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The upcoming Mu3e experiment aims to search for the lepton flavour violatingdecay $\mu^+ \to e^+ e^- e^+$ with an unprecedented final sensitivity of onesignal decay in $10^{16}$ observed muon decays by making use of an innovativeexperimental design based on novel ultra-thin silicon pixel sensors. In a firstphase, the experiment is operated at an existing muon beam line with rates ofup to $10^8$ muons per second. Detailed simulation studies confirm thefeasibility of background-free operation and project single event sensitivitiesin the order of $10^{-15}$ for signal decays modelled in an effective fieldtheory approach. The precise tracking of the decay electrons and largegeometric and momentum acceptance of Mu3e enable searches for physics beyondthe Standard Model in further signatures. Examples of which are searches forlepton flavour violating two-body decays of the muon into an electron and anundetected boson as well as for electron-positron resonances in $\mu^+ \to e^+e^- e^+ \bar{\nu}_\mu \nu_e$ which could result for instance from a dark photondecay. The Mu3e experiment is expected to be competitive in all of thesechannels already in phase I.

The Rare and Forbidden: Testing Physics Beyond the Standard Model with Mu3e