What have we learned from Anisotropic Flow at RHIC ?

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What have we learned from Anisotropic Flowat
RHIC ?

• Hiroshi Masui
• for the PHENIX Collaboration
• 2006 RHIC AGS Annual Users meeting
• June 5 9, 2006 at Brookhaven National
  Laboratory
• Workshop 8 How perfect is this matter ?

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Perfect liquid at RHIC

• Strong collective flow, nearly perfect liquid

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Definitions
Py
Pz
Z
Px
Reaction plane
Y
X

• Anisotropic Flow
• Azimuthal correlation to reaction plane
• Elliptic flow (v2)

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Outline

• Elliptic Flow and Hydrodynamics
• PHENIX experiment
• Particle identification, event plane
• Eccentricity scaling and speed of sound
• Kinetic energy (Hydro) scaling and Partonic
  collectivity
• Summary

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v2 and hydrodynamics
PHENIX PRL 91, 182301 (2003)
D. Teaney PRC 68, 034913 (2003)

• Large elliptic flow at RHIC
• Elliptic flow is well described by hydrodynamics
• Magnitude, particle type up to pT 1.5 GeV/c
• Indicate early thermalization ? lt 1 fm/c,
  extremely low viscosity lt 0.1

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PHENIX experiment

• Hadron identification
• Time-of-Flight
• ? lt 0.35, ? lt ?/4
• EM Calorimeter
• ? lt 0.35, ? lt ?/2
• Event plane
• Beam Beam Counter, 3 lt ? lt 3.9, full azimuth

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Hadron identification

• Time-of-flight
• ? lt ?/4, ? lt 0.35
• Timing resolution 120 ps
• ?/K separation 2 GeV/c
• K/p separation 4 GeV/c
• Good timing resolution

• EM Calorimeter
• ? lt ?/2, ? lt 0.35
• Timing resolution 400 ps
• ?/K separation 1 GeV/c
• K/p separation 2 GeV/c
• Large acceptance

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Event plane _at_ 3lt?lt4

• Large rapidity gap
• Central arm ? lt 0.35 BBC 3 lt ? lt
  4
• Smaller non-flow contribution

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v2 from ideal fluid dynamics
cs 1/?3 t0 0.6 fm/c
b 8 fm
transverse size of system
R. S. Bhalerao, J.P. Blaizot, N. Borghini, J.-Y.
Ollitrault, PLB 627, 49, (2005)

• v2 scales initial eccentricity (?)
• v2/? is independent on system size R
• v2 grows with cs
• Can we test these relations from the data ?

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Can we test eccentricity scaling of v2 ?

• Does v2 scale eccentricity ?
• Centrality dependence of v2/?
• Is v2/? independent of system size ?
• AuAu vs CuCu
• Estimate of speed of sound can be made from the
  measurement of v2/?

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Eccentricity and integrated v2

• Eccentricity is usually estimated by Glauber
  Model
• Integrated v2 is proportional to eccentricity
• Advantage of integrated v2
• Reduce large systematic error from Glauber MC,
  typically 20 30
• Cancel systematic error from event plane
  determination

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Eccentricity scaling
PHENIX PRELIMINARY
k 3.1 obtained from data

• Scaling holds for a broad range of centrality
• Centrality 30 -40 , b 8.7 fm
• Independent of system size

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Estimate of cs
v2/? _at_ ltpTgt 0.45 GeV/c
NOTE v2 value is typically factor 2 lager than

• Cs 0.35 ? 0.05
• Indicate softer EOS compared to cs1/?3
• v2/? 0.1 (peripheral) 0.2 (central) at STAR
  and PHOBOS
• Integrated v2 does not develop so much in the
  late hadronic stage

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Kinetic energy scaling
M. Issah, A. Taranenko, nucl-ex/0604011
K0S, ? (STAR) PRL 92, 052302 (2004) ? (STAR)
PRL 95, 122301 (2005) ?, K, p (PHENIX)
preliminary
Meson v2
Baryon v2
Kinetic energy of a particle in a relativistic
fulid KET mT m0 at y 0
Hadron mass

• Kinetic energy scaling works up to KET 1 GeV
• Indicate hydrodynamic behavior
• Possible hint of quark degrees of freedom at
  higher KET

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What can we learn from identified hadrons ?

• NCQ (Number of Constituent Quark) scaling of v2
  indicate partonic collectivity at RHIC
• ? meson is a good probe to test NCQ scaling
• No re-scattering in hadronic stage
• Longer life time 40 fm/c
• Thermal s-quark coalesce/recombine to form ? meson

QM2005, M. Oldenburg, STAR
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Clear ? signal

• ? ? KK-
• Typical S/N 0.3
• Centrality 20 60
• S/N is good
• Event plane resolution is good
• Separation of v2 between meson and baryon is good
• Magnitude of v2 do not vary very much

Before subtraction
Signal Background
Background
After subtraction
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? Meson v2
N. Borghini, J.-Y. Ollitrault, PRC 70, 064905
(2004)

• Obtained from invariant mass fit method
• Consistent with standard subtraction method
• Smaller systematic error
• pT lt 2 GeV/c
• Consistent with mass ordering from hydrodynamics

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Partonic Collectivity (i)
Hydro. (KET) scaling
Hydro. Nquark scaling
SQM2006, S. Blyth, STAR

• Hydro NCQ scaling works for ? meson
• STAR result favors NCQ2 for ?
• Consistent with other multi-strange hadrons (?,
  ?) from STAR
• ? Collective flow of s-quark

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Partonic Collectivity (ii)
PHENIX PRELIMINARY
WWND 2006, M. Issah
SQM2006, S. Esumi
Data QM2005, PHENIX
K0S, ? (STAR) PR 92, 052302 (2004) ? (STAR)
PRL 95, 122301 (2005) ? (STAR) preliminary
STAR preliminary 0-80 AuAu 200GeV Yan Lu
SQM05 P. Sorensen SQM05 M. Oldenburg QM05
K0S ? ? ?

• Hydro NCQ scaling describes v2 for a variety of
  particles measured at RHIC
• Scaling breaks for higher pT

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Summary

• What have we learned from anisotropic flow
  hydrodynamics at RHIC ?
• Strongly interacting partonic matter
• Large v2 ? Early thermalization, ? lt 1 fm/c
• v2 scales eccentricity, independent of system
  size (Au, Cu)
• Estimated speed of sound 0.35 ? 0.05
• Partonic Collectivity
• Kinetic energy NCQ scaling works for a broad
  set of particles
• What more can be learned ?
• Centrality, energy dependence of v2
• v4/(v2)2 as a probe for degree of thermalization
• PHENIX talks in this session
• 225 PM S. Sakai, heavy flavor electron v2
• 420 PM J. Newby, HBT

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Thank you
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Back up
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v2/?, STAR, PHOBOS
v2/?part
v2/?
CIPANP 2006, S. Voloshin, STAR QM2005, S. Manly,
PHOBOS

• v2/? 0.1 0.2