The most important task of theoretical heavy-ion physics in this context is to link experimental observables to the fundamental physics and the microscopic structure of the different phases of strongly interacting matter. Model calculations and predictions need to be tested against data, which is critical for deducing mechanisms underlying the observed spectral modifications. The proposed observables have to be implemented in realistic event generators and the sensitivity of the respective experiments has to be evaluated by means of Monte Carlo simulations.
A direct consequence of spontaneously broken chiral symmetry in the vacuum is the lifting of the spectral degeneracy of hadrons of opposite parity. It is a strict prediction of QCD that, as chiral symmetry gets restored, this degeneracy re-emerges. Using spectral functions calculated by using many-body approach, Functional Renormalization Group or chiral mixing in a chiral mean field model, we compute electromagnetic rates that are consistent with the basic requirements of chiral symmetry and thus provide a direct link to the temperature and chemical potential evolution of the quark condensate. This includes possible chiral phase transitions and critical points. To infer experimental signals in the entire phase diagram of QCD matter we use transport theory or hydrodynamic description for realistic simulations of relativistic heavy-ion collisions.
As spectral functions at different values of chemical potentials (μB, μπ) and temperatures are difficult to implement in microscopic transport approaches, Coarse Graining has been proposed. This method allows to obtain thermodynamic variables such as temperature and net-baryon density via an equation of state (EoS) in a local space-time volume of the fireball. The chemical potentials and temperatures are locally calculated in the 4-volume of a collision in cells to extract the local emission of dileptons with spectral functions from different calculation ansatzes.