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). Mathematically, the lepton number is defined by where is the number of leptons and is the number of antileptons. Lepton number was introduced in 1953 to explain the absence of reactions such as in the Cowan–Reines neutrino experiment, which instead observed 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 the electron number, for the electron and the electron neutrino; the muon number, for the muon and the muon neutrino; and the tau number, for the tauon and the tau neutrino. Prominent examples of lepton flavor conservation are the muon decays and 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: One neutrino carries through the lepton number of the decaying heavy lepton, (a tauon in this example, whose faint residue is a tau neutrino) and an antineutrino that cancels the lepton number of the newly created, lighter lepton that replaced the original. (In this example, an muon antineutrino with that cancels the muon's .) Violations of the lepton number conservation laws Lepton flavor is only approximately conserved, and is notably not conserved in neutrino oscillation. 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 hypothetical decay 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 and plans to