We study the QCD phase diagram using effective theories with the respective degrees of freedom for the different phases of QCD. In the deconfined phase we employ the dynamical quasiparticle model (DQPM), that is able to describe the dynamics of hot QCD at vanishing chemical potential. We extend to model to momentum-dependent selfenergies in order to match the correct perturbative limit of the propagators at high momenta. Within this generalized quasiparticle approach, denoted as DQPM∗, we can simultaneously reproduce the lattice QCD (lQCD) equation of state (EoS) and baryon number susceptibility. Using thermodynamic consistency we extend the model to finite baryon chemical potential exceeding the application range of lQCD by far. We give predictions for the EoS and the most important transport coefficients. In the confined phase the medium is composed of hadrons. At large temperatures they interact predominantly by resonant scatterings, which can be well described in terms of a hadron-resonance gas (HRG). At large chemical potential and low temperature the nature of the interaction changes from resonant scatterings to meson exchange as described by relativistic meanfield theories. We combine both approaches to get an interacting HRG (IHRG), that is compatible to the lQCD EoS (µ ≈ 0, T > 0) and the nuclear EoS (T ≈ 0, µ > 0). For a complete description of the phase diagram we have to switch between the partonic and the hadronic model. In accordance with heavy-ion simulations we define the transition at lines of constant thermodynamics. The resulting EoS is valid up to µB ≈ 450 MeV. We perform heavy-ion simulations with the PHSD transport approach and determine the region in the QCD phase diagram that is probed by different collision energies. The EoS constructed from the DQPM∗ and the IHRG can be used to describe collisions at low beam energies down to √s ≈ 7.7 GeV. Using simulations at even lower beam energies we determine the conditions necessary for the discovery of the critical point in the QCD phase diagram.
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