Principal Component Analysis of Event-by-Event Fluctuations.

We apply principal component analysis to the study of event-by-event fluctuations in relativistic heavy-ion collisions. This method brings out all the information contained in two-particle correlations in a physically transparent way. We present a guide to the method, and apply it to multiplicity fluctuations and anisotropic flow, using ALICE data and simulated events. In particular, we study elliptic and triangular flow fluctuations as a function of transverse momentum and rapidity. This method reveals previously unknown subleading modes in both rapidity and transverse momentum for the momentum distribution as well as elliptic and triangular flows.

[1]  U. Heinz,et al.  Fluctuating flow angles and anisotropic flow measurements , 2013, 1302.3535.

[2]  S. Voloshin,et al.  Flow analysis with cumulants: Direct calculations , 2010, 1010.0233.

[3]  M. Luzum,et al.  Eliminating experimental bias in anisotropic-flow measurements of high-energy nuclear collisions , 2012, 1209.2323.

[4]  P. Bożek,et al.  Torqued fireballs in relativistic heavy-ion collisions , 2010, 1011.3354.

[5]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[6]  Xin-Nian Wang,et al.  Hadron production in p+p, p+Pb, and Pb+Pb collisions with the hijing 2.0 model at energies available at the CERN Large Hadron Collider , 2010, 1008.1841.

[7]  G. Odyniec,et al.  Transverse momentum analysis of collective motion in relativistic nuclear collisions , 1985, 2109.05308.

[8]  K. Gulbrandsen,et al.  Generic framework for anisotropic flow analyses with multiparticle azimuthal correlations , 2013, 1312.3572.

[9]  L. Pang,et al.  Effects of initial flow velocity fluctuation in event-by-event (3+1)D hydrodynamics , 2012, 1205.5019.

[10]  L. Csernai,et al.  Longitudinal fluctuations of the center of mass of the participants in heavy-ion collisions , 2013, 1306.5208.

[11]  James S. Harris,et al.  Harmonic decomposition of two-particle angular correlations in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV , 2011, 1109.2501.

[12]  Analysis of anisotropic flow with Lee-Yang zeroes , 2003, nucl-th/0310016.

[13]  C. Henderson,et al.  Non-flow correlations and elliptic flow fluctuations in Au+Au collisions at sq root(s{sub NN})=200 GeV , 2010 .

[14]  Flow analysis from multiparticle azimuthal correlations , 2001, nucl-th/0105040.

[15]  M. Luzum,et al.  Breaking of factorization of two-particle correlations in hydrodynamics , 2012, 1211.0989.

[16]  M. Luzum.  Collective flow and long-range correlations in relativistic heavy ion collisions , 2010, 1011.5773.

[17]  Saclay,et al.  New method for measuring azimuthal distributions in nucleus-nucleus collisions , 2000, nucl-th/0007063.

[18]  S.Manly,et al.  Importance of correlations and fluctuations on the initial source eccentricity in high-energy nucleus-nucleus collisions , 2007, 0711.3724.

[19]  Bin Zhang,et al.  Multiphase transport model for relativistic heavy ion collisions , 2005 .

[20]  V. M. Ghete,et al.  Measurement of higher-order harmonic azimuthal anisotropy in PbPb collisions at s NN =2.76 TeV , 2014 .

[21]  A. Bzdak,et al.  Longitudinal fluctuations of the fireball density in heavy-ion collisions , 2012, 1210.1965.

[22]  Gunther Roland,et al.  Collision-geometry fluctuations and triangular flow in heavy-ion collisions , 2010, 1003.0194.

[23]  J. Ollitrault,et al.  Effects of flow fluctuations and partial thermalization on v(4) , 2009, 0907.4664.

[24]  Momentum spectra, anisotropic flow, and ideal fluids , 2005, nucl-th/0506045.

[25]  C. Henderson,et al.  System size, energy, pseudorapidity, and centrality dependence of elliptic flow. , 2006, Physical review letters.

[26]  A.M.Poskanzer,et al.  Methods for analyzing anisotropic flow in relativistic nuclear collisions , 1998, nucl-ex/9805001.

[27]  S. Jeon,et al.  HYDRODYNAMIC MODELING OF HEAVY-ION COLLISIONS , 2013, 1301.5893.

[28]  R. Snellings,et al.  Collective Flow and Viscosity in Relativistic Heavy-Ion Collisions , 2013, 1301.2826.

[29]  W. Xie,et al.  Decomposition of flow and nonflow in relativistic heavy-ion collisions , 2012, 1204.2815.

[30]  K. J. Foley,et al.  Elliptic flow from two-and four-particle correlations in Au ¿ Au collisions at A sNN Ä 130 GeV , 2002 .

[31]  Heng Tao Shen,et al.  Principal Component Analysis , 2009, Encyclopedia of Biometrics.

[32]  G. Roland,et al.  Erratum: Collision-geometry fluctuations and triangular flow in heavy-ion collisions [Phys. Rev. C 81, 054905 (2010)] , 2010 .

[33]  M. Luzum.  Flow fluctuations and long-range correlations: elliptic flow and beyond , 2011, 1107.0592.