What have we learned
from Anisotropic Flowat RHIC ?
Hiroshi Masui
for the PHENIX Collaboration
2006 RHIC & AGS Annual User’s meeting
June 5 – 9, 2006 at Brookhaven National Laboratory
Workshop 8 : How perfect is this matter ?

Hiroshi Masui / University of Tsukuba

1“Perfect liquid” at RHIC

• Strong collectiveflow, nearly perfectliquid
Hiroshi Masui / University of Tsukuba

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Definitions
Py

PzPx

ReactionplaneZYX• Anisotropic Flow
– Azimuthal correlation to reaction plane– Elliptic flow (v2)
Hiroshi Masui / University of Tsukuba3Outline• Elliptic Flow and Hydrodynamics• PHENIX experiment– Particle identification, event plane• Eccentricity scaling and speed of sound• Kinetic energy (Hydro) scaling andPartonic collectivity• SummaryHiroshi Masui / University of Tsukuba

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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 τ < 1 fm/c, extremely lowviscosity < 0.1
Hiroshi Masui / University of Tsukuba

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PHENIX experiment• Hadronidentification– Time-of-Flight• |η| < 0.35, |φ| <π/4

– EM Calorimeter• |η| < 0.35, |φ| <π/2

• Event plane– Beam Beam
Counter, 3 < |η| <3.9, full azimuth
Hiroshi Masui / University of Tsukuba

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Hadron identification• Time-of-flight• EM Calorimeter– |φ| < π/4, |η| < 0.35
– Timing resolution ~ 120 ps– |φ| < π/2, |η| < 0.35
– Timing resolution ~ 400 ps• π/K separation ~ 2 GeV/c• K/p separation ~ 4 GeV/c• π/K separation ~ 1 GeV/c• K/p separation ~ 2 GeV/c• Good timing resolution• Large acceptance

Hiroshi Masui / University of Tsukuba

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Event plane @ 3<|η|<4• Large rapidity gap– Central arm |η| < 0.35
BBC 3 < |η| < 4– Smaller non-flow contribution
Hiroshi Masui / University of Tsukuba

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v2 from ideal fluidd yn a m i c scs = 1/√3
t0 = 0.6 fm/c

b = 8 fmtransverse size of system••••

R. S. Bhalerao, J.P. Blaizot, N. Borghini, J.-Y. Ollitrault,
PLB 627, 49, (2005)

v2 scales initial eccentricity (ε)
v2/ε is independent on system size R
v2 grows with cs
Can we test these relations from the data ?
Hiroshi Masui / University of Tsukuba

9Can we test eccentricity
scaling of v2 ?
• Does v2 scale eccentricity ?
– Centrality dependence of v2/ε

• Is v2/ε independent of system size ?
– Au+Au vs Cu+Cu• Estimate of speed of sound can be madefrom the measurement of v2/εHiroshi Masui / University of Tsukuba

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Eccentricity andintegrated v2• Eccentricity is usually estimated byGlauber 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

Hiroshi Masui / University of Tsukuba

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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
Hiroshi Masui / University of Tsukuba

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Estimate of csv2/ε @ <pT> ~ 0.45 GeV/c

NOTEv2 value is typically factor 2lager than• Cs = 0.35 ± 0.05
– Indicate softer EOS compared to cs=1/√3– v2/ε ~ 0.1 (peripheral) – 0.2 (central) at
STAR and PHOBOS– Integrated v2 does not develop so much in
the late hadronic stage
Hiroshi Masui / University of Tsukuba

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Kinetic energy scaling
Meson v2

K0S, Λ (STAR) : PRL 92, 052302(2004)

Baryon v2

Ξ (STAR) : PRL 95, 122301 (2005)

M. Issah, A. Taranenko, nucl-ex/0604011

π, K, p (PHENIX) : preliminary* Kinetic energy of a particle
in a relativistic fulid
KET ~ mT – m0 at y ~ 0Hadron mass

• Kinetic energy scaling works up to KET ~ 1 GeV– Indicate hydrodynamic behavior• Possible hint of quark degrees of freedom at higher KET
Hiroshi Masui / University of Tsukuba

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What can we learn
from identified hadrons ?
• NCQ (Number ofConstituent Quark)scaling of v2 indicate
partonic collectivity atRHIC• φ meson is a good probe
to test NCQ scaling– No re-scattering inhadronic stage– Longer life time ~ 40 fm/c– Thermal s-quark
coalesce/recombine toform φ meson
QM2005, M. Oldenburg, STARHiroshi Masui / University of Tsukuba

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Clear φ signal• φ Æ K+K– Typical S/N ~ 0.3
Before subtraction
Signal + Background
Background

After subtraction• Centrality 20 –60 %– S/N is good
– Event plane
resolution is good
– Separation of v2
between meson andbaryon is good
– Magnitude of v2 do
not vary very much

Hiroshi Masui / University of Tsukuba

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φ 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 < 2 GeV/c– Consistent with mass ordering from hydrodynamics
Hiroshi Masui / University of Tsukuba

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Partonic Collectivity (i)Hydro. (KET) scaling

SQM2006, S. Blyth, STAR

Hydro. + Nquark scaling• Hydro + NCQ scaling works for φmeson– STAR result favors NCQ=2 for φ– Consistent with other multi-strange
hadrons (Ω, Ξ) from STARÆ Collective flow of s-quark

Hiroshi Masui / University of Tsukuba

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Partonic Collectivity (ii)
PHENIX PRELIMINARY

WWND 2006, M. IssahSQM2006, S. Esumi

Data :QM2005, PHENIX

K0S, Λ (STAR) : PR 92, 052302 (2004)
Ξ (STAR) : PRL 95, 122301 (2005)
φ (STAR) : preliminary• Hydro + NCQ scaling
describes v2 for a variety ofparticles measured at RHIC

K0S

ΛΞ

Ω

STAR preliminary
0-80% Au+Au 200GeV
Yan Lu SQM05
P. Sorensen SQM05
M. Oldenburg QM05

– Scaling breaks for higher pT
Hiroshi Masui / University of Tsukuba

19Summary• What have we learned from anisotropic flow +hydrodynamics at RHIC ?
• Strongly interacting partonic matter– Large v2 Æ Early thermalization, τ < 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– 2:25 PM : S. Sakai, heavy flavor electron v2– 4:20 PM : J. Newby, HBT
Hiroshi Masui / University of Tsukuba20

Thank you

Hiroshi Masui / University of Tsukuba

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Hiroshi Masui / University of Tsukuba22

v2/ε, STAR, PHOBOS
v2/εpartv2/ε

CIPANP 2006, S. Voloshin, STAR
QM2005, S. Manly, PHOBOS• v2/ε ~ 0.1 – 0.2

Hiroshi Masui / University of Tsukuba

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