Systematic Study of Elliptic Flowat RHIC-PHENIX

Maya SHIMOMURA for the PHENIX Collaborations
University of Tsukuba

September 11, DIFFRACTION 2008

Universidade de São Paulo, Instituto de Física, Caixa Postal 66318, São Paulo CEP05315-970, Brazil
Institute of Physics, Academia Sinica, Taipei 11529, Taiwan
China Institute of Atomic Energy (CIAE), Beijing, People's Republic of China
Peking University, Beijing, People's Republic of China
Charles University, Ovocnytrh 5, Praha 1, 116 36, Prague, Czech RepublicCzech Technical University, Zikova 4, 166 36 Prague 6, Czech Republic
Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2,
182 21 Prague 8, Czech Republic
Helsinki Institute of Physics and University of Jyväskylä, P.O.Box 35, FI-40014 Jyväskylä, Finland
Dapnia, CEA Saclay, F-91191, Gif-sur-Yvette, France
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route de Saclay,
F-91128, Palaiseau, France
Laboratoire de Physique Corpusculaire (LPC), Université Blaise Pascal, CNRS-IN2P3,
Clermont-Fd, 63177 Aubiere Cedex, France
IPN-Orsay, Universite Paris Sud, CNRS-IN2P3, BP1, F-91406, Orsay, France
SUBATECH (Ecole des Mines de Nantes, CNRS-IN2P3, Université de Nantes)
BP 20722 - 44307, Nantes, FranceInstitut für Kernphysik, University of Münster, D-48149 Münster, Germany
Debrecen University, H-4010 Debrecen, Egyetem tér 1, Hungary
ELTE, Eötvös Loránd University, H - 1117 Budapest, Pázmány P. s. 1/A, Hungary
KFKI Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Sciences (MTA KFKI RMKI),
H-1525 Budapest 114, POBox 49, Budapest, Hungary
Department of Physics, Banaras Hindu University, Varanasi 221005, India
Bhabha Atomic Research Centre, Bombay 400 085, India
Weizmann Institute, Rehovot 76100, Israel
Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo,
Tokyo 113-0033, Japan
Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan
KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan
Kyoto University, Kyoto 606-8502, Japan
Nagasaki Institute of Applied Science, Nagasaki-shi, Nagasaki 851-0193, JapanRIKEN, The Institute of Physical and Chemical Research, Wako, Saitama 351-0198, Japan
Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan
Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan
Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan
Waseda University, Advanced Research Institute for Science and Engineering, 17 Kikui-cho,Shinjuku-ku, Tokyo 162-0044, Japan
Chonbuk National University, Jeonju, Korea
Ewha Womans University, Seoul 120-750, Korea
KAERI, Cyclotron Application Laboratory, Seoul, South Korea
Kangnung National University, Kangnung 210-702, South Korea
Korea University, Seoul, 136-701, Korea
Myongji University, Yongin, Kyonggido 449-728, Korea
System Electronics Laboratory, Seoul National University, Seoul, South Korea
Yonsei University, IPAP, Seoul 120-749, Korea
IHEP Protvino, State Research Center of Russian Federation, Institute for High Energy Physics,
Protvino, 142281, Russia
Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia
Russian Research Center "Kurchatov Institute", Moscow, Russia
PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia
Saint Petersburg State Polytechnic University, St. Petersburg, Russia
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Vorob'evy Gory,
Moscow 119992, Russia
Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden

