1

Measurement of Centrality Dependence of Elliptic Flow for Identified Hadrons in sNN = 200 GeV Au+Au Collisions

益井　宙益井　宙数理物質科学研究科物理学専攻５年次数理物質科学研究科物理学専攻５年次

TACTAC セミナー セミナー 44 月月 2424 日日 (2007)(2007)

2Outline

• IntroductionIntroduction– Why Elliptic Flow ?

• MotivationMotivation• AnalysisAnalysis

– PHENIX subsystem– Event plane method

• Results and DiscussionsResults and Discussions• ConclusionConclusion

3Quark Gluon Plasma (QGP)

• Ultimate goal of high energy Ultimate goal of high energy heavy ion collision experimeheavy ion collision experimentnt– Create and study the propertie

s of Quark Gluon Plasma (QGP)

• Quark-hadron phase transitiQuark-hadron phase transitionon– Degeneracy factor (g) increas

e by O(g)• g(massless ) = 3 (Nf=2)

– Lattice QCD calculation• Energy density jumps at Tc

– Tc ~ 150 - 170 MeV c ~ 1 GeV/fm3

• What is the probe for QGP ?What is the probe for QGP ?

F. Karsch, Lect. Notes Phys. 583, 209 (2002)

8 gluons, 2 spins.2 spins, 2 charges,3 colors, 2 quark flavors

Non-interactingMassless quarks and gluons

4Experimental probes for QGP

• Transverse collective flowTransverse collective flow– Introduced & found at 1970’s

– Transverse collective emission of particles related to the reaction plane

• 3 main types of flow3 main types of flow– Radial flow

– Directed flow (v1)

– Elliptic flow (v2)

• Quantitative study can be done with Quantitative study can be done with FFourier expansion series of azimuthal diourier expansion series of azimuthal distributionstribution for emitted particles for emitted particles

S. Voloshin and Y. Zhang, Z. Phys. C70, 665 (1996)A. M. Poskanzer and S. A. Voloshin, PRC58, 1671 (1998)

5

Rea

ctio

n pl

ane

X

Z

Y

Px

Py Pz

Why Elliptic flow ?

• Why do we use elliptic flow as the probe of QGP ?Why do we use elliptic flow as the probe of QGP ?1. Clear origin

• Initial geometry overlap (eccentricity)• re-interaction among particles + density distribution• Pressure gradient is the driving force of elliptic flow

2. Sensitive to the phase transition equation of state (EOS)3. Signal is self-quenching with time early signal4. Sensitive to the local thermal equilibrium ( vs R, :mean free path

R: characteristic length scale of the system) • Free streaming v2 = 0

6

P. Kolb et al, PRC62, 054909 (2000) B. Zhang et al, PLB455, 45 (1999)

How early ?

• Reach asymptotic value well before the hadroReach asymptotic value well before the hadronization !nization !– Parton cascade (left) ~ 2 fm/c– Ideal hydrodynamics (right) ~ 5 fm/c

Au+Au sNN = 200 GeV b=7.5 fm

Pb+Pb b=7 fm

7

Hydrodynamical modelHydrodynamical model Keep mass orderingKeep mass ordering Increase linearlyIncrease linearly

DataData Meson vMeson v22 start to saturate start to saturate vv22(p) > v(p) > v22(( or K) or K)

Are there any mechanisms Are there any mechanisms to explain this behavior of vto explain this behavior of v22 ? ?

SPS vs RHIC

• SPS: hydrodynamical model overestimate vSPS: hydrodynamical model overestimate v22

• RHIC: good agreement for pRHIC: good agreement for pTT < 2 GeV/c < 2 GeV/c

Rapid (Rapid (0 ~ 1 fm/c) thermalization at RHIC

SPS (sNN = 17 GeV) RHIC (sNN = 200 GeV)

NA

49

: nu

cl-ex/0

60

60

26

(20

07

)

PHENIX: PRL 91, 182301 (2003)

Hydrodynamical model: 1st order phase transition,Tc=165 MeV, Tf=120 MeV, 0 = 0.8 fm/c

