Small Shear Viscosity of a Quark-Gluon Plasma Implies Strong Jet Quenching

We derive an expression relating the transport parameter $\hat{q}$ and the shear viscosity $\eta$ of a weakly coupled quark-gluon plasma. A deviation from this relation can be regarded as a quantitative measure of ``strong coupling'' of the medium. The ratio $T^3/\hat{q}$, where $T$ is the temperature, is a more broadly valid measure of the coupling strength of the medium than $\eta/s$, where $s$ denotes the entropy density. Different estimates of $\hat{q}$ derived from existing RHIC data are shown to imply radically different structures of the produced matter.