Heavy Quark Diffusion as a Probe of the Quark-Gluon Plasma

We report on recent research on the properties of elementary particle matter governed by the strong force at high temperatures, where QCD predicts hadrons to dissolve into the Quark-Gluon Plasma (QGP). After a short introduction to the basic elements of QCD in the vacuum, most notably quark confinement and mass generation, we discuss how these phenomena relate to phase changes in strongly interacting matter at high temperature. We briefly review the main experimental findings at the Relativistic Heavy Ion Collider (RHIC) which provide strong evidence that a QGP has been produced, with unprecedentedly small viscosity and large opacity. We discuss how heavy quarks (charm and bottom) can be utilized to quantitatively probe the transport properties of a strongly coupled QGP (sQGP). The large heavy-quark (HQ) mass allows to set up a Brownian motion approach, which can serve to evaluate different approaches for HQ interactions in the sQGP. The implementation of lattice QCD based HQ potentials generates pre-hadronic resonance structures in HQ scattering in the medium, leading to large interaction rates and small diffusion coefficients. The resonance correlations are strongest close to the critical temperature (T_c), suggesting an intimate connection to the hadronization of the QGP. The implementation of HQ transport into Langevin simulations of an expanding QGP fireball at RHIC enables quantitative comparisons with experiment. The extracted HQ diffusion coefficients are employed for schematic estimates of the shear viscosity, corroborating the notion of a strongly-coupled QGP in the vicinity of T_c.