We study $D$ meson resonances in hot, dense quark matter within the Nambu–Jona-Lasinio 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.

• Received 22 July 2011

DOI:https://doi.org/10.1103/PhysRevD.85.034005