14 Countries; 69 Institutions

July 2007
Abilene Christian University, Abilene, TX 79699, U.S.
Collider-Accelerator Department, Brookhaven National Laboratory, Upton, NY 11973-5000, U.S.
Physics Department, Brookhaven National Laboratory, Upton, NY 11973-5000, U.S.
University of California - Riverside, Riverside, CA 92521, U.S.
University of Colorado, Boulder, CO 80309, U.S.
Columbia University, New York, NY 10027 and Nevis Laboratories, Irvington, NY 10533, U.S.
Florida Institute of Technology, Melbourne, FL 32901, U.S.
Florida State University, Tallahassee, FL 32306, U.S.
Georgia State University, Atlanta, GA 30303, U.S.
University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S.
Iowa State University, Ames, IA 50011, U.S.
Lawrence Livermore National Laboratory, Livermore, CA 94550, U.S.
Los Alamos National Laboratory, Los Alamos, NM 87545, U.S.
University of Maryland, College Park, MD 20742, U.S.
Department of Physics, University of Massachusetts, Amherst, MA 01003-9337, U.S.
Muhlenberg College, Allentown, PA 18104-5586, U.S.
University of New Mexico, Albuquerque, NM 87131, U.S.
New Mexico State University, Las Cruces, NM 88003, U.S.
Oak Ridge National Laboratory, Oak Ridge, TN 37831, U.S.
RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973-5000, U.S.
Chemistry Department, Stony Brook University, Stony Brook, SUNY, NY 11794-3400, U.S.
Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, NY 11794, U.S.
University of Tennessee, Knoxville, TN 37996, U.S.
Vanderbilt University, Nashville, TN 37235, U.S.

2

Contents
Introduction
QGP
RHIC-PHENIX
Elliptic Flow (v2)
Motivation

Results
Energy dependence
System size dependence
Universal v2

Conclusion
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Quark Gluon Plasma (QGP)
Phase diagram ; QGP & hadron

Prediction from Lattice QCD
T ~ 170 MeV
ε~ 1.0 GeV/fm3

Quarks become de-comfinedPhase transition to QGP* Normal Nucleus: ε ~ 0.2 GeV/fm3

High energy nuclear collision
Au+Au √s＝200GeV
RHIC : 5 ~ 15 GeV/fm3
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Relativistic Heavy Ion Collider (RHIC)
Brookhaven National Laboratory
First relativistic heavy ion collider in the world
Circumference 3.83 km、2 rings
Collision species (Au+Au, Cu+Cu, d+Au, p+p)
Energy (A+A); up to 100 GeV/nucleon
PHENIX is the one of the main experiment group

Time-evolution after collision
Thermalfreezeout

PHENIX Experiment

Chemicalfreezeout
hadronization
QGP
thermal equilibrium

collision
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Elliptic Flow (v2)
v2 is the strength of the elliptic anisotropy of produced particles.
A sensitive probe for studying properties of the hot dense matter made by heavy ion collisions.
Ｙ

non central collision

beam axiszφＹ

x (Reaction Plane)

ReactionplanexFourier expansion of the
distribution of produced
particle angle, Φ, to RP

v2 is the coefficient of the second term
→ indicates ellipticitydN= n {1 + 2 V2 cos [2( φ - Φ RP ) ]} If yield is (x direction)>(y direction), v >0.
2
dφ
The initial geometrical anisotropy is transferred by the pressure gradients into a
momentum space anisotropy Æ the measured v2 reflects the dense matterproduced in the collisions.
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Motivation
From the results at 200GeV
ｖ２ at low pT (< ~2 GeV/c) → can be explained by a hydro-dynamical modelｖ２ at mid pT (<4~6 GeV/c) → is consistent with recombination model
The results are consistent with Quark number +KET scaling.
PRL 91, 182301

PRL 98, 162301

How about other systems and energies !?
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KET = mT-m0

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Results
Energy dependence
System size dependence
Eccentricity scaling

Universal v2
Quark number + KET scaling
Universal scaling

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<words>
Npart --- Number of nucleons participating the collision
Ncoll --- Number of binary collisions
eccentricity(ε) --- geometirical eccentricity of participant nucleons

ε =y2 - x2
y2 + x2-Nucleus formed by wood-Saxon shape-Monte-Carlo simulation with Glauber model- Participant eccentricity which is calculated with long and shortaxis determined by distribution of participants at each collision.
ε vs. Npart

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Comparison Table
EnergyParticle
species

Size
SystemCentrality(CuCu, AuAu)

nq+KETscaling
AuAu 200
AuAu 62
CuCu 200
CuCu 62

Already known
Is going to check next
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Comparison Table
EnergyParticle
species

Size
SystemCentrality(CuCu, AuAu)

nq+KETscaling
AuAu 200
AuAu 62
CuCu 200
CuCu 62

Already known
Is going to check next
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Energy dependence
Comparison of√s = 62.4 and 200 GeV- dependence of centrality (Npart)- compare the results in Cu + Cu which issmaller collision size than Au+Au- comparison of PID hadrons. pi/K/p Ænext page

