The muon to electron conversion process and the Mu2e experiment at Fermilab

The Mu2e experiment at Fermi National Accelerator Laboratory will search for the Charged Lepton Flavour Violating (CLFV) neutrino-less coherent conversion of a muon into an electron in the eld of a nucleus with a single event sensitivity of 3 ·10−17, which is an improvement of four order of magnitude over the existing limits. The muon conversion probes new physics at a scale that cannot be reached with direct searches at present or planned colliders and complements similar searches for CLFV performed by the MEG-II experiment at Paul Scherrer Institut. In this paper, we report on the Mu2e physics motivations, the design of the muon beamline and the detectors employed by the experiment, which include a tracking spectrometer, a calorimeter and a cosmic ray veto. Mu2e is currently being constructed at the Fermilab Muon Campus and is expected to begin data taking in 2025 (Run 1) with a reduced average beam intensity. Run 1 will continue for two years. After a shutdown for the upgrade of Fermilab accelerator complex, Mu2e data taking will be resumed at full beam intensity in 2029 (Run 2).