Wing Sheung Chan

14 The Standard Model and lepton flavour violation Table 1.6.: Possible vertices for electroweak interactions in the Standard Model and their corresponding vertex factors. Vertex Vertex factor γ ¯ q / ¯ ` q / ` − ieQγ µ W + ¯ d / ¯ ν u / ` − i g 2 √ 2 γ µ (1 − γ 5 ) Z ¯ f f − i g 2 cos θ w γ µ ( C V − C A γ 5 ) 1.2.4. Symmetries and conservations The Standard Model exhibits several symmetries. According to Noether’s theorem [19] , every symmetry is associated to a conservation law. These symmetries are the essence of the Standard Model. They are either postulated symmetries that were used to construct and constrain the model in the first place, or are observed symmetries that have survived many experiments so far. The conservation laws also help physicists make predictions and design experiments more easily. First, there is the external, global symmetry for translation, rotation and Lorentz transformation. It is also known as the Poincaré symmetry. Without this symmetry, energy and momentum would no longer be conserved and the SM would violate special relativity. Then, there is also the internal, local symmetry for the gluon, weak isospin and