Cu+Cu

Au+Au
black 200GeV

2.0-4.0 GeV/cblack 200GeV

red 62.4GeV

1.0-2.0 GeV/c

red 62.4GeV

1.0-2.0 GeV/c

0.2-1.0 GeV/c

0.2-1.0 GeV/c
PHENIX PRELIMINARYPHENIX PRELIMINARY

v2 of 200GeV and 62GeV are consistent
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Energy dependence

Mean pT- identified hadrons (π/K/p)- pT dependence
Au+Au

v2 vs. pT

close: positivep

PHENIX PRELIMINARYKπ

PRL 94, 232302<pT> of 62.4 GeV and 200 GeV are consistent within errors on pi/K/ｐ.
Therefore v2 agree at any pT region in figures.

v2 of √s = 17GeV (SPS) decreases to about 50% of RHIC energies.
Higher collision energy has larger v2 up to RHIC energy.
Above 62.4 GeV, v2 is saturated.
Æ indicate the matter reached thermal equilibrium state at RHIC
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Produced by

open: negative

System Size Dependence
Eccentricity Scaling
What can change the size of collision system.
•Species of collision nucleus (Au+Au ,Cu+Cu)•Centrality

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Comparison Table

scaling

EnergyParticle
speciesno change

nq+KET

Size
SystemCentrality(CuCu, AuAu)

AuAu 200
AuAu 62
CuCu 200
CuCu 62
Already known
Is going to check next
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System size dependence
Compare v2 normalized by eccentricity (ε) in the collisions of different size.
v2 vs. Npart

0.2<pT<1.0 [GeV/c]

PHENIX PRELIMINARY

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System size dependence
Compare v2 normalized by eccentricity (ε) in the collisions of different size.
v2 vs. Npart

0.2<pT<1.0 [GeV/c]v2/ε vs. Npart

PHENIX PRELIMINARY

v2/ε (Au+Au) = v2/ε (Cu+Cu) !

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Systematic errors from
eccentricity is notincluded here.

17System size dependence
Compare v2 normalized by eccentricity (ε) in the collisions of different size.
v2 vs. Npart

0.2<pT<1.0 [GeV/c]v2/ε vs. Npart

PHENIX PRELIMINARY

v2/ε (Au+Au) = v2/ε (Cu+Cu) !
but v2/ε is not constant and it shades depending on Npart .

Æv2 can be normalized by ε at same Npart ,2008/09/11
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but ε is not enough to determine
v2 .

Systematic errors from
eccentricity is notincluded here.

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System size dependence
0.2<pT<1.0 [GeV/c]

Dividing by Npart1/3

v2 vs. Npartv2/ε vs. Npart

V2/ε/Npart1/3 vs. Npart

PHENIX PRELIMINARY

Systematic errors from
eccentricity is notincluded here.

v2/ε (Au+Au) = v2/ε (Cu+Cu)
v2/eccentricity is scaled by Npart1/3 and not dependent on the collision system.
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System size dependence
Dividing by Npart1/3

1.0<pT<2.0 [GeV/c]v2 vs. Npartv2/ε vs. Npart

V2/ε/Npart1/3 vs. Npart

PHENIX PRELIMINARY

Systematic errors from
eccentricity is notincluded here.

v2/eccentricity is scaled by Npart1/3 and not dependent on the collision system.
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System size dependence
Dividing by Npart1/3

2.0<pT<4.0 [GeV/c]v2 vs. Npartv2/ε vs. Npart

V2/ε/Npart1/3 vs. Npart

PHENIX PRELIMINARY

Systematic errors from
eccentricity is notincluded here.

v2/eccentricity is scaled by Npart1/3 and not dependent on the collision system.
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Comparison Table

scaling

Size

EnergyParticle
species(CuCu, AuAu)

no change

nq+KETeccentricity

SystemCentrality
Npart1/3

AuAu 200
AuAu 62
CuCu 200
CuCu 62
Already known
Is going to check next
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Universal v2
Quark number + KET scaling
Universal Scaling