8Radial flow

• mmTT scaling in p+p scaling in p+p

• Larger kick for heaviLarger kick for heavier particles in A+Aer particles in A+A heavier particles can

be pushed higher pT

Strong radial flow lead larger proton v2

E. Schnedermann et al, PRC48, 2462 (1993)

PHENIX: Au+Au: PRC 63, 034909 (2004);p+p: PRC74, 024904 (2006)

9Quark recombinationFragmentationRecombination

Carry only a fraction (z < 1) of the initial quark momentum

Hadrons from coalescence have larger momentum than the quark momentum

There can be a region where quark recombination There can be a region where quark recombination process becomes dominantprocess becomes dominant

when parton phase space density quickly drops with increasing pwhen parton phase space density quickly drops with increasing pTT

At RHIC, it is expected quark recombination is dominant At RHIC, it is expected quark recombination is dominant for intermediate pfor intermediate pTT region, p region, pTT ~ 2 - 6 GeV/c ~ 2 - 6 GeV/c

R. C. Hwa and C. B. Yang, PRC66, 025205 (2002); V. Greco et al, PRL90, 202302 (2003);R. J. Fries et al, PRL90, 202303 (2003)

10

ST

AR

:PR

L 92, 052302 (2004) ; PH

EN

IX:P

RL 91, 182301 (2003)

Quark number scaling of v2(pT)

• Quark recombination scQuark recombination scenario predict existence enario predict existence of universal quark vof universal quark v22 for l for light quarksight quarks– Scaling works well for pT r

ange where recombination is dominant

• Is this scenario really uniIs this scenario really unique explanation of vque explanation of v22 be behavior for intermediate phavior for intermediate p

TT ? ?

Quark number scaling of v2

D. Molnar and S. A. Voloshin, PRL91, 092301 (2003)Z. Lin and C. M. Ko, PRL89, 202302 (2002)

11Mass or quark numbers ?

meson is the good probe to test quark number scalimeson is the good probe to test quark number scaling of vng of v22 because: because:– Early freeze-out than other hadrons– Small hadronic cross section– Relatively longer lived life time ~ 40 fm/c– Mass ~ proton

• Important to understand contributions from hadronic Important to understand contributions from hadronic phasephase– Use deuterons to study radial flow effect

• Heavier hadrons are more sensitive to radial flow

– Deuteron v2 can be used as a “benchmark” of quark (hadron) recombination/coalescence scenario

12Motivation

• Measure centrality dependence of identiMeasure centrality dependence of identified hadron elliptic flow (fied hadron elliptic flow (, K, p, d and , K, p, d and ) ) in in ssNNNN = 200 GeV Au+Au collisions = 200 GeV Au+Au collisions

• Goal:Goal:– Test the validity of quark number scaling of

v2 with and d– Shed light on the thermodynamic propertie

s, especially for freeze-out temperature and radial flow velocity from centrality dependence of , K, and p v2

13My contributionsM1, M2M1, M2

2001 - 2002 2003 2004

D1D1 D2D2

D3D32005 2006

D4D42004

(Time-Of-Flight Detector): Timing calibration, offline software maintenance

Year-3 d+Au timing calibrationYear-4 Au+Au 200 GeV & 62.4 GeV timing calibration

Year-5 Cu+Cu 200 GeV timing calibration

(Aerogel Cherenkov Counter): Offline software development, maintenance. Simulation for online LVL-2 trigger

(Event Plane calibration): Offline software development. Calibration for Year-4 & Year-5 Event plane for several different subsystems.

High pT charged hadron Elliptic Flow

Directed Flow analysis by using Elliptic Event plane

Fast track analsis for 62.4 GeV Au+Au PID hadron v2

200 GeV Year-4 Au+Au and Year-5 Cu+Cu, Elliptic Flow analysis

Quark Matter 2002 Fall DNP

Quark Matter 2004

Quark Matter 2005

RNP workshop CIPANP

RHIC-AGS user’s meeting

62.4 GeV: PRL62.4 GeV: PRL9494, 232302 (2005), 232302 (2005)

Au+Au & Cu+Cu: PRLAu+Au & Cu+Cu: PRL9898, 162301 (2007), 162301 (2007)

d & d & : nucl-ex/0703024: nucl-ex/0703024

14

Analysis

15RHIC• The first heavy ion collideThe first heavy ion collide

r in the worldr in the world– 2 counter-circulating ring

s

– 3.8 km circumference

• Top energies:Top energies:– 100 GeV/nucleon A+A

– 250 GeV/nucleon p+p

RRelativistic elativistic HHeavy eavy IIon on CColliderolliderBrookhaven National Laboratory

