Event-plane correlators

Introduction.−High-energy heavy-ion collision experiments at the Relativistic Heavy-Ion Collider (RHIC), BNL and the Large Hadron Collider (LHC), CERN have firmly established the formation of strongly interacting matter which exhibits a strong collective flow [1–3]. This not only suggests that the matter formed is close to local thermal equilibrium but also provides a window to the initial state of the fireball immediately after the collision. Collective flow in the plane transverse to the beam axis is typically measured in terms of two-particle angular correlations [4–7] and its small anisotropies captured in its Fourier harmonics [8–11]. Recently, a new tool, namely correlations among event planes corresponding to different harmonics [12–14], is emerging with a promise to throw additional light on the initial-state phenomena. Pair correlations (i.e., the single-particle anisotropic flow vn extracted from two-particle correlations) are reasonably well understood . Event-plane correlators represent higher-order correlations, involving at least three particles. Such higher-order correlations thus open a new direction in heavy-ion physics, much in the same way as studies of non-Gaussian fluctuations  in the early Universe. They bring in a large number of new observables which provide new, detailed insight into the hydrodynamic response and on the initial stage, and will significantly improve our understanding of heavy-ion collisions. The ATLAS collaboration  has recently released preliminary measurements of eight two-plane correlators (e.g., the correlation between the second and fourth harmonics) and six three-plane correlators (e.g., the mixed correlation between second, third and fifth harmonics) in Pb-Pb collisions at √ sNN = 2.76 TeV, as a function of the centrality of the collision. These correlators are qualitatively understood within event-by-event hydrodynamics [16] and provide new insight [17] into the interplay between the linear and nonlinear [18] hydrodynamic response [19, 20] to the initial density profile. The ATLAS analysis is very demanding in terms of detector acceptance: each event plane is determined in a separate pseudorapidity window; windows must be pairwise separated by gaps in order to suppress nonflow correlations; finally, each window must be wide enough to achieve a significant resolution in every Fourier harmonic up to order six. In this article, we show that the analysis can be done more simply, and that even three- and four-plane correlators can be safely analyzed with just two symmetric pseudorapidity windows, in the same way as two-plane correlators. The analysis can thus be performed by other experiments with smaller detector acceptance. We also explain in detail how to generalize the scalar-product method used earlier for two-particle flow analysis [21], to mixed correlations, so as to eliminate the ambiguity brought about by the event-plane method . We carry out realistic simulations within a multiphase transport (AMPT) model [23]. Results are for the first time in quantitative agreement with the ATLAS measurements. In addition, we present predictions for several new correlators, in particular four-plane correlators. Method.−The azimuthal distribution of outgoing particles is decomposed in Fourier harmonics in each collision event. The flow vector in harmonic n is defined as [24],