1. 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
Providence RI, August 9-13, 2011 1

2. 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
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3. 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)
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4. 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
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5. 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
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6. 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.
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7. 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
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8. 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
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9. DPF@Brown, Providence RI, August 9-13, 2011
Comparison with ALICE
n = 2
CMS Collaboration:
Physics Analysis Summary,
ALICE Collaboration,
Phys. Rev. Lett., 105, (2011)
CMS cumulant measurements compare well with ALICE
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10. 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
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11. 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.
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12. Collision Energy Dependence of v2
Integrated v2 increases from RHIC to LHC
Reflects both an increase in <pT> and an increase in v2
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13. 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
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14. Comparison of v2/εpart with RHIC
Moderate increase from RHIC to LHC
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15. 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
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16. Closer Inspection of v2 Rapidity Dependence
PRC72: (2005)
Shape evolution with centrality apparent
Similar to observation by PHOBOS
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17. Triangular Flow: v3(pT) for |η| ≤ 0.8
CMS Collaboration:
Physics Analysis Summary,
v3 exhibits weak centrality dependence, driven by fluctuations
Non-flow effects evident in peripheral collisions
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18. 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
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19. v4 and v6 from LYZ Method for |η| ≤ 0.8
v6 increases from central to peripheral collisions
Reaches ~6% in centrality 40-45%
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20. Fifth Order Flow: v5(pT) for |η| ≤ 0.8
B. Alver et al. PRC82: , 2010
(RHIC, centrality 0-5%)
v5 rises quadratically with pT
Similar trend to hydro predictions with small η/s
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21. 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
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22. 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
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23. DPF@Brown, Providence RI, August 9-13, 2011
v4/v22
PHENIX (PRL 105, (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: )
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24. 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
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25. DPF@Brown, Providence RI, August 9-13, 2011
Backup Slides
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26. 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:
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27. Details of the Cumulant Method
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28. 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
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