Run1 2000 Au+Au 130 GeVRun2 2001-2002 Au+Au, p+p 200 GeVRun3 2002-2003 d+Au, p+p 200 GeV

Run4 2003-2004 Au+Au 200, 62.4 GeVRun5 2004-2005 Cu+Cu 200, 62.4, 22.5GeV, p+p 200 GeVRun6 2005-2006 p+p 200, 62.4 GeVRun7 2006-2007 Au+Au 200 GeV (running)

16PHENIX experiment

• Global information (Trigger, centrGlobal information (Trigger, centrality, collision vertex, etc)ality, collision vertex, etc)

– Beam-Beam Counter (BBC), =2, ||=3-4

– Zero Degree Calorimeter (ZDC) and Shower Maximum Detector (SMD) =2, ||>5

• Central armCentral arm =, ||<0.35

• Tracking, momentumTracking, momentum– Drift Chamber (DC), R=2.2m– Pad Chamber (PC), R=2.5m (P

C1), 4.9m (PC3)

• Particle identificationParticle identification– Time-Of-Flight (TOF), R=5m,

=/4

z

y x

17Global Detectors

• The role of BBC and ZDC+SMDThe role of BBC and ZDC+SMD– Minimum bias trigger, Collision z-vertex, Centrality, Event plane (BBC, SM

D), Start timing for Time-Of-Flight Detector (BBC)

106mm

220mm

45o 53mm

beam

120mm

BBC- Mesh-dynode PMT (1 inch diameter)- 3 cm quartz Cherenkov radiator - 64 PMT elements on each BBC

ZDC (+SMD)-Sampling calorimeter (Tungsten, Scintillator) 3 module-2 int / module-SMD is located between 2nd and 3rd ZDC- 8 8 bins in (x,y) space

beam

18Centrality

• Geometry of heavy ion cGeometry of heavy ion collisionollision– Impact parameter Number of participant nucl

eons Multiplicity, energy of spec

tator neutrons

• Number of Participant (NNumber of Participant (N

partpart))– Calculate Npart by Glauber

Model

• Glauber ModelGlauber Model– Thickness function– Woods-saxon density distr

ibution

BBC

ZDC

Participant

Spectator

Spectator

19Tracking

• Drift ChamberDrift Chamber

: incident angle, K : effective field integral, p : momentum

– Momentum determination• Momentum resolution :

p/p = 0.7 % 1 % p

• Pad chamberPad chamber– 3 dimensional hit point (st

raight line)– Reconstruct pz (PC1)

• Associate DC tracks to oAssociate DC tracks to outer detectors (PC3, TOuter detectors (PC3, TOF)F)

X

Y

20Particle identification: /K/p/d

• TOF (Flight time TOF (Flight time Mass square) Mass square)– Timing resolution: TOF ~ 120 ps, EMC ~ 500

ps

• Particle separationParticle separation– TOF

/K ~ 3 GeV/c– Can be extended up to pT ~ 4 GeV/c by using

asymmetric cuts

• K/p ~ 5 GeV/c, d :1 - 4 GeV/c

– EMC /K ~ 1.5 GeV/c

21Particle identification:

KK++KK--

– Branching ratio = 49 %

• Reconstruct Reconstruct meson by inv meson by invariant massariant mass– 1 < pT < 4 GeV/c– Kaon from TOF detector, use

also EMCal to increase the statistics at low pT

• Combinatorial background iCombinatorial background is estimated by event mixing s estimated by event mixing techniquetechnique– Background distribution is nor

malized in M = 1.2 - 1.3 GeV/c2

• Signal extractionSignal extraction– Breit-wigner + constant

22Event plane @ PHENIX

• Event plane determined at BBC (|Event plane determined at BBC (|| = 3 - 4)| = 3 - 4)– Cover full azimuth (Half of full azimuth in Cent

ral arm)

