A derivation of the source term induced by a fast parton from the quark energy-momentum tensor

The distribution of energy and momentum deposited by a fast parton in a medium of thermalized quarks, or the source term, is evaluated in perturbative thermal field theory. The calculation is performed by directly evaluating the thermal expectation value of the quark energy-momentum tensor. The fast parton is coupled to the medium by adding an interaction term to the Lagrangian. I show that this approach is very general and can be modified to consider more realistic modeling of fast parton propagation, such as a fast parton created in an initial hard interaction or the evolution of a parton shower due to medium induced radiation. For the scenario considered here, it is found that local excitations fall sharply as a function of the energy of the fast parton. These local excitations couple directly to the sound mode in hydrodynamics and are important for generating an observable shockwave structure. This may have implications for the trigger p_T dependence of measurements of azimuthal dihadron particle correlations in heavy-ion collisions. In particular, one would be less likely to observe a conical emission pattern for increasing trigger p_T.