  We use an improved version of the SU(3) flavour parity-doublet quark-hadron
model to investigate the higher order baryon number susceptibilities near the
chiral and the nuclear liquid-gas transitions. The parity-doublet model has
been improved by adding higher-order interaction terms of the scalar fields in
the effective mean field Lagrangian, resulting in a much-improved description
of nuclear ground-state properties, in particular the nuclear compressibility.
The resulting phase diagram of the model agrees qualitatively with expectations
from lattice QCD, i.e., it shows a crossover at zero net baryo-chemical
potential and a critical point at finite density. Using this model, we
investigate the dependence of the higher-order baryon number susceptibilities
as function of temperature and chemical potential. We observe a strong
interplay between the chiral and liquid-gas transition at intermediate baryo
chemical potentials. Due to this interplay between the chiral and the nuclear
liquid-gas transitions, the experimentally measured cumulants of the net baryon
number may show very different beam energy dependence, subject to the actual
freeze-out temperature.
