Heavy flavour in high-energy nuclear collisions: a theoretical overview

The peculiar role of heavy-flavour observables in relativistic heavy-ion collisions is discussed. Produced in the early stage, c and b quarks cross the hot deconfined plasma arising from the collision, interacting strongly with the latter, until they hadronize. Transport calculations are the tools to follow their propagation in the medium: their formulation as well as their conceptual basis are briefly reviewed. Depending on the strength of the interaction heavy quarks may or not approach kinetic equilibrium with the plasma, tending in the first case to follow the collective flow of the expanding fireball. The presence of a hot deconfined medium may also affect heavy-quark hadronization, being possible for them to recombine with the surrounding light thermal partons, so that the final heavy-flavour hadrons inherit part of the flow of the medium. Here we show how it is possible to develop a complete transport setup allowing one to describe heavy-flavour production in high-energy nuclear collisions. The ultimate goal will be to extract from the experimental data the heavy-flavour transport coefficients in the Quark-Gluon Plasma: we will comment on how far we are from this achievement. Information coming from recent lattice-QCD simulations concerning both the heavy-flavour transport coefficients in the hot QCD plasma and the nature of the charmed degrees around the deconfinement transition is also presented. Finally, the possibility that the formation of a hot deconfined medium even in small systems (high-multiplicity p-Au and d-Au collisions, so far) may affect also heavy-flavour observables is investigated. (paper)