Sound Produced by a Fast Parton in the Quark-Gluon Plasma is a “Crescendo”

We calculate the total energy deposited into the medium per unit length by fast partons traversing a quark-gluon plasma. The medium excitation due to collisions is taken to be given by the well-known expression for the collisional drag force. The radiative energy loss of the parton contributes to the energy deposition because each radiated gluon acts as an additional source of collisional energy loss in the medium. We derive a differential equation which governs how the spectrum of radiated gluons is modified when this energy loss is taken into account. This modified spectrum is then used to calculate the additional energy deposition due to the interactions of radiated gluons with the medium. Numerical results are presented for the medium response for the case of two energetic back-to-back partons created in a hard interaction.