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 ($\eta \mathrm{/}s$) and bulk ($\zeta \mathrm{/}s$) 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 $0.17<(\eta \mathrm{/}s{)}_{\mathrm{e}\mathrm{f}\mathrm{f}}<0.21$, and $(\zeta \mathrm{/}s{)}_{\mathrm{e}\mathrm{f}\mathrm{f}}<0.08$, 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.