  Massive neutron stars (NS) are expected to possess a quark core. While the
hadronic side of the NS equation of state (EOS) can be considered well
established, the quark side is quite uncertain. While calculating the EOS of
hadronic matter we have used the Brueckner-Bethe-Goldstone formalism with
realistic two-body and three-body forces, as well as a relativistic mean field
model. For quark matter we employ the MIT bag model constraining the bag
constant by exploiting the recent experimental results obtained at CERN on the
formation of a quark-gluon plasma. We calculate the structure of NS interiors
with the EOS comprising both phases, and we find that the NS maximum masses
fall in a relatively narrow interval, $1.45 M_\odot \leq M_{\rm max} \leq 1.65
M_\odot$, near the lower limit of the observational range.
