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

The upcoming Mu3e experiment aims to search for the lepton flavour violating decay $\mu^+ \to e^+ e^- e^+$ with an unprecedented final sensitivity of one signal decay in $10^{16}$ observed muon decays by making use of an innovative experimental design based on novel ultra-thin silicon pixel sensors. In a first phase, the experiment is operated at an existing muon beam line with rates of up to $10^8$ muons per second. Detailed simulation studies confirm the feasibility of background-free operation and project single event sensitivities in the order of $10^{-15}$ for signal decays modelled in an effective field theory approach. The precise tracking of the decay electrons and large geometric and momentum acceptance of Mu3e enable searches for physics beyond the Standard Model in further signatures. Examples of which are searches for lepton flavour violating two-body decays of the muon into an electron and an undetected 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 photon decay. The Mu3e experiment is expected to be competitive in all of these channels already in phase I.