Nonlinear hydrodynamic response confronts LHC data

Higher harmonics of anisotropic flow (vn with n≥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. By assuming that higher flow harmonics are the superposition of medium nonlinear and linear responses to initial anisotropies, we propose a set of nonlinear response coefficients χn's, which are independent of initial state by construction. In experiments, χn's can be extracted as the ratio between higher order harmonic flow measured in the plane constructed by v2 and v3, and moments of lower order harmonic flow. Simulations with single-shot hydrodynamics and AMPT model lead to results of these nonlinear response coefficients in good agreement with the experimental data at the LHC energy. Predictions for v7 and v8 measured with respect to plane of lower order harmonics are given accordingly.