Exploring terra incognita in the phase diagram of strongly interacting matter -- Experiments at FAIR and NICA

The fundamental properties of dense nuclear matter, as it exists in the core of massive stellar objects, are still largely unknown. The investigation of the high-density equation of state (EOS), which determines mass and radii of neutron stars and the dynamics of neutron star mergers, is in the focus of astronomical observations and of laboratory experiments with heavy-ion collisions. Moreover, the microscopic degrees-of-freedom of strongly interacting matter at high baryon densities are also unknown. While Quantum-Chromo-Dynamics (QCD) calculations on the lattice find a smooth chiral crossover between hadronic matter and the quark-gluon plasma for high temperatures at zero baryon chemical potential, effective models predict a 1st order chiral transition with a critical endpoint for matter at large baryon chemical potentials. Up to date, experimental data both on the high-density EOS and on a possible phase transition in dense baryonic matter are very scarce. In order to explore this terra incognita, dedicated experimental programs are planned at future heavy-ion research centres: the CBM experiment at FAIR, and the MPD and BM@N experiments at NICA. The research programs and the layout of these experiments will be presented. The future results of these laboratory experiments will complement astronomical observations concerning the EOS, and, in addition, will shed light on the microscopic degrees of freedom of QCD matter at neutron star core densities.