• Measure particles with respect to the event plMeasure particles with respect to the event plane at BBCane at BBC– Large rapidity gap (|| ~ 3) reduce non-flow e

ffects** contribute the flow signal NOT originated from re

action plane

PH

OB

OS

: PR

L9

1, 0

52

30

3 (2

00

3)

23Flattening correction

• Reconstructed EP usually not eReconstructed EP usually not exactly flatxactly flat– Detector acceptance

– Detector response

– Beam position offset

– Etc …

• Overall “shift” correctionOverall “shift” correction– Remove almost all bias (black -

> blue)

• Flattening correctionFlattening correction– remove remaining non-flat contr

ibutions (blue -> red)– Requirement

should be small• Isotropic distribution -> vanishing of k-th F

orier moment of the new distribution ()

shift

Flattening

24

** Valid only equal multiplicity event Event plane resolution of each sub-event is same

Event plane resolution & Extract v2

Central

Peripheral

Small v2

Low multiplicity

25

Results &Discussions

26/K/p v2: Basic checks

• Increase statistics fIncrease statistics from Run2 (rom Run2 (20)20)– Run2 ~ 30 M event,

Run4 ~ 600 M event

sin(2[sin(2[--BBCBBC])]) = 0 = 0

as we expect as we expect • No charge dependeNo charge depende

ncence• Consistent with RuConsistent with Ru

n2 resultsn2 results

• Consistent with KConsistent with K00ss

and and ’s from STAR ’s from STAR experimentexperiment

Systematic errorSystematic errorEvent plane: ~ 6 % at mid-central, ~20 % at central and peripheral

Track matching cuts, PID cuts, energy loss cuts ~ 3 %

ppTT > 3 GeV/c > 3 GeV/c

Random background, ~1 - 10 % (centrality dependent)

Mis-identification for Kaon, ~2 - 12 % (centrality dependent)

27Centrality dependence: /K/p

• vv22(p(pTT) increase with centrality) increase with centrality– Consistent with the centrality dependence of initial

geometry overlap

28Glauber Model simulation

• Woods-saxon density profileWoods-saxon density profile– R = 6.38 fm, a = 0.53 fm, 0 = 0.17 fm-3

• Nuclear thickness functionNuclear thickness function NNNN = 42 mb = 42 mb• Calculate number of participating nucleCalculate number of participating nucle

onsons– In p+p, Npart = 2

29Eccentricity scaling

• Eccentricity scaling of vEccentricity scaling of v22

– Remove geometry effect on v2

– increase and saturate with Npa

rt

– proportional to Npart1/3

=

30Extract d & v2

• Simultaneous fitting of Simultaneous fitting of relative yield and vrelative yield and v22

• Fitting mass distributioFitting mass distributions by signal + backgrons by signal + backgroundund

– S/B depends on mass

• Parameterize S/(S+B) Parameterize S/(S+B) and B/(S+B) vs massand B/(S+B) vs mass

• Fitting vFitting v22obsobs vs mass wit vs mass wit

h 2 free parameters vh 2 free parameters v22SS

and vand v22BB

d

N. Borghini and J.-Y. OllitraultPRC70, 064905 (2004)

31Deuteron & v2

• Deuteron (Deuteron () v) v22 is smaller than others for p is smaller than others for pTT < < 2 (1.5) GeV/c2 (1.5) GeV/c

• For pFor pTT > 2 (1.5) GeV/c, v > 2 (1.5) GeV/c, v22 is as large as other is as large as other hadronshadrons

32Centrality dependence: d,

• Sizeable vSizeable v22 for both d and for both d and – Centrality dependence ?

