Fluctuation induced equality of multi-particle eccentricities for four or more particles

Abstract

We discuss eccentricities (ellipticity and triangularity) generated in nucleus-nucleus and proton-nucleus collisions. We define multi-particle eccentricities n{m} which are associated with the n′th angular multipole moment for m particles. We show that in the limit of fluctuation dominance all of the n{m}’s are approximately equal for m ≥ 4. For dynamics linearly responding to these eccentricities such as hydrodynamics or proposed in this paper weakly interacting field theory, these relations among eccentricities are translated into relations among flow moments vn{m}. We explicitly demonstrate it with hydrodynamic calculations. 1