Characterization and analysis of azimuthally sensitive correlations

Abstract

Abstract. 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][6][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.

Measurement of ϕ -meson production in Cu+Au collisions at sNN=200

“…To obtain the azimuthal-angle dependence of φ-meson production, the φmeson raw yields are measured in a selected p T range as a function of the K + K − pair angle with respect to the reactionplane orientation in six equally spaced bins of ϕ = ϕ pair − 2 covering the range 0 < ϕ < π/2. Assuming elliptic flow is the dominant source of the ϕ variation in the φ-meson yields [39][40][41], the v 2 coefficients are then extracted from a fit to the distribution dN φ /d ( ϕ) using the function [18] dN φ…”

“…An alternative method to evaluate φ-meson v 2 is the invariant mass fit method, described in [18,34,39,41]. In this analysis it is used to perform cross-check and for the evaluation of systematic uncertainties.…”

“…The investigation of elliptic-flow coefficients (v 2 ) can provide insight on how the initial transverse coordinatespace anisotropy of heavy ion collisions is converted to a momentum-space anisotropy in the transverse plane [18]. Previous studies of v 2 at RHIC in symmetric collision systems (Au + Au, Cu + Cu) show that v 2 values for light hadrons depend on the number of valence quarks in the hadron (n q ), the second-order-participant eccentricity (ε 2 ), and the number of nucleons participating in the interaction ( N part ) [19,20].…”

Global conservation laws and femtoscopy of small systems

“…Danielewicz [15], and later Borghini, Dinh and Ollitraut [16], considered EMCIC-type effects on two-particle azimuthal correlations (elliptic flow v 2 ). They considered transverse momentum ( P T ) conservation only, but Borghini later [17] generalized to the case of an arbitrary number D of independent (orthogonal) spatial dimensions and very re-cently considered momentum conservation effects on threeparticle analyses of jet-like behavior [18].…”