Transport coefficients from energy loss studies in an expanding QGP

We use linear viscous hydrodynamics to describe the energy and momentum deposited by a fast moving parton in a quark gluon plasma. This energy-momentum is used to compute the probability density for the production of soft partons by means of the Cooper-Frye formula. Using this probability density, we render manifest a relation between the average transverse momentum given to the fast moving parton from the medium, q̂, the shear viscosity to entropy density ratio, η/s, and the energy lost by the fast moving parton, ΔE, in an expanding medium under similar conditions to those generated in nucleus-nucleus collisions at the LHC and RHIC energies. We find that q̂ increases with ΔE. On the other hand, η/s is more stable with ΔE. The behavior of q̂, with ΔE is understood as arising from the length of medium the parton traverses from the point where it is produced. However, since η/s is proportional to the ratio of the length of medium traversed by the fast parton and the average number of scatterings it experiences, it has a milder dependence on the energy it loses. This study represents a tool to obtain a direct connection between transport coefficients and the description of in-medium energy loss within a linear viscous hydrodynamical evolution of the bulk.