Characterization and analysis of azimuthally sensitive correlations

A unified framework for describing the azimuthal dependence of two-particle correlations in heavy-ion collisions is introduced, together with the methods for measuring the corresponding observables. The generalization to azimuthal correlations between more than two particles is presented. The high amount of data that modern nucleus-nucleus experiments can accumulate allow novel types of measurements, giving new information on the physics involved. An emerging class of experimental analyses thus consists in studying the dependence in azimuth of various observables in non-central collisions, investigating correlations with the impact-parameter direction. A celebrated example of such a correlation with the reaction plane is the azimuthal dependence of single-particle emission, the so-called (one-particle) anisotropic flow (for a review, see [1]). In the following, we shall focus on the dependence with the azimuth of two-particle production. If the single-particle production is azimuthally dependent, the two-particle production depends on the azimuth as well. Beyond that, two arbitrary particles may also be correlated, for various reasons: a) they may be the decay products of a short-lived particle that decays before reaching the detectors, or b) they may both belong to a (di)jet originating from a hard parton scattering, or c) they may be identical particles whose wave-functions interfere. Whatever the physical mechanism involved, the resulting two-particle correlation will depend on the azimuths of the particles if the short-lived parent particles flow (case a), or because the anisotropy of the interacting region results in anisotropic patterns of parton energy loss [2] (case b) and interferometry [3] (case c). The purpose of this paper is to present model-independent observables that characterize in a general way azimuthally-sensitive two-particle correlations, without any prejudice on the underlying physical mechanism [4]. We then discuss the experimental measurement of these observables, i.e., the measurement of the particlepair distribution with respect to the reaction plane. In particular, we shall mention methods of analysis that do not require to estimate the reaction plane, in opposition to those currently used [5–7]. Finally, we comment on the last step of the analysis, namely relating the observables we propose to models of the two-particle correlations. Quite obviously, that procedure is model-dependent, and we shall present several possible ways to tackle the issue. We shall conclude by generalizing the overall approach to correlations between more than two particles. Azimuthally sensitive correlations 2 1. Two-particle anisotropic flow In this section, we shall introduce general observables for decribing the azimuthal dependence of two-particle correlations. A convenient approach consists in starting from the azimuthal dependence of one-particle emission, i.e., single-particle anisotropic flow; the generalization to two-body correlations then follows in a natural way. Consider particles of a given type in a given rapidity y and transverse momentum pT window. Denoting by ΦR the orientation of the reaction plane (throughout the paper, azimuthal angles are measured with respect to a fixed direction in the laboratory), the probability distribution of the particle azimuth φ may be written as a Fourier series [8]: