Heavy quark collisional energy loss in a nonextensive quark-gluon plasma

In this study, we derive the longitudinal and transverse gluon self-energies and the corresponding dielectric functions for a nonextensive QGP, based on nonextensive statistical mechanics and a kinetic theory framework. The nonextensive parameter $q$ enters these quantities primarily through the modification of the Debye mass. Utilizing the derived dielectric functions, we then calculate the collisional energy loss for a heavy quark using two established formalisms: the plasma physics-based Thoma-Gyulassy formula and the thermal field theory-originated Kirzhnits-Thoma formula. Our results show that for both formalisms, the collisional energy loss increases with the nonextensive parameter $q$ with this enhancement being more significant at higher incident quark momenta and suppressed for a heavier quark mass. The energy loss predicted from the Kirzhnits-Thoma formula is substantially larger than that from the Thoma-Gyulassy formula, and the nonextensive effect on the energy loss is more pronounced in the former. Furthermore, the mass suppression of the nonextensive effect on the energy loss is weaker in the Kirzhnits-Thoma approach. These calculations demonstrate that nonextensive statistics can significantly alter the energy loss in the QGP.