  The Mu2e experiment at Fermilab aims at measuring the neutrinoless conversion
of a negative muon into an electron and reach a single event sensitivity of
2.5x10^{-17} after three years of data taking. The monoenergetic electron
produced in the final state, is detected by a high precision tracker and a
crystal calorimeter, all embedded in a large superconducting solenoid (SD)
surrounded by a cosmic ray veto system. The calorimeter is complementary to the
tracker, allowing an independent trigger and powerful particle identification,
while seeding the track reconstruction and contributing to remove background
tracks mimicking the signal. In order to match these requirements, the
calorimeter should have an energy resolution of O(5)% and a time resolution
better than 500 ps at 100 MeV. The baseline solution is a calorimeter composed
of two disks of BaF2 crystals read by UV extended, solar blind, Avalanche
Photodiode (APDs), which are under development from a JPL, Caltech, RMD
consortium. In this paper, the calorimeter design, the R&D studies carried out
so far and the status of engineering are described. A backup alternative setup
consisting of a pure CsI crystal matrix read by UV extended Hamamatsu MPPC's is
also presented.
