  The Mu2e Experiment at Fermilab will search for coherent, neutrino-less
conversion of negative muons into electrons in the field of an Aluminum
nucleus, $\mu^- + Al \to e^- +Al$. Data collection start is planned for the end
of 2021.
  The dynamics of such charged lepton flavour violating (CLFV) process is well
modelled by a two-body decay, resulting in a mono-energetic electron with an
energy slightly below the muon rest mass. If no events are observed in three
years of running, Mu2e will set an upper limit on the ratio between the
conversion and the capture rates
  %\convrate of $\leq 6\ \times\ 10^{-17}$ (@ 90$\%$ C.L.). R$_{\mu e} =
\frac{\mu^- + A(Z,N) \to e^- +A(Z,N)}{\mu^- + A(Z,N) \to \nu_{\mu} ^-
+A(Z-1,N)} $ of $\leq 6\ \times\ 10^{-17}$ (@ 90$\%$ C.L.).
  This will improve the current limit of four order of magnitudes with respect
to the previous best experiment.
  Mu2e complements and extends the current search for $\mu \to e \gamma$ decay
at MEG as well as the direct searches for new physics at the LHC. The
observation of such CLFV process could be clear evidence for New Physics beyond
the Standard Model. Given its sensitivity, Mu2e will be able to probe New
Physics at a scale inaccessible to direct searches at either present or planned
high energy colliders. To search for the muon conversion process, a very
intense pulsed beam of negative muons ($\sim 10^{10} \mu/$ sec) is stopped on
an Aluminum target inside a very long solenoid where the detector is also
located. The Mu2e detector is composed of a straw tube tracker and a CsI
crystals electromagnetic calorimeter. An overview of the physics motivations
for Mu2e, the current status of the experiment and the required performances
and design details of the calorimeter are presented.
