  The Mu2e experiment at Fermilab searches for the charged-lepton flavour
violating (CLFV) conversion of a negative muon into an electron in the field of
an aluminum nucleus, with a distinctive signature of a mono-energetic electron
of energy slightly below the muon rest mass (104.967 MeV). The Mu2e goal is to
improve by four orders of magnitude the search sensitivity with respect to the
previous experiments. Any observation of a CLFV signal will be a clear
indication of new physics. The Mu2e detector is composed of a tracker, an
electro- magnetic calorimeter and an external veto for cosmic rays surrounding
the solenoid. The calorimeter plays an important role in providing particle
identification capabilities, a fast online trigger filter, a seed for track
reconstruction while working in vacuum, in the presence of 1 T axial magnetic
field and in an harsh radiation environment. The calorimeter requirements are
to provide a large acceptance for 100 MeV electrons and reach at these
energies: (a) a time resolution better than 0.5 ns; (b) an energy resolution <
10% and (c) a position resolution of 1 cm. The calorimeter design consists of
two disks, each one made of 674 undoped CsI crystals read by two large area
arrays of UV-extended SiPMs. We report here the construction and test of the
Module-0 prototype. The Module-0 has been exposed to an electron beam in the
energy range around 100 MeV at the Beam Test Facility in Frascati. Preliminary
results of timing and energy resolution at normal incidence are shown. A
discussion of the technical aspects of the calorimeter engineering is also
reported in this paper.
