Energy dependence of jet transport parameter and parton saturation in quark-gluon plasma

We study the evolution and saturation of the gluon distribution function in the quark-gluon plasma as probed by a propagating parton and its effect on the computation of jet quenching or transport parameter (q) over cap. For thermal partons, the saturation scale Q(s)(2) is found to be proportional to the Debye screening mass mu(2)(D). For hard probes, evolution at small x = Q(s)(2)/6ET leads to jet energy dependence of (q) over cap. We study this dependence both for a conformal gauge theory in weak and strong coupling limit and for (pure gluon) QCD. The energy dependence can be used to extract the shear viscosity eta of the medium, since eta can be related to the transport parameter for thermal partons in a transport description. We also derive upper bounds on the transport parameter for both energetic and thermal partons. The latter leads to a lower bound on the shear viscosity to entropy density ratio which is consistent with the conjectured lower bound eta/s >= 1/4 pi. We also discuss the implications of these results on the study of jet quenching at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider and the bulk properties of the dense matter.