Principal-component analysis of two-particle azimuthal correlations in PbPb and pPb collisions at CMS

Abstract

For the first time a principle-component analysis is used to separate out different orthogonal modes of the two-particle correlation matrix from heavy ion collisions. The analysis uses data from √ s NN = 2.76 TeV PbPb and √ s NN = 5.02 TeV pPb collisions collected by the CMS experiment at the LHC. Two-particle azimuthal correlations have been extensively used to study hydrodynamic flow in heavy ion collisions. Recently it has been shown that the expected factorization of two-particle results into a product of the constituent single-particle anisotropies is broken. The new information provided by these modes may shed light on the breakdown of flow factorization in heavy ion collisions. The first two modes ("leading" and "subleading") of two-particle correlations are presented for elliptical and triangular anisotropies in PbPb and pPb collisions as a function of p T over a wide range of event activity. The leading mode is found to be essentially equivalent to the anisotropy harmonic previously extracted from two-particle correlation methods. The subleading mode represents a new experimental observable and is shown to account for a large fraction of the factorization breaking recently observed at high transverse momentum. The principle-component analysis technique has also been applied to multiplicity fluctuations. These also show a subleading mode. The connection of these new results to previous studies of factorization is discussed.

pT -dependent particle number fluctuations from principal-component analyses in hydrodynamic simulations of heavy-ion collisions

“…We also have some data accumulated for two centrality windows (0-5 and 20-30%) at √ s = 2.76 TeV and their compatibility with flow observables more subtly related to fluctuations (scaled harmonic flow distributions, factorization breaking ratio) has been tested [30]. This code is therefore an interesting tool for a first investigation of the PCA results obtained recently by CMS at the LHC [17].…”

“…To get more detailed information on fluctuations in the initial state, a useful observable is the factorization breaking ratio [7][8][9][10][11][12][13], which encodes the correlations of flow harmonics at different transverse momenta or pseudorapidities. More recently a new more precise tool was proposed, the Principal Component Analysis (PCA) for event-by-event fluctuations [14][15][16] and first experimental results for such an analysis have been presented by the CMS collaboration [17]. The aim of this paper is to present a hydrodynamical study of these observables and point out an interesting difference between data and some hydrodynamic simulations for the n = 0 leading and sub-leading components, corresponding to multiplicity fluctuations.…”

Measuring momentum-dependent flow fluctuations in heavy-ion collisions

“…We shall show that momentum-dependent multiplicity fluctuations have startling consequences for the n = 0 PCA of Refs. [13,18]. n .…”

“…The importance of multiplicity fluctuations to the standard PCA of flow fluctuations is a result of the remarkable sensitivity of the subleading PCA mode, the small size of the actual subleading flow V (2) n and, of course, the choice of the covariance matrix of Eq. (9) in [13,18]. Since particle number fluctuations can be measured separately and directly, they represent a redundant and unwanted background to principal component analyses of anisotropic flow.…”

“…displays PCA data from the CMS collaboration, obtained using Eqs. (9) and (10)[18]. The solid curves are the measured subleading PCA modes of the elliptic and triangular flow, while the dashed ones represent the combination V…”