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Comparison Table

scaling

Size

EnergyParticle
species(CuCu, AuAu)

no change

nq+KETeccentricity

SystemCentrality
Npart1/3

AuAu 200
AuAu 62
CuCu 200
CuCu 62
Already known
Is going to check next
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Quark number + KET scaling (AuAu 62.4GeV)
Centrality 10-40 %PHENIX: Error bars include both statistical and systematic errors.
STAR: Error bars include statistical errors. Yellow band indicates systematic errors.

v2 vs. pT

v2/nq vs. pT/nq

Star results : Phys. Rev. C 75

v2/nq vs. KET/nq

quark number + KET scaling is OK at 62.4 GeV, too!
v2(pT) /nquark vs. KET/nquark is the universal curve
independent on particle
species.
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v2 vs. pT at Cu+Cu in 200GeV collision

Centrality dependence of PID v2 vs. pT for Cu+Cu 200GeV is measured.
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Quark number + KET scaling

Cu+Cu √s = 200GeVAt all centrality,(between 0- 50 %) v2 of
π/K/p is consistent toquark number + KET
scaling.

quark number + KET scaling seems to works out at Cu+Cu 200GeV.
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Summary of Scaling
Collision energyÆ no change
Eccentricity of participants Æ eccentricity scaling
Particle species
Æ nq +KET scaling
Number of participantsÆ Npart1/3 scaling

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Comparison Table

scaling

Size

EnergyParticle
species(CuCu, AuAu)

no change

nq+KETeccentricity

SystemCentrality
Npart1/3

AuAu 200
AuAu 62
CuCu 200
CuCu 62
Already known
Is going to check next
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Universal Scaling

ex. Au+Au 200GeV π

quark number + KET scaling.

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Universal Scaling
quark number + KET scaling.

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ex. Au+Au 200GeV π+ eccentricity scaling

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Universal Scaling
quark number + KET scaling.

ex. Au+Au 200GeV π+ eccentricity scaling+ Npart1/3 scalingv2(KET/nq)/nq/εpar/Npart1/3 is consistent at 0-50% centralities.
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Universal Scaling Different System (Au+Au, Cu+Cu) Different Energy (200GeV - 62.4GeV)
v2(KET/nq)/nq/epar/Npart1/3
 Different Centrality (0-50%)
 Different particles (π/ K /p)v2 ( K ET / nq )

χ2/ndf = 8.1

nq × ε × N

1/ 3
part

Universal Curve !!

Large symbol - AuAu
Small symbol - CuCu

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Conclusion
v2 were measured at 4 systems.
(Au+Au, Cu+Cu) x (62.4GeV, 200GeV)

Same v2(pT) are obtained in different collisionenergies (√s = 62.4 - 200GeV)
v2(pT) of various hadron species are scaled by quark
number + KET scaling at these three systems. (noresults for Cu+Cu 62.4GeV )v2(Npart) scaled by participant Eccentricity are
consistent between Au+Au and Cu+Cu collisions
v2(pT) /εpar are scaled by Npart1/3 .
v2(KET/nq)/nq/εpar/Npart1/3 has Universal Curve.

ÆThis indicates v2 are determined by the initial geometricalanisotropy and its time evolution effect depending on theinitial volume.

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Calculation by simple expansion model
Assumption

Calculation is done by Dr.Konno

Time until chemical freeze-out is proportional to Npart1/3.
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Summary of v2 production and development
Low to mid pTTime tcollision

Determine initial geometricaleccentricity, ε, with the participant.

thermalequilibrium

Determine pressure gradient from ε.
v2 is expanding during finite time.

expandinghadronization

freeze out

Not depending on the kind of quarks.
This finite time becomes longer with larger collision system,and the v2 increases proportionally.

radial flow depending on eachmass expands.
No change

Measurement
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Summary (1)When the systems have same Npart, v2 is scaled by ε of paricipant geometry.
result v2B

result v2Asame Npart
B

A

v2A/εA = v2B/εB
eccentricity εAeccentricity εBresult v2C

same
eccentricity

C

v2C ≠ v2D

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If v2 only depends on eccentricity
of initial participant geometry, v2/εshould be constant at any Npart,but it is not.

result v2D

D

Therefore, to explain v2, in
addition to the initialgeometrical eccentricity,
there are something
related to Npart.

