  The measurement of the charmonium ($J/\psi$, $\psi'$) and bottomonium
($\Upsilon$, $\Upsilon'$, ${\Upsilon''}$) resonances and $Z^0$ boson in
nucleus-nucleus collisions provides crucial information on high density QCD
matter. The observation of anomalous suppression of $J/\psi$ at the CERN-SPS
and RHIC is well established but the clarification of some important questions
requires equivalent studies of the $\Upsilon$ family, only possible at LHC
energies. The $Z^0$ boson will be produced for the first time in heavy-ion
collisions at the LHC and, since its dominant production channel is through
$q{\bar q}$ fusion, it is an excellent probe of the nuclear modification of
quark distribution functions. This paper reports the capabilities of the CMS
detector to study quarkonium and $Z^0$ production in Pb-Pb collisions at 5.5
TeV, through the dimuon decay channel.
