v4v4, v5v5, v6v6, v7v7: Nonlinear hydrodynamic response versus LHC data

Higher harmonics of anisotropic flow (vnvn with n≥4n≥4) in heavy-ion collisions can be measured either with respect to their own plane, or with respect to a plane constructed using lower-order harmonics. We explain how such measurements are related to event-plane correlations. We show that CMS data on v4v4 and v6v6 are compatible with ATLAS data on event-plane correlations. If one assumes that higher harmonics are the superposition of non-linear and linear responses, then the linear and non-linear parts can be isolated under fairly general assumptions. By combining analyses of higher harmonics with analyses of v2v2 and v3v3, one can eliminate the uncertainty from initial conditions and define quantities that only involve nonlinear hydrodynamic response coefficients. Experimental data on v4v4, v5v5 and v6v6 are in good agreement with hydrodynamic calculations. We argue that v7v7 can be measured with respect to elliptic and triangular flow. We present predictions for v7v7 versus centrality in Pb–Pb collisions at the LHC.