Wing Sheung Chan

8 The Standard Model and lepton flavour violation Table 1.2.: Properties of leptons [6] . Limit on the electron mean life is measured at 90% confidence level. Limits on the neutrino rest masses are measured at 95% confidence level and are on the mass expectation values of the weak eigenstates. Generation Lepton Rest mass [MeV] Mean life [s] Electric charge [ e ] 1 e − 0 . 511 ± 3 . 1 × 10 − 9 > 2 . 1 × 10 36 − 1 ν e < 2 . 0 × 10 − 6 0 2 µ − 105 ± 2 . 4 × 10 − 6 2 . 20 × 10 − 6 ± 2 . 2 × 10 − 12 − 1 ν µ < 0 . 19 0 3 τ − 1776 . 9 ± 0 . 12 (290 . 3 ± 0 . 5) × 10 − 15 − 1 ν τ < 18 . 2 0 fermions in the SM. All of them are spin- 1 2 . They can be further classified into leptons and quarks. Leptons are fermions that only participate in electroweak interactions but not in strong interactions. There are three generations of leptons, each consist of a charged lepton ( ` ) and a neutrino ( ν ). Charged leptons carry electric charges. The electron ( e − ), the first discovered elementary particle, is the first-generation charged lepton. It is also the only stable charged lepton. The muon ( µ − ) and tau ( τ − ) are the second- and third-generation charged leptons respectively. In the SM, the charged leptons are distinguished only by their rest masses. Charged leptons of higher generations have higher rest masses. Associated with each charged lepton, there is a neutrino of the same flavour. The neutrinos are named accordingly as the electron neutrino ( ν e ), muon neutrino ( ν µ ) and tau neutrino ( ν τ ). Neutrinos are special in the SM because they are the only fermions that do not carry charges (hence the name) and exist with only one chirality: there are only left-handed neutrinos, but no right-handed ones. Neutrinos only participate in weak (and gravitational) interactions. A summary of the properties of leptons [6] is given in Table 1.2. The charged leptons, especially the τ lepton, are going to play an important role in this thesis. Quarks ( q ) are another class of elementary fermions in the SM. Similar to leptons, there are three generations of quarks in the SM. Each generation consists of an up-type quark that carries an electric charge of 2 3 e and a down-type quark that carries an electric charge of − 1 3 e . The three up-type quarks are named up ( u ), charm ( c ) and top ( t ), while the three down-type quarks are named down ( d ), strange ( s ) and bottom ( b ). A summary of the properties of quarks [6] is given in Table 1.3. Quarks differ from leptons in that they carry colour charges. As a result, they do not only participate in electroweak interactions, but also in strong interactions. Quarks can be bound together by strong interactions to form compound particles known as hadrons.