Collisional processes of on-shell and off-shell heavy quarks in vacuum and in the quark-gluon plasma.

We study the heavy-quark scattering on partons of the quark-gluon plasma (QGP), being especially interested in the collisional (elastic) scattering processes of heavy quarks Q on light quarks q and gluons g. We calculate the different cross sections for perturbative partons (massless on-shell particles in the vacuum) and for dynamical quasiparticles (off-shell particles in the QGP medium as described by the dynamical quasiparticles model "DQPM") using the leading-order Born diagrams. Our results show clearly the effect of a finite parton mass and width on the perturbative elastic [q(g)Q→q(g)Q] cross sections which depend on temperature T, energy density ε, the invariant energy vs, and the scattering angle θ. Our detailed comparisons demonstrate that the finite width of the quasiparticles in the DQPM--which encodes the multiple partonic scattering--has little influence on the cross section for qQ→qQ as well as gQ→gQ scattering, except close to thresholds. Thus, when studying the dynamics of energetic heavy quarks in a QGP medium the spectral width of the degrees-of-freedom may be discarded. We have, furthermore, compared the cross sections from the DQPM with corresponding results from hard-thermal-loop (HTL) approaches. The HTL-inspired models--essentially fixing the regulators by elementary vacuum cross sections and decay amplitudes instead of properties of the QGP at finite temperature--provide quite different results, especially with respect to the temperature dependence of the qQ and gQ cross sections (in all settings). Accordingly, the transport properties of heavy quarks will be very different as a function of temperature when compared to DQPM results. [ABSTRACT FROM AUTHOR]