Design, status and perspective of the Mu2e crystal calorimeter

The Mu2e experiment at Fermilab will search for the charged lepton flavor violating process of neutrino-less $\mu \to e$ coherent conversion in the field of an aluminum nucleus. Mu2e will reach a single event sensitivity of about $2.5\cdot 10^{-17}$ that corresponds to four orders of magnitude improvements with respect to the current best limit. The detector system consists of a straw tube tracker and a crystal calorimeter made of undoped CsI coupled with Silicon Photomultipliers. The calorimeter was designed to be operable in a harsh environment where about 10 krad/year will be delivered in the hottest region and work in presence of 1 T magnetic field. The calorimeter role is to perform $\mu$/e separation to suppress cosmic muons mimiking the signal, while providing a high level trigger and a seeding the track search in the tracker. In this paper we present the calorimeter design and the latest R$\&$D results.