Measuring momentum-dependent flow fluctuations in heavy-ion collisions

Abstract

Momentum-dependent two-particle correlations in heavy-ion collisions can be fully characterized by a principal component analysis (PCA). In particular, subleading PCA modes of azimuthal Fourier harmonics are expected to reveal new information about hydrodynamic flow fluctuations. However, we find that as currently measured, it can instead be dominated by fluctuations of particle number, which can be measured independently and therefore represent redundant information that serves as an unwanted background. Here we propose a redefinition of the PCA observables which is insensitive to multiplicity fluctuations and thus free of redundancies. The proposed observables isolate novel sources of flow fluctuations from two-particle correlations and can provide fresh insight into the properties of the initial stages of the system at small length scales.

Probing the structure of the initial state of heavy-ion collisions with $p_T$-dependent flow fluctuations

“…While a precise measurement of the covariance matrix in Eq. ( 5) might be a challenge, this matrix was shown to be nearly equivalent to the alternative one introduced in [18], which in turn should be straightforward to measure.…”

“…[11]. This original proposal was further explored in several papers [12][13][14][15][16][17][18][19] and experimentally measured by the CMS Collaboration [20]. While an event-by-event determination of the azimuthal distribution of particles, and thus of the flow harmonics V n (p T ), is severely hindered by the limited number of particles, a covariance matrix reflecting correlations among different bins can be safely extracted from two-particle correlations.…”

“…Within this framework, it is possible to estimate how -and to what extent -anisotropic flow observables respond to initial-state fluctuations at different scales [8][9][10]. The purpose of the present paper is to investigate the connection between subleading modes of anisotropic flow fluctuations [11][12][13][14][15][16][17][18][19][20] and the aspects of the initial state of heavy-ion collisions, especially at smaller scales.…”

“…( 2), indicated by the spread of the blue squares in Fig. 1, might be experimentally studied through a principal component analysis (PCA) of anisotropic flow fluctuations [11][12][13][14][15][16][17][18][19][20]. In particular, we explore which features of the initial geometry are most relevant for understanding this analysis.…”

“…In Section II, we present the PCA of flow fluctuations to be employed in our analysis [18]. In Section III, we discuss a mapping of hydrodynamic response which extends Eq.…”