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 the RHIC, we find evidence for a small eta/s approximate to 0.04 in the QCD crossover 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.