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Summary (2)With same eccentricity, v2 is scaled by (number of participants)1/3.
result v2C

same eccentricity

result v2D

v2 becomes consistent after
scaled by not only ε but also
Npart1/3 .

DIs it because of thickness
increasing along beam axis thenenergy per unit area increasing ?

v2C ≠ v2DC

v2C /NpartC1/3= v2D/NpartD1/3#of participant NpartC

result v2Esame Npartv2(200GeV) = v2(62.4GeV)#of participant NpartD

result v2F

F

E

Ｘ

Ｘ

v2E = v2F

= 62GeV
2008/09/11= 200GeVThis concludes that increasing
dN/dy doesn’t change v2 at
RHIC energy.

It might be because that
number of participant to 1/3(like length) is proportional to
the time period taken to
freeze out v2 , and v2 expands
proportional to that period.

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Back Up
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3 systemes comparison

Various scalings.
Eccentricity of Npart and Npart1/3 looks best.

40Comparison of AuAu to CuCu
Cu+Cu and Au+Au, 200GeV, PID by EMC
Apply quark number + KET scaling, eccentricity scaling and Npart1/3 scaling.

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Energy dependence

FOPI : Phys. Lett. B612, 713 (2005). E895 : Phys. Rev. Lett. 83, 1295 (1999)
CERES : Nucl. Phys. A698, 253c (2002). NA49 : Phys. Rev. C68, 034903 (2003)
STAR : Nucl. Phys. A715, 45c, (2003). PHENIX : Preliminary.
PHOBOS : nucl-ex/0610037 (2006)

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Quark number + KET scaling (AuAu 200GeV)

Quark number + KET scaling exists.
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Additional quark number + KET scaling (PbPb 17.2GeV)v2 of p, π, Λ - C. Alt et al (NA49 collaboration) nucl-ex/0606026 submitted to PRLv2 of K0 (preliminary) - G. Stefanek for NA49 collaboration (nucl-ex/0611003)

Pb+Pb at 158A GeV, NA49-

Taken from A. Tranenko’s talk at QM 2006

Quark number + KET scaling doesn’t seem to work out at SPS.
No flow at partonic level due to nonexistence of QGP ?
Errors are to big to conclude it.
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tf0 vs. Npart

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Comparison between Au+Au and Cu+Cu

Both behave same at mid central.
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Additional Npart scaling
Au+Au 200GeVAt high pT (> 6GeV/c), scaling
might work out but errors are
too large to conclude.
Æneed to analyze the data withhigher statistics. (ex.Run7)

By spectra analysis, thestrength of the suppression
seems to be consistent at same
Npart. It doesn’t depend on the
nucleus species of collisionsystem (Au+Au, Cu+Cu).
ÆRAA can be scaled by Npart.
2008/09/11*PRL 91 072303 (2003)

RAA – yield normalized byDIFFRACTION2008
p+p superposition.
It would be 1 without suppression.

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Analysis<Data set for this analysis>
Au+Au Cu+Cu collision
taken in 2003-2005 at RHIC-PHENIX
Collision energy ：200, 62.4 GeV/2
nucleons<PHENIX detectors>
EMCAL
for Particle
Identification

DC + PC1
for good track
selection and to
determine p

TOF
forParticle
IdentificationBBC
to determine
reaction planeand vertex

resolution=380ps

resolution=120ps<PID by TOF measurement><Reaction Plane determination>

Using TOF or EMC with BBC, theflight time of the particles isobtained. Mass of the particle iscalculated by the flight time and themomentum measured by DC.

The reaction plane is obtained bymeasurement of the anisotropic
distribution for the produced particles
with north and south BBCs located48at|η| ~ 3 – 4.

Resolution Calculation of Reaction Plane
resolution =< cos[ 2 ( Ψmeasured - Ψtrue )] > ~< cos[ 2 ( Ψ A - Ψ B )] >ΨA,B : reaction plane determined for each sub sample.

measured

v2

real

v2
=
resolution

BBC North + South combined
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