Wing Sheung Chan

26 The Standard Model and lepton flavour violation either leptonically ( τ lep ) or hadronically ( τ had ). While there are efforts in both the `τ lep and `τ had search channels, this thesis will focus mainly on the `τ had channel. The existing limits: B ( Z → eτ ) < 9 . 8 × 10 − 6 and B ( Z → µτ ) < 1 . 2 × 10 − 5 were both set by experiments at the Large Electron-Positron Collider (LEP) [58, 60] . More than 20 years have passed since these limits were set and they had remained the most stringent. However, in this thesis, it is the author’s main goal to push the limits and finally reach new sensitivities using data from the Large Hadron Collider and the ATLAS detector.