33Hadron coalescence

• Check the coalescence or rCheck the coalescence or recombination lead scaling recombination lead scaling relation of velation of v22

– Hadron coalescence : d p + n

• Assume neutron v2 = proton v2

• Ratio of scaled vRatio of scaled v22(d) to v(d) to v22(p) (p) is ~ 1is ~ 1

• Hadron coalescence of dHadron coalescence of d Scaling relations betwee d aScaling relations betwee d a

nd pnd p

34Quark number scaling of v2

• Close to 1 at intermediate pClose to 1 at intermediate pTT

• Scaled vScaled v22 show remaining dif show remaining dif

ference among different partference among different particle species at low picle species at low pTT

• Are there any variables to scAre there any variables to scale vale v22 from low to intermedia from low to intermedia

te pte pTT ? ?

Transverse kinetic energy scTransverse kinetic energy scaling (maling (mTT scaling) of v scaling) of v22

35

meson

baryon

Transverse kinetic energy scaling

• KET scaling holds up to ~ 1 GeVKET scaling holds up to ~ 1 GeV– Pressure gradient collective kinetic energy

• Clear splitting for mesons and baryonsClear splitting for mesons and baryons– Possible hint of quark d.o.f become apparent at higher KET

• Quark number scaling for vQuark number scaling for v22(KE(KETT) !) !

PHENIX: nucl-ex/0608033

36Centrality dependence: /K/p

• KEKETT scaling scaling– 10 - 20 % systematics. Better than pT scaling

37Scaled v2 for meson

• Deuterons and Deuterons and meson scale together meson scale together

• KEKETT scaling better ! scaling better !

38Centrality dependence: d,

• KEKETT + quark number scaling also works for d and + quark number scaling also works for d and

39Summary (1)

• Centrality dependence of vCentrality dependence of v22

– Increase with increasing centrality for all particles species Consistent with centrality dependence of initial spatial anisot

ropy ( v2 )

– v2/ increase, saturate with centrality ( Npart1/3 )

Dynamical collectivity increase with system size

• Quark number scaling of vQuark number scaling of v22

– Transverse kinetic energy (KET) + quark number scaling

– KET is the relevant scaling quantity to explain the v2(pT) from low to mid pT range

Collective pressure drives partonic flow

40“Thermometer” of QGP ?

• Thermal model fit + single pThermal model fit + single pTT spectra gives temperature at “kinet spectra gives temperature at “kinetic freeze-out”ic freeze-out”

• Elliptic flow saturate very early times (~ a few fm/c)Elliptic flow saturate very early times (~ a few fm/c) Does Elliptic flow have sensitivity to the early temperature on QDoes Elliptic flow have sensitivity to the early temperature on Q

GP phase ?GP phase ? Use Elliptic flow as the “Thermometer” of QGP !Use Elliptic flow as the “Thermometer” of QGP !

time A. Kiyomichi: PhD thesis

41Thermal model

• AssumptionsAssumptions– Hadronization just after local ther

mal equilibrium• No chemical, kinetic freeze-out• No dynamical evolution

– Constant temperature

– Density gradient distributions• = Boost magnitude & direction• Determine the boost anisotropy

– Spatial anisotropy is fixed by initial overlap density

• Free parametersFree parameters– Temperature: T

– Magnitude of boost velocity: T

reactionplane

42Density & gradient distributions

• Calculate NCalculate Npartpart(x, y) from Woods-saxon density profile(x, y) from Woods-saxon density profile– Direction of density gradient direction of boost

• Length = magnitude of boost

43Thermal model fit

• Minimize Minimize 22 by fitting by fitting , K , K and p simultaneouslyand p simultaneously

• Lower temperature meanLower temperature means longer QGP phases longer QGP phase

• ResultsResults– pT spectra and v2 cannot b

e fitted with same parameter sets• pT spectra: T = 117 (MeV)

– Overestimate v2

• v2: T = 204 (MeV)– Flatter slope of pT spect

ra

A hint of early saturation of v2

RightRight- Fit v2

- Draw fitting results for

pT spectra

LeftLeft- Fit pT spectra

- Draw fitting results for v2

442 contour of (T, T)

• ppTT spectra fit spectra fit– Anti-correlation

• Larger (smaller) T, smaller (larger) T

• Flatter pT spectra for larger T and T

• vv22 fit fit– Positive correlation

• Larger (smaller) T, larger (smaller) T

• Smaller v2 for larger T• Larger v2 for larger T (at l

arge T)

