v4,v5,

Abstract

Higher harmonics of anisotropic flow (v n 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. We explain how such measurements are related to event-plane correlations. We show that CMS data on v 4 and v 6 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 v 2 and v 3 , one can eliminate the uncertainty from initial conditions and define quantities that only involve nonlinear hydrodynamic response coefficients. Experimental data on v 4 , v 5 and v 6 are in good agreement with hydrodynamic calculations. We argue that v 7 can be measured with respect to elliptic and triangular flow. We present predictions for v 7 versus centrality in Pb-Pb collisions at the LHC.

Latest results on anisotropy flow of light and heavy flavors in PbPb collisions at CMS

“…The AMPT model describes the experimental results for all harmonics well. Comparisons to hydrodynamic model with a deformed symmetric Gaussian density profile [2] and with iEBE-VISHNU hydrodynamic [3], where both calculations have been performed with η/s = 0.08, show a strong sensitivity of the non-linear response coefficients to the initial-state conditions. It also shows that the sensitivity increases with an increase of the harmonic order n. The comparison to the hydrodynamic model [3] calculated with the same KLN initial-state condition but with different η/s values which is performed in [9] shows that the non-linear response coefficients are sensitive to the η/s values too, especially for the odd harmonics.…”

“…The higher order v n harmonics (n >3) have a non-linear contribution [1] which may be composed of lower order harmonics (n <4) [2]. The influence of the initial-state fluctuations on the hydrodynamic flow can be studied by the correlations between v n {Ψ n } harmonics measured with respect to their own plane, and mixed harmonics v n {Ψ mkl } (m, k, l < n) measured with respect to the direction of multiple lower order harmonics.…”

“…The influence of the initial-state fluctuations on the hydrodynamic flow can be studied by the correlations between v n {Ψ n } harmonics measured with respect to their own plane, and mixed harmonics v n {Ψ mkl } (m, k, l < n) measured with respect to the direction of multiple lower order harmonics. The following relations [2,3] decompose higher order harmonics into their linear (V nL ) and non-linear contributions…”

“…[2,3] provide the definitions of the mixed higher order harmonics v 4 {Ψ 22 }, v 5 {Ψ 23 }, v 6 {Ψ 222 }, v 6 {Ψ 33 } and v 7 {Ψ 223 }, and the corresponding non-linear response coefficients, χ mkl . The sensitivity of the v n {Ψ mkl } and the χ mkl to the initial-state conditions and transport properties of the formed medium could be used to test theoretical models.…”

Studies of three-particle correlations and reaction-plane correlators from STAR

“…The observable C m,n,m+n can be approximated as correlations of flow harmonics, v n s, and corresponding event plane angles, Ψ n s, as v m v n v m+n cos(mΨ m + nΨ n − (m + n)Ψ m+n ) . Theoretical studies show that such an observable can probe non-linear hydrodynamic response and therefore become more sensitive to viscosity than individual flow harmonics v n [1][2][3][4][5][6][7][8][9][10]. Better sensitivity to viscous effects can be very useful towards more precise extraction of different transport parameters and possibly their temperature dependence by comparison to hydrodynamic simulations [11,12].…”