This report reviews the study of open heavy-flavour and quarkonium production in high-energy hadronic collisions, as tools to investigate fundamental aspects of Quantum Chromodynamics, from the proton and nucleus structure at high energy to deconfinement and the properties of the Quark–Gluon Plasma. Emphasis is given to the lessons learnt from LHC Run 1 results, which are reviewed in a global picture with the results from SPS and RHIC at lower energies, as well as to the questions to be addressed in the future. The report covers heavy flavour and quarkonium production in proton–proton, proton–nucleus and nucleus–nucleus collisions. This includes discussion of the effects of hot and cold strongly interacting matter, quarkonium photoproduction in nucleus–nucleus collisions and perspectives on the study of heavy flavour and quarkonium with upgrades of existing experiments and new experiments. The report results from the activity of the SaporeGravis network of the I3 Hadron Physics programme of the European Union 7 Framework Programme.

We investigate the properties of scalar and pseudo-scalar mesons at finite temperature and quark chemical potential in the framework of the Nambu-Jona-Lasinio (NJL) model coupled to the Polyakov loop (PNJL model) with the aim of taking into account features of both chiral symmetry breaking and deconfinement.The mesonic correlators are obtained by solving the Schwinger-Dyson equation in the RPA approximation with the Hartree (mean field) quark propagator at finite temperature and density.In the phase of broken chiral symmetry a narrower width for the σ meson is obtained with respect to the NJL case; on the other hand, the pion still behaves as a Goldstone boson.When chiral symmetry is restored, the pion and σ spectral functions tend to merge. The Mott temperature for the pion is also computed.

We investigate the behavior of a pair of heavy fermions, denoted by Q andQ, in a hot/dense medium. Although we have in mind the situation where Q andQ denote heavy quarks, our treatment will be limited to simplified models, which bear only some general similarities with QCD. We study in particular the limiting case where the mass of the heavy fermions is infinite. Then a number of results can be derived exactly: a Schrödinger equation can be established for the correlator of the heavy quarks; the interaction effects exponentiate, leading to a simple instantaneous effective potential for this Schrödinger equation. We consider simple models for the medium in which the QQ pair propagates. In the case where the medium is a plasma of photons and light charged fermions, an imaginary part develops in this effective potential. We discuss the physical interpretation of this imaginary part in terms of the collisions between the heavy particles and the light fermions of the medium; the same collisions also determine the damping rate of the heavy fermions. Finally we study the connection between the real-time propagator of the heavy fermion pair and its Euclidean counterpart, and show that the real part of the potential entering the Schrödinger equation for the real-time propagator is the free energy calculated in the imaginary-time formalism. J Q (t; r 1 , r 2 ) ≡ χ(t, r 2 )ψ(t, r 1 ), J † Q (t; r 1 , r 2 ) ≡ ψ † (t, r 1 )χ † (t, r 2 ), (2)