Hydrodynamic Flow in Pb + Pb Collisions Observed by the CMS Experiment via Azimuthal Correlations of Charged Hadrons Charles F. Maguire for the CMS Collaboration Version v1 12:30 PM CDT July 29 DPF@Brown, Providence RI, August 9-13, 2011 1

DPF@Brown, Providence RI, August 9-13, 2011 Motivation anisotropic flow coefficients v2 has been extensively studied, and to a lesser extent v4 and v6 v3 and v5 were surprisingly found to be non-negligible An understanding all the harmonics will provide new insights on the properties of the quark-gluon-plasma “near-perfect” liquid CMS has measured vn , with n = 2 - 6, in PbPb collisions at √sNN = 2.76 TeV using two-particle and multi-particle techniques Non-flow effects such as resonance decays and jets will complicate the hydrodynamic analysis of the particle correlations DPF@Brown, Providence RI, August 9-13, 2011 2

A Closer Look at Anisotropic Flow Schematic of a heavy ion collision: Analogous system: A strongly-interacting degenerate fermi-gas of atoms. Initial State Position Anisotropy impact parameter Fourier decompose the azimuthal angle of the particle emission spectrum with respect to the reaction plane: Second Fourier coefficient n=2 quantifies the particle emission “in-plane” versus “out-of plane” Final State Momentum Anisotropy Measuring the v2 coefficient can constrain hydrodynamic and transport properties of the hot and dense medium produced in the collision. K. M. O'Hara et.al, Science, 298, 2179 (2002) DPF@Brown, Providence RI, August 9-13, 2011 3

Detectors Used in Flow Analysis Minimum Bias Trigger and Centrality Determination 3.8 T Magnet BSC and HF Detectors Silicon Pixel and Strip Detectors Tracking and Event Plane Reconstruction CASTOR HCAL ECAL Muon Detectors DPF@Brown, Providence RI, August 9-13, 2011 4

Centrality Determination Tight correlation between # of pixels fired and sum of energy in HF Centrality determined from total energy in HF After trigger selection and vertex cuts, total number of min bias events ~ 2.3M Future event samples will contain an order of magnitude more MB events DPF@Brown, Providence RI, August 9-13, 2011 5

DPF@Brown, Providence RI, August 9-13, 2011 Tracking CMS Inner Tracker comprises: Pixel detector (65M pixels) Silicon strip detector (10M silicon strips) from Hydjet η ≤ ± 2.5 Tracks with pT > 0.9 GeV/c reconstructed using both the silicon strip and pixel detectors Second tracking iteration used “pixel-only” tracks down to pT ~ 0.2 GeV/c Two iterations merged, using only “full” tracks with a pT above 1.5 GeV/c, and using “pixel-only” tracks below 1.8 GeV/c. In the process, duplicate tracks are removed. DPF@Brown, Providence RI, August 9-13, 2011 6

Four Methods Used for Extracting v2 Signal Event Plane based on particle correlations with the event plane gives an estimate of the reaction plane requires corrections for the detector acceptance 4th Order Cumulant based on 4-particle correlations removes lower order non-flow effects Lee-Yang Zeros based on all particle correlations in each event removes non-flow effects ... 2nd Order Cumulant based on 2-particle correlations Higher order harmonics up to v6 were measured using select methods: n = 5 n = 2 n = 3 n = 6 DPF@Brown, Providence RI, August 9-13, 2011 7

v2(pT) at Mid-Rapidity for |η| ≤ 0.8 0-20% n = 2 20-40% .. 40-80% Values of v2(pT) from different methods are compatible with the effects of non-flow and fluctuations DPF@Brown, Providence RI, August 9-13, 2011 8

DPF@Brown, Providence RI, August 9-13, 2011 Comparison with ALICE n = 2 CMS Collaboration: Physics Analysis Summary, http://cdsweb.cern.ch/record/1347788 ALICE Collaboration, Phys. Rev. Lett., 105, 252302 (2011) CMS cumulant measurements compare well with ALICE DPF@Brown, Providence RI, August 9-13, 2011 9

Centrality Dependence of v2 Centrality dependence shows two groups of curves compatible with the influence of non-flow and fluctuations v2{2} consistent with AMPT model predictions DPF@Brown, Providence RI, August 9-13, 2011 10

Centrality Dependence Comparison with ALICE Apply same pT and η cuts for CMS data as in ALICE Good agreement of v2{2}, v2{4} and v2{LYZ} between CMS and ALICE, with differences appearing in most peripheral collisions. DPF@Brown, Providence RI, August 9-13, 2011 11

Collision Energy Dependence of v2 Integrated v2 increases from RHIC to LHC Reflects both an increase in <pT> and an increase in v2 DPF@Brown, Providence RI, August 9-13, 2011 12

