Radiative heavy quark energy loss in a strongly interacting quark gluon plasma

Heavy quark production and attenuation provide unique tomographic probes of QCD matter produced at Ultrarelativistic Heavy Ion Collisions. In this thesis, we establish the theory of heavy quark radiative energy loss to all orders in opacity, including dynamic polarization and finite size transition radiation.; We first study the non-abelian analog of a Ter-Mikayelian effect. This effect addresses how the radiative energy loss changes due to the color dielectric modification of the gluon dispersion relation in a dense QCD medium. We then improve the Ter-Mikayelian effect by computing the transition radiation; which accounts for the finite size effects that are characteristic for the medium created in Ultrarelativistic Heavy Ion Collisions. Finally, we consider the medium induced radiation, which is a dominant radiative energy loss effect. The medium induced energy loss is computed to all orders in number of scatterings and the obtained analytic expression generalizes the GLU opacity expansion to the case of heavy partons. The computed energy loss is folded in the pQCD hadron production phenomenology to predict the moderate- and high- pT open charm and beauty yield in Au + Au collisions at RHIC and LHC energies. The obtained theoretical predictions of the radiative heavy quark jet quenching can be tested in the upcoming experiments measuring D-meson suppression in Ultrarelativistic Heavy Ion Collisions.