leptons and the number of antileptons in an elementary particle reaction.^[2] 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 ${\displaystyle L}$ is defined by $${\displaystyle L=n_{\ell }-n_{\overline {\ell }},}$$ where

• ${\displaystyle n_{\ell }\quad }$ is the number of leptons and
• ${\displaystyle n_{\overline {\ell }}\quad }$ 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⁺
.^[3]

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.