leptonnumber

Lepton number is a conserved quantum number used in particle physics to categorize leptons. It is defined by assigning L = +1 to leptons (electrons, muons, tau leptons and their corresponding neutrinos) and L = -1 to their antiparticles; all other particles have L = 0. The total lepton number of a system is the sum of the lepton numbers of its constituents.

In the Standard Model, lepton number is an accidental global symmetry: all perturbative interactions conserve the total lepton number. There are also lepton-family numbers, L_e, L_μ, and L_τ, associated with electron-, muon-, and tau-flavor leptons. These family numbers are approximately conserved in many processes, but neutrino oscillations demonstrate that lepton flavor is not an exact symmetry, since neutrinos can change flavor as they propagate.

Lepton number need not be conserved in theories beyond the Standard Model. If neutrinos are Majorana particles, total lepton number is violated by two units, which would allow processes such as neutrinoless double beta decay. Non-perturbative electroweak effects, known as sphalerons, can also violate lepton and baryon numbers in the early universe, though they conserve B−L.

Experimentally, no unambiguous lepton-number-violating process has been observed. Searches for neutrinoless double beta decay place stringent limits on the effective Majorana neutrino mass. Neutrino oscillation experiments confirm flavor change but do not by themselves prove lepton number violation; the total lepton number remains a viable symmetry in the Dirac-neutrino picture.

In cosmology, lepton-number violation plays a role in leptogenesis, a class of mechanisms that generate a primordial lepton asymmetry that is partly converted into the observed baryon asymmetry of the universe through sphaleron processes.