Wing Sheung Chan

The Standard Model and lepton flavour violation 15 weak hypercharge gauge fields. It implies the conservation of colour charge, weak isospin, weak hypercharge, and consequently the electric charge. Other than the Poincaré and gauge symmetries, there are also several accidental symmetries in the SM that are not postulated when the SM was formulated. They correspond to the global phase invariance of the quark fields as a whole, and that of the electron, muon and tau fields individually. The phase invariance of the quark fields implies conservation of baryon number. Similarly, the phase invariance of the lepton fields implies conservation of electron number, muon number and tau number independently. The electron, muon and tau numbers are defined as (number of neutrinos and charged leptons − number of antineutrinos and charged antileptons) of the respective flavours. They are collectively known as the lepton family numbers. To date, in no experiments has the conservation of baryon number been violated. Meanwhile, the observation of neutrino oscillations has shown that lepton family numbers are indeed not conserved in Nature. It is one of the pieces of evidence that exposed the incompleteness of the SM. As a summary, Table 1.7 shows all of the symmetries and the associated conserved quantities in the SM. Table 1.7.: Symmetries in the Standard Model and the associated conserved quantities. Symmetry Lie group Type Conserved quantities Poincaré R 1 , 3 ⊗ O(1,3) external, global energy, momentum Gauge SU(3) ⊗ SU(2) ⊗ U(1) internal, local colour charge, weak isospin, weak hypercharge, electric charge Quark phase U(1) accidental, global baryon number Lepton phase U(1) accidental, global lepton family numbers 1.2.5. Flavour violation in the Standard Model The weak charged-current interaction is the only process in the SM that does not conserve fermion flavours. Not only does it couple up- and down-type quarks, or neutrinos and charged leptons in the same generation. It also mixes fermions in different generations. This is directly due to the mismatch of the mass eigenstates and the weak interaction eigenstates of fermions. Quark mixing The quark doublets that participate in charged-current interaction do not just consist of up- and down-type quarks of the same generation, but superpositions of quarks in