DPF@Brown, Providence RI, August 9-13, 2011 v2 (εpart) If matter is fully equilibrated, then v2 will scale with εpart v2 is linear with εpart up to εpart ~ 0.3 and then decreases for peripheral collisions since hydrodynamic model no longer applies DPF@Brown, Providence RI, August 9-13, 2011 13

Comparison of v2/εpart with RHIC Moderate increase from RHIC to LHC DPF@Brown, Providence RI, August 9-13, 2011 14

Rapidity Dependence of v2 Similar to the pT dependence, two groups of curves emerge A convex shape for v2(η) develops with decreasing centrality Input to hydro models of the longitudinal expansion of medium DPF@Brown, Providence RI, August 9-13, 2011 15

Closer Inspection of v2 Rapidity Dependence PRC72: 051901 (2005) Shape evolution with centrality apparent Similar to observation by PHOBOS DPF@Brown, Providence RI, August 9-13, 2011 16

Triangular Flow: v3(pT) for |η| ≤ 0.8 CMS Collaboration: Physics Analysis Summary, http://cdsweb.cern.ch/record/1361385 v3 exhibits weak centrality dependence, driven by fluctuations Non-flow effects evident in peripheral collisions DPF@Brown, Providence RI, August 9-13, 2011 17

Fourth Order Flow: v4(pT) for |η| ≤ 0.8 The magnitudes of v4 from three different estimates (v4{3}, v4{5} and v4{LYZ} ) are similar DPF@Brown, Providence RI, August 9-13, 2011 18

v4 and v6 from LYZ Method for |η| ≤ 0.8 v6 increases from central to peripheral collisions Reaches ~6% in centrality 40-45% DPF@Brown, Providence RI, August 9-13, 2011 19

Fifth Order Flow: v5(pT) for |η| ≤ 0.8 B. Alver et al. PRC82: 034913, 2010 (RHIC, centrality 0-5%) v5 rises quadratically with pT Similar trend to hydro predictions with small η/s DPF@Brown, Providence RI, August 9-13, 2011 20

The Full Harmonic Spectrum εn : Glauber participant eccentriciy Even harmonics have similar centrality dependence v3 has weaker centrality dependence, finite for central collisions v3/ε3 decreases from central to peripheral collisions DPF@Brown, Providence RI, August 9-13, 2011 21

DPF@Brown, Providence RI, August 9-13, 2011 v4/v22 Y. Bai (STAR) v4/v22 proposed as a probe of degree of thermalization Slight increase in the ratio when comparing similar estimates from RHIC and LHC Value of v4/v22 is method dependent, need to assess influence of non-flow and flow fluctuations DPF@Brown, Providence RI, August 9-13, 2011 22

DPF@Brown, Providence RI, August 9-13, 2011 v4/v22 PHENIX (PRL 105, 062301 (2010)) pT = 1.6 – 2.4 GeV/c v4/v22 appears larger than at RHIC for same pT cuts Ratio predicted to be higher at LHC (PRC81: 054910) DPF@Brown, Providence RI, August 9-13, 2011 23

DPF@Brown, Providence RI, August 9-13, 2011 Summary CMS has measured of vn , n = 2-6, in PbPb collisions at √sNN = 2.76 TeV over a broad pT and η range v2(pT) at mid-rapidity is comparable to the highest RHIC energy v2 exhibits weak η dependence for central and mid-central collisions, stronger dependence for peripheral collisions. v3 and v5 measurements consistent with being primarily generated by fluctuations Different centrality dependencies observed for odd and even harmonics v4/v22 seems larger than at RHIC More detailed study needed to disentangle non-flow and fluctuations More results on higher-order flow harmonics to come from CMS DPF@Brown, Providence RI, August 9-13, 2011 24

DPF@Brown, Providence RI, August 9-13, 2011 Backup Slides DPF@Brown, Providence RI, August 9-13, 2011 25

Details of the Event Plane Method Uses 3-subevent event plane resolution correction. A. M. Poskanzer and S. A. Voloshin, Phys. Rev. C58 (1998) 1671 - Standard flattening procedure to remove azimuthal detector asymmetries (21st order Fourier decomposition) E877 Collaboration, Phys. Rev. C56 (1997) 3254 1. Event Plane is Determined from the Azimuthal Correlations themselves: 3. Extracted v2 signal is corrected for the resolution: 2. Resolution correction factor is determined by splitting particles into three sub-events based on pseudorapidity: DPF@Brown, Providence RI, August 9-13, 2011 26

Details of the Cumulant Method DPF@Brown, Providence RI, August 9-13, 2011 27

Details of the Lee-Yang Zeros Method For each centrality, define the complex-valued Sum generating function : weight : , : fixed angle Then Integrated flow is : is first minimum of , Then Differential flow is : is a Bessel function of the first kind, with m=1 for v2 The LYZ method is less biased by non-flow correlations than other methods, less biased by auto-correlations, and less biased by detector asymmetry. A second Product generating function can be used in LYZ. It gives the same results for v2 DPF@Brown, Providence RI, August 9-13, 2011 28