Heavy flavours in AA collisions: production, transport and final spectra

A multi-step setup for heavy-flavour studies in high-energy nucleus-nucleus (AA) collisions --- addressing within a comprehensive framework the initial Q-Qbar production, the propagation in the hot medium until decoupling and the final hadronization and decays --- is presented. The initial hard production of Q-Qbar pairs is simulated using the POWHEG pQCD event generator, interfaced with the PYTHIA parton shower. Outcomes of the calculations are compared to experimental data in pp collisions and are used as a validated benchmark for the study of medium effects. In the AA case, the propagation of the heavy quarks in the medium is described in a framework provided by the relativistic Langevin equation. For the latter, different choices of transport coefficients are explored (either provided by a perturbative calculation or extracted from lattice-QCD simulations) and the corresponding numerical results are compared to experimental data from RHIC and the LHC. In particular, outcomes for the nuclear modification factor R_AA and for the elliptic flow v_2 of D/B mesons, heavy-flavour electrons and non-prompt J/\psi's are displayed