Hot and dense strong-interaction (QCD) matter plays an important role in the quark-hadron transition shortly after the big bang, in the element production in stars and the inner core of neutron stars. Its properties can be studied in relativistic heavy-ion collisions. Several countries operate facilities or have plans to build new accelerator systems, such as FAIR at Darmstadt and NICA at Dubna, to investigate hot and dense nuclear matter in heavy-ion collisions. Current experiments are conducted at GSI in Darmstadt, the RHIC (Relativistic Heavy Ion Collider) in Brookhaven and at the LHC (Large Hadron Collider) at CERN in Geneva. The primary aim of the experiments at the high-energy frontier is to study a new state of matter, the ‘quark-gluon-plasma’ (QGP) and to infer its equation of state and transport properties. The interpretation of the data involves substantial theoretical efforts in non-perturbative and perturbative QCD, as well as in large-scale hydrodynamical and transport simulations.
As matter gets heated and compressed it ultimately undergoes a transition from confined hadrons to quasi-free quarks and gluons. The current understanding is, that the resulting change in degrees of freedom leads to a smooth cross-over transition at small quark chemical potential in which spontaneously broken chiral symmetry is restored and quarks and gluons are liberated. Although detailed lattice studies of the equation of state (EoS) in this regime have converged to realistic answers, the computation of transport properties of strong-interaction matter remains a theoretical challenge. At high chemical potential, it is expected that the QCD phase diagram is very rich, featuring phases familiar from condensed matter physics. Here the hadron-to-quark transition and especially the role of baryonic degrees of freedom is poorly understood. Because of the fermion sign problem, lattice simulations fail at present to make ab-initio predictions in this region of the phase diagram and one has to resort to ‘QCD inspired' models.
To interpret heavy-ion data, complex numerical simulations of the collision dynamics are necessary. These include relativistic hydrodynamics and precise knowledge of the initial state as well as hadronic transport theory at the final stages of the collision. Of particular interest are hydrodynamical descriptions with non-ideal fluid components in the energy-momentum tensor. At present, a detailed understanding of the transport coefficients of strong-interaction matter is still lacking. Other uncertainties are fluctuations in the initial conditions of the hydro evolution and the consequences on collective flow variables. The latter are being measured very precisely in the ALICE, ATLAS and CMS experiments.
Heavy-ion experiments at very high center-of-mass energies, presently conducted at RHIC as well as the LHC probe strong-interaction matter at high temperatures but small net-baryon densities. The results are thus of direct relevance for the state of the early universe a few microseconds after the big bang. Here questions of the high-temperature EoS, the propagation of partons through hot and dense quark-gluon matter, charm production and the radiation of photons and di-leptons are at the focus of intense research programs. Another field of great current interest is the characterization of the very early, far-from-equilibrium conditions of the collisions and the rapid thermalization that is required for a hydrodynamical description of the fireball evolution.
The RHIC low-energy run and planned heavy-ion experiments at NICA and FAIR are designed to explore regions of high baryo-chemical potential in the QCD phase diagram. Here a chiral critical endpoint, the occurrence of inhomogeneous chiral phases and color superconducting states of quark matter are expected. One of the interesting questions is the interplay between the restoration of spontaneously broken chiral symmetry and the transition to deconfined quark matter. It remains a challenging task to come up with signals in the collision of heavy-ions for these exciting predictions from theory.
Proton-proton and proton-nucleus collisions at high energy serve as a reference for relativistic nucleus-nucleus collisions, in particular to discriminate against effects related to the formation of the QGP. With growing particle multiplicity, pp and pA collisions possibly enter the domain where the macroscopic description becomes applicable and hydrodynamic behavior should ensue even in these systems. The question is whether the high-multiplicity events recently observed at the LHC support this conjecture and if yes how does this impact our understanding of AA collisions.