Moving forward to constrain the shear viscosity of QCD matter

We demonstrate that measurements of rapidity differential anisotropic flow in heavy ion collisions can constrain the temperature dependence of the shear viscosity to entropy density ratio {\eta}/s of QCD matter. Comparing results from hydrodynamic calculations with experimental data from RHIC, we find evidence for a small {\eta}/s $\approx$ 0.04 in the QCD cross-over region and a strong temperature dependence in the hadronic phase. A temperature independent {\eta}/s is disfavored by the data. We further show that measurements of the event-by-event flow as a function of rapidity can be used to independently constrain the initial state fluctuations in three dimensions and the temperature dependent transport properties of QCD matter.