Energy loss of a heavy quark in a collisional quark-gluon plasma

We extend our previous work on the energy loss of a heavy fermion in a QED plasma to the quark-gluon plasma, using the same Bhatnagar-Gross-Krook collisional kernel. The calculation is carried out with a theoretical method where the hard-thermal-loop resummed gluon propagator is used for arbitrary momentum transfer in the scattering processes. Encoding the collision effect in a self-consistent manner, the resummed gluon propagator regulates the infrared divergence in the scattering amplitude without introducing an artificial cutoff for the transferred momenta and makes the analysis on the hard and soft processes in a unified framework. To place our computation on a more solid foundation, we also explicitly demonstrate the gauge independence of the interaction rate as well as the elimination of unphysical gluon polarizations by the ghost field under the use of the resummed gluon propagator. In addition, with our complete QCD calculation by including both quark-quark and quark-gluon scatterings, we provide a quantitatively reliable result on the collisional energy loss of a heavy quark where the new contribution from quark-gluon scatterings accounts for a larger portion of the total energy loss. In general, collisions between the thermal partons result in an increased energy loss which becomes more pronounced with increasing gauge coupling. Considering a typical coupling constant in QCD, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>α</a:mi> <a:mi>s</a:mi> </a:msub> <a:mo>=</a:mo> <a:mn>0.3</a:mn> </a:math> , the energy loss increases <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mo>∼</c:mo> <c:mn>8</c:mn> <c:mo>%</c:mo> </c:math> at large incident velocities as compared to the collisionless limit. Such a collision-induced correction is still moderate, although it is slightly suppressed as compared to our previous estimate based on a QED calculation using couplings consistent with those expected to be generated in the quark-gluon plasma.