Collisional energy loss distribution of a fast parton in a hot or dense QCD medium
We compute the probability distribution for collisional energy loss of an ultrarelativistic parton crossing a quark-gluon plasma. This collisional quenching weight has not been determined previously, unlike the average collisional loss per unit distance, although it should be a more accurate quantity to use in jet-quenching phenomenology. The quenching weight is obtained from a well-known kinetic equation which resums an arbitrary number of elastic scatterings of the energetic parton with the medium, providing a complete description of the stochastic energy exchange, including the possibility of energy gain from thermal fluctuations. The formulation also naturally extends the standard treatment of collisional energy loss to finite path lengths, which could be relevant not only for heavy-ion collisions, but also for light-ion, and possibly proton-nucleus and proton-proton collisions. We predict the quenching weight in a setup where individual elastic scatterings are described using the hard thermal loop approximation for soft exchanges, with a smooth matching to the hard domain.