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 epsilon(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 nu(n){4}/nu 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 nu(n){4}, nu(n){6}, and nu(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.