Searching for Charged Lepton Flavour Violation with Mu3e

The observation of lepton flavour violation (LFV) in the charged lepton sector would be an unambiguous sign of physics beyond the Standard Model (BSM), and thus, it is the channel of choice for many BSM searches. LFV searches in muon decays in particular benefit from the fact that muons can be easily produced at high rates. There is a global effort to search for LFV at high-intensity muon sources to which the upcoming Mu3e experiment at the Paul Scherrer Institute (PSI) will contribute. The Mu3e Collaboration aims to perform a background-free search for the LFV decay ${\mu }^{+}\to e^{+}{e}^{-}{e}^{+}$ with an unprecedented sensitivity in the order of ${10}^{-15}$ in the first phase of operation and ${10}^{-16}$ in the final phase - an improvement over the preceding SINDRUM experiment by four orders of magnitude. The high muon stopping rates and low momenta of the decay electrons make high demands on momentum and time resolution and on the data acquisition. The innovative experimental concept is based on a tracking detector built from novel ultra-thin silicon pixel sensors and scintillating fibres and tiles as well as online event reconstruction and filtering in real time.