Effective shear and bulk viscosities of the quark-gluon plasma: QCD versus heavy-ion data

In recent years, there has been a significant effort to extract the temperature-dependent shear ($\eta/s$) and bulk ($\zeta/s$) viscosity over entropy ratios of the quark-gluon plasma from a global comparison of heavy-ion data with results of hydrodynamic simulations. However, anisotropic flow, which is arguably the most sensitive probe of viscosity, is only sensitive to an {\it effective\/} viscosity over entropy ratio, which is obtained by taking a weighted average over the temperature, and summing the contributions of shear and bulk. We estimate this effective viscosity using existing first-principles calculations, which give $0.17<(\eta/s)_{\rm eff}<0.21$, and $(\zeta/s)_{\rm eff}<0.08$, implying that the damping of anisotropic flow at the LHC is mostly due to shear viscosity. The values extracted from global data analyses are compatible with these theory predictions.