45Conclusions

• Measure elliptic flow (vMeasure elliptic flow (v22) parameter of identified hadr) parameter of identified hadrons for a broad range of centrality and pons for a broad range of centrality and pTT

• Centrality dependence of vCentrality dependence of v22

– Consistent with centrality dependence of initial spatial anisotropy

Elliptic flow drives Initial geometry

• Transverse Kinetic energy (KETransverse Kinetic energy (KETT) + Quark Number sc) + Quark Number scalingaling– Holds for all particles species in measured centrality bins 　 Partonic flow by collective pressure

• Thermal model fitThermal model fit– pT spectra and v2 cannot be fitted with same parameter sets

• Larger temperature from v2 fit compared to pT spectra fit

A possible hint of early saturation of v2

46To do

• Study radial flow effect on vStudy radial flow effect on v22

• Thermal model fitThermal model fit– Show only 20 - 30 % centrality bin

– Fit pT spectra and v2 for other centrality bin, study centrality dependence of (T, T) systematics

– Use high statistics pT spectra from year-4 results• Use year-2 result in this presentation

– Comparison of results with different assumptions

47

Back up

48Sign of v2

• Sign of vSign of v22 is important is important– Initial geometry + density gradient lead positive v2

• But sign of vBut sign of v22 cannot be determined by 2 cannot be determined by 2ndnd harmonic harmonic EPEP

• Direction of true reaction planeDirection of true reaction plane 11stst harmonic event plane harmonic event plane

Py

Px

reactionplane or

v2 > 0 v2 < 0

49Event plane correlations

• Positive correlations of 2Positive correlations of 2ndnd harmonic EP between harmonic EP between– BBC’s, and CNT (Central arm) - BBC Same direction of flow at CNT and BBC

501st harmonic event plane

• Correlation between 1Correlation between 1stst harmonic and 2 harmonic and 2ndnd harmonic E harmonic EPP

– Spectator neutron at ZDC-SMD gives direction of true reaction plane

22BBC

1

SM

D

- 0-

0

-/2

/2

22BBC

1

SM

D

- 0-

0

-/2

/2

v2 > 0 v2 < 0

51Positive v2 !

• Correlation between 2Correlation between 2ndnd harmonic BBC EP and 1 harmonic BBC EP and 1stst harmonic SMD EP harmonic SMD EP– Positive correlation positive v2 !

– Measured correlation is consistent with expected value

Possible hint that v2 is driven by initial geometry

52Eccentricity

• Estimate eccentricity by Glauber ModelEstimate eccentricity by Glauber Model– 10 - 20 % systematic error depending on

centrality

• Participant eccentricity (Participant eccentricity (partpart) > standard e) > standard eccentricity (ccentricity (stdstd))– due to fluctuation of positions for participa

nt nucleons

53System size dependence

• Different vDifferent v22 for same N for same Npartpart

– Due to different eccentricity

• Different systems (Au, Cu) does not scale witDifferent systems (Au, Cu) does not scale with standard eccentricityh standard eccentricity

54Participant eccentricity

• vv22 in different systems scales by in different systems scales by partpart

Participant eccentricity is a relevant geometric Participant eccentricity is a relevant geometric quantity !quantity !

55Eccentricity scaling

• Eccentricity scaling removes geometry effectEccentricity scaling removes geometry effect– No particle type dependence

– v2/ increase and saturate with Npart

56Quark number scaling of v2

• KEKETT + Quark number scaling is better (~10 %) than usual quark + Quark number scaling is better (~10 %) than usual quark

number scaling by pnumber scaling by pTT

57Parameterization of Glauber model

• Density distribution of nucleonDensity distribution of nucleon– Woods-saxon density profile

• R = 6.38 fm, a = 0.53 fm, 0 = 0.17 fm-3

• Nuclear thickness functionNuclear thickness function

• Number of participant (NNumber of participant (Npartpart), Number of binar), Number of binar

y collisions (Ny collisions (Ncollcoll))

58