Heavy Ion Initial Conditions and Correlations Between Higher Moments in the Spatial Anisotropy

Fluctuations in the initial conditions for relativistic heavy ion collisions are proving to be crucial to understanding final state flow and jet quenching observables. The initial geometry has been parametrized in terms of moments in the spatial anisotropy (i.e. $\epsilon_2, \epsilon_3, \epsilon_4, \epsilon_5...$), and it has been stated in multiple published articles that the vector directions of odd moments are uncorrelated with the even moments and the reaction place angle. In this article, we demonstrate that this is incorrect and that a substantial correlation exists between the even and odd moments in peripheral Au+Au collisions. These correlations persist for all centralities, though at a very small level for the 0-55% most central collisions.