Lepton number

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

• L_e , the electron number, for the electron and the electron neutrino;
• L_μ , the muon number, for the muon and the muon neutrino; and
• L_τ , the tau number, for the tau and the tau neutrino.

Prominent examples of lepton flavor conservation are the muon decays ${\displaystyle \mu ^{-}\to e^{-}+{\overline {\nu }}_{e}+\nu _{\mu }}$ and ${\displaystyle \mu ^{+}\to e^{+}+\nu _{e}+{\overline {\nu }}_{\mu }}$. In these, 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.

Lepton flavor is only approximately conserved, and is notably not conserved in neutrino oscillation.[4] However, total lepton number is still conserved in the Standard Model.

Numerous searches for physics beyond the Standard Model incorporate searches for lepton number or lepton flavor violation, such as the decays ${\displaystyle \mu ^{-}\to e^{-}+\gamma }$.[5] Experiments such as MEGA and SINDRUM have searched for lepton number violation in muon decays to electrons; MEG set the current branching limit of order 10⁻¹³ and plans to lower to limit to 10⁻¹⁴ after 2016.[6] Some theories beyond the Standard Model, such as supersymmetry, predict branching ratios of order 10⁻¹² to 10⁻¹⁴.[5] The Mu2e experiment, in construction as of 2017, has a planned sensitivity of order 10⁻¹⁷.[7]

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 commonly conserved in Grand Unified Theory models.

If neutrinos turn out to be Majorana fermions, neither the lepton number nor B − L would be conserved, e.g. in neutrinoless double beta decay.

• Baryon number