  We study D meson resonances in hot, dense quark matter within the NJL model
and its Polyakov-loop extension. We show that the mass splitting between D^+
and D^- mesons is moderate, not in excess of 100 MeV. When the decay channel
into quasifree quarks opens (Mott effect) at densities above twice saturation
density, the decay width reaches rapidly the value of 200 MeV which entails a
spectral broadening sufficient to open J/psi dissociation processes. Contrary
to results from hadronic mean-field theories, the chiral quark model does not
support the scenario of a dropping D meson masses so that scenarios for J/psi
dissociation by quark rearrangement built on the lowering of the threshold for
this process in a hot and dense medium have to be reconsidered and should
account for the spectral broadening.
