System Size and Centrality Dependence of Strange Hadron Elliptic Flow

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System Size and Centrality Dependence of Strange
Hadron Elliptic Flow

• Yan Lu
• University of Science and Technology of China
• Collaborated with
• S. Shi (IOPP/LBL), F. Liu (IOPP)
• A. Tang (BNL), N. Xu (LBL)

Many thanks to X-N Wang, D. Zhou and the
organizer.
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Outline

• Introduction and motivation
• Number-of-quark scaling --- partonic flow
• Thermalization and hydrodynamic limit
• STAR experiment
• Results and discussion
• System size and centrality dependence
• Ideal hydrodynamic limit with transport
  model approach
• Summary

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Hydrodynamic flow

• In high-energy nuclear collisions, interaction
  among constituents and density distribution will
  lead to
• pressure gradient ? collective flow
• Pressure gradient only depends on the density
  gradient and interactions
• No thermalization is needed. Enough
  interactions will lead to (local) thermalization.

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NQ scaling - partonic flow

• Mass ordering of v2
• collective flow
• Sizable v2 for multi-strange hadrons
• small hadronic cross section
• Number of Quark (NQ) scaling
• vs (mT - mass)/nq
• Partonic collectivity
• Deconfinement

H. Masui, ATHIC2008
PHENIX Phys. Rev. Lett. 98, 162301 (2007) STAR
Phys. Rev. Lett. 99, 112301 (2007),
Phys. Rev. C77, 054901 (2008) Hydro results Pasi
Huovinen, private communication P. Huovinen and
P. V. Ruuskanen, Annu. Rev. Nucl. Part. Sci. 56,
133 (2006)
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Thermalization and hydro limit?
S. Voloshin, QM2006
Ideal hydro curves for b 7 fm in Pb Pb
collisions show little sensitivity to centrality.
Data S. Voloshin, nucl-ex/ 0701038 Hydro Kolb,
Sollfrank, Heinz, PRC 62 (2000) 054909
Is thermalization and ideal hydrodynamic limit
reached at RHIC?
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Transport model approach

• Knudsen number
• degrees of equilibration
• Reach hydro limit when K -gt 0
• Transport model results (symbols) can be
  reproduced by the formula below
• K0 0.7, cs2 1/3

hydro limit
v2
Knudsen number K
C. Gombeaud and J.-Y. Ollitrault, PRC77, 054904
(2008)
s parton cross section cs speed of sound S
transverse area (obtained by Glauber MC)
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Extract hydro limit with PID
Extract hydro limit with v2 of (multi-)strange
hadron to connect partonic collectivity to
hydrodynamic flow limit.
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STAR detector

• TPC dE/dx PID pion/kaon pT 0.6 GeV/c
  proton pT 1.2 GeV/c
• Acceptance full azimuthal coverage
  pseudo-rapidity coverage ? lt 1
• Designed for resonance reconstruction,
  event-wise correlations.

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STAR experimental

• Large acceptance
• Main TPC ? lt 1, full azimuth
• K0S, ?, ? 0.2 lt pT lt 4 GeV/c
• Cu Cu at 200 GeV
• 24 M events
• Centrality 0 - 60
• 0 - 20 and 20 - 60
• Event plane
• Forward TPC, 2.5 lt ? lt 4
• Rapidity gap could reduce non-flow effects

multiplicity ? collision centrality
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Particle identification

• Reconstructed by weak decay topology
• Daughter hadrons are identified by dE/dx in TPC
• Signal to background ratio 3 - 20

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pT dependence
Ideal hydro from Pasi Huovinen, private
communication Tc 170 MeV, Tf 125 MeV, first
order phase transition, EOS Q

• Below pT 2 GeV/c, smaller v2 for heavier
  hadrons
• Above pT 2 GeV/c
• v2(?) gt v2(K0S)
• Sizable v2(?)
• Ideal hydro fails to
• reproduce centrality
• dependence
• Fluctuation of v2?
• Viscosity ?
• Incomplete thermalization ?

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Number-of-quark scaling

• Number of Quark (NCQ) scaling works well in all
  centrality bins
• Partonic flow !

D. Molnar and S. Voloshin, PRL91, 092301
(2003) R. J. Fries et. al., PRC68, 044902
(2003) V. Greco et. al, PRC68, 034904 (2003) J.
Jia and C. Zhang, PRC75, 031901(R) (2007)...
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Centrality dependence

• Stronger collective flow in more central
  collisions
• Similar centrality dependence in different
  systems

Au Au PRC77, 054901 (2008)
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Energy dependence

• v2 in Cu Cu (Au Au) at 200 and 62.4 GeV are
  consistent within statistical errors

v2 at Cu Cu 62.4 GeV 12.5 M events - Same
procedure used for 200 GeV. - Event plane
resolution is 0.088 0.004 in 0 - 60 , about
factor 2 smaller than that in 200 GeV due to
lower multiplicity.
STAR Au Au 200 GeV PRC77, 054901 (2008)
Au Au 62.4 GeV PRC75, 054906 (2007)
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System Size Dependence I

• Stronger collective flow in larger system

Au Au PRC77, 054901 (2008)
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System Size Dependence II

• Stronger collective flow in more central
  collisions.
• Similar flow pattern in similar Npart between Au
  Au and Cu Cu.
• v2 v2(e, Npart)

Does v2 at most central reach ideal hydrodynamic
limit ?
Au Au PRC77, 054901 (2008)
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v2/? vs. transverse density

• Ideal hydro v2/e
• e from optical glauber model
• Simultaneous fit well describe the data with the
  same scs
• Fitting hydro limits (arrows) increase as a
  function of mass

Au Au K0S, ? Phys. Rev. C77, 054901
(2008) Ideal Hydro. P. Huovinen and P. V.
Ruuskanen, Annu. Rev. Nucl. Part. Sci. 56, 163
(2006) and private communication
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Ideal Hydrodynamic Limit

• Universal curve
• Hydrodynamic limit has not been reached at RHIC
  within the transport model approach

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Summary

• Elliptic flow (v2) for K0S, ? and ? have been
  measured in Cu Cu 200 GeV at STAR
• Heavier hadrons have smaller v2 in pT lt 2 GeV/c
• Baryon/meson effect in pT gt 2 GeV/c v2(K0S) lt
  v2(?), sizable v2(?)
• Ideal hydro failed to reproduce centrality and mT
  - mass dependence of v2
• v2 at 62.4 GeV is consistent with that at 200 GeV
  in Cu Cu collisions
• Number of constituent Quark (NCQ) scaling of v2
• Strange hadrons follow the NCQ scaling in Cu Cu
  ? Partonic flow
• Centrality dependence of v2/e in Au Au Cu
  Cu 200 GeV
• Stronger collective flow for more central
  collisions
• Transport model fit with finite Knudsen number
• Hydrodynamic limit has not been reached at RHIC
  within the transport model approach

Coming LHC will give the answer!
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• Thanks!