Perturbative and nonperturbative properties of heavy quark transport in a thermal SU(3) gluon plasma

We investigate the perturbative and nonperturbative aspects of heavy quark transport in a thermal SU(3) gluon plasma. Based on the soft-hard factorized model, we extend the original perturbative framework to the near-critical temperature region, where nonperturbative effects become significant. The transition behavior of the semi-quark-gluon-plasma (semi-QGP) is described via a temperature-dependent background field incorporated in the background field effective theory. By implementing this approach, we quantitatively evaluate the collisional energy loss and momentum diffusion coefficients of charm and bottom quarks as functions of the incoming energy and medium temperature. Our results show a distinct suppression of both the energy loss and the diffusion coefficients relative to conventional perturbative estimates, especially near the critical temperature. This suppression originates from the emergence of a temperature-dependent color background field, which effectively reduces the color charge screening of the medium. These findings provide important theoretical insight into the phenomenology of heavy-flavor probes, offering a unified theoretical framework applicable across both high- and low-momentum regimes.