Abstract
Elliptic flow, $v_2$, and triangular flow, $v_3$, are to a good approximation linearly proportional to the corresponding spatial anisotropies of the initial density profile, $\varepsilon_2$ and $\varepsilon_3$. Using event-by-event hydrodynamic simulations, we point out when deviations from this linear scaling are to be expected. When these deviations are negligible, relative $v_n$ fluctuations are equal to relative $\varepsilon_n$ fluctuations, and one can directly probe models of initial conditions using ratios of cumulants, for instance $v_n\{4\}/v_n\{2\}$. We argue that existing models of initial conditions tend to overestimate flow fluctuations in central Pb+Pb collisions, and to underestimate them in peripheral collisions. We make predictions for $v_3\{6\}$ in noncentral Pb+Pb collisions, and for $v_3\{4\}$ and $v_3\{6\}$ in high-multiplicity p+Pb collisions.
Highlights
Anisotropic flow is the key observable providing evidence for the creation of a collective medium in ultrarelativistic heavy-ion collisions
We argue that existing models of initial conditions tend to overestimate flow fluctuations in central Pb+Pb collisions, and to underestimate them in peripheral collisions
Hydrodynamic simulations [3,4,5] show that elliptic flow, v2, and triangular flow, v3, correlate almost linearly with the initial eccentricity, ε2, and triangularity, ε3, respectively, of the system
Summary
Anisotropic flow is the key observable providing evidence for the creation of a collective medium in ultrarelativistic heavy-ion collisions. The initial anisotropies εn probe the geometrical shape of the initial density profile, and, provide an information which is independent of the final multiplicity distribution, which is the typical observable to which models are tuned. III, we compute the lowest non-trivial ratios of cumulants, v2{4}/v2{2} and v3{4}/v3{2}, in eventby-event hydrodynamic simulations of Pb+Pb collisions, and we determine in which centrality intervals they are compatible with the ratios of cumulants of the corresponding initial anisotropies, εn In these centrality intervals, we compute ratios of cumulants using models of initial conditions, that can in this way be tested directly against experimental data on vn{4}/vn{2}. To make our analysis as inclusive as possible, we test a wide variety of initial condition models, covering the spectrum of models typically used in hydrodynamic calculations We employ these initial state parametrizations to predict v3{6}/v3{4} in Pb+Pb collisions. We employ the stateof-the-art Monte Carlo model of initial conditions for p+Pb collisions to make predictions for v3{4}/v3{2}, and v3{6}/v3{4}
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