Universal fluctuation-driven eccentricities in proton-proton, proton-nucleus and nucleus-nucleus collisions

We show that the statistics of fluctuation-driven initial-state anisotropies in proton-proton, proton-nucleus and nucleus-nucleus collisions is to a large extent universal. We propose a simple parametrization for the probability distribution of the Fourier coefficient $\varepsilon_n$ in harmonic $n$, which is in good agreement with Monte-Carlo simulations. Our results provide a simple explanation for the 4-particle cumulant of triangular flow measured in Pb-Pb collisions, and for the 4-particle cumulant of elliptic flow recently measured in p-Pb collisions. Both arise as natural consequences of the condition that initial anisotropies are bounded by unity. We argue that the initial rms anisotropy in harmonic $n$ can be directly extracted from the measured ratio $v_n\{4\}/v_n\{2\}$: this gives direct access to a property of the initial density profile from experimental data. We also make quantitative predictions for the small lifting of degeneracy between $v_n\{4\}$, $v_n\{6\}$ and $v_n\{8\}$. If confirmed by future experiments, they will support the picture that long-range correlations observed in p-Pb collisions at the LHC originate from collective flow proportional to the initial anisotropy.