anisotropic flow @ rhic

1

Anisotropic Flow@ RHIC

Hiroshi Masui / Univ. of TsukubaHiroshi Masui / Univ. of Tsukuba

Feb./11/2007Feb./11/2007RHICRHIC 高エネルギー原子核反応の物理研究会、高エネルギー原子核反応の物理研究会、

RHICRHIC 現象論松本合宿現象論松本合宿

Feb/11/2007 H. Masui / Univ. of Tsukuba

2Outline

• IntroductionIntroduction– Anisotropic flow, eccentricity

• ResultsResults– Several scaling relations have been observ

ed especially for elliptic flow• Eccentricity scaling• Scaling of higher order anisotropy

• mT and NCQ scaling of elliptic flow

• SummarySummary


3

Definition& Terminology


4Anisotropic Flow

• What ?What ?– Azimuthally anisotropic emi

ssion of particles with respect to the reaction plane

• Why ?Why ?– The probe for early time– Driven by

• initial eccentricity of overlap zone

• Re-interactions among the particles (pressure gradient)

– Initial eccentricity --> Final momentum anisotropy

React

ion

plan

e

X

Z

Y

Px

Py Pz


5Observables

• Particle azimuthal distriParticle azimuthal distributions by Fourier expabutions by Fourier expansionnsion– Odd harmonics (v1, v3,

…) vanish at mid-rapidity in symmetric collision

• vv22 = “Elliptic Flow” = “Elliptic Flow”

S. Voloshin and Y. Zhang, Z. Phys. C70, 665 (1996)A. M. Poskanzer and S. A. Voloshin, Phys. Rev. C58, 1671 (1998)


6Methods

Event plane method Multi-particle correlation

Advantage & disadvantage

Assume all correlations are flow

(ii) Easy to implement for identified hadrons

(iii) Need to determine event plane

(i) Reduce non-flow contribution by higher order correlation

(ii) No event plane

(iii) Larger statistical error

Stat. / Sys. error and non-flow effects

Typically, order of stat. error is same as k=1 in right eq.

Di-jet contributions can be removed by rapidity gap Stat. (sys.) error increase (decrea

se) for higher order correlation

References J.-Y. Ollitrault, Phys. Rev. D48, 1132 (1993)

A. M. Poskanzer and S. A. Voloshin, Phys. Rev. C58, 1671 (1998)

N. Borghini, P. M. Dinh, J.-Y. Ollitrault, Phys. Rev. C63, 054906 (2000); Phys. Rev. C64, 054901 (2001)

R. S. Bhalerao, N. Borghini, J.-Y. Ollitrault, Nucl. Phys. A727, 373 (2003); Phys. Lett. B580, 157 (2004)

Two main types of methods


7Event plane method

• Brackets denote average over all events and all partiBrackets denote average over all events and all particles, cles, kk

nn is “event plane resolution” is “event plane resolution”

• w (weight) is chosen to maximize the event plane resw (weight) is chosen to maximize the event plane resolution (ex. polution (ex. pTT, multiplicity etc), multiplicity etc)

– The best weight is vn itself


8Event plane @ PHENIX

• Event plane determination @ Beam-Beam Counter Event plane determination @ Beam-Beam Counter (BBC), |(BBC), || ~ 3 - 4| ~ 3 - 4

• Large rapidity gap between measured particles (Large rapidity gap between measured particles ( ~ ~ 0) and event plane 0) and event plane Reduce non-flow effects Reduce non-flow effects– di-jet contribution is negligible (nucl-ex/0609009)


9Multi-particle correlation

• Non-flow effects contribute orderNon-flow effects contribute order– 1/N in 2-particle correlation– 1/N3 in 4-particle correlation

2-particle correlation

4-particle correlation


10Terminology

stdstd : standard eccentricity : standard eccentricity– Spatial anisotropy in coordinate space

partpart : Participant eccentricity : Participant eccentricity– Effect from the fluctuations in the positions of participant nucle

ons

• vv22{{EPEP22} : v} : v22 with respect to the 2 with respect to the 2ndnd harmonic harmonic EEvent vent PPlanlan

ee– v2{BBC} : v2{EP2} by BBC in PHENIX

– v2{FTPC} : v2{EP2} by Forward-TPC in STAR

– v2{EP}(AA-pp) : Modified event plane method

• vv22{{nn} : v} : v22 from from nn-th particle cumulants-th particle cumulants

• vv44{n} : v{n} : v44 from n-th particle cumulants from n-th particle cumulants


11Eccentricity : definition

• Participant eccentricity in a giveParticipant eccentricity in a given event is defined by the axes n event is defined by the axes (x’, y’)(x’, y’) … denote average over all partic

ipant nucleons and events in the same impact parameter

– {…} denote the average over all participants in one collision event


12Eccentricity vs centrality

• Fluctuations lead significant increase of Fluctuations lead significant increase of eccentricity at most central and peripheraleccentricity at most central and peripheral


13

Results (i)non-identified hadrons


14Integrated v2

• ~ 50 % increase from SPS to RHIC~ 50 % increase from SPS to RHIC• Hadron cascade underestimate the magnitude of vHadron cascade underestimate the magnitude of v22 at at

RHICRHIC– Due to the small transverse pressure in early times

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)

QM2005, H. Masui

RQMD


15Eccentricity scaling (i)

• Assume Assume = k = k v v22

• A Glauber model estiA Glauber model estimate of mate of gives gives – k = 3.1 0.2

• vv22 scales with scales with and th and th

e scaled ve scaled v22 values are values are

independent of the syindependent of the system sizestem size

Scale invariance of iScale invariance of ideal hydrodynamicsdeal hydrodynamics

nucl-ex/0608033


16Eccentricity scaling (ii)

• Scaling of vScaling of v22//partpart in Cu+Cu in Cu+Cu

and Au+Auand Au+Au• Participant eccentricity is relParticipant eccentricity is rel

evant geometric quantity for evant geometric quantity for generating elliptic flowgenerating elliptic flow

PRL: nucl-ex/0610037 PRC C72, 051901R (2005) PHOBOS Collaboration

PRL: nucl-ex/0610037

Cu+Cu200 GeV

Au+Au 200 GeV

Statistical errors only


17Eccentricity scaling (iii)

• Linear increase from SPS to RHICLinear increase from SPS to RHIC

• Eccentricity scaling of vEccentricity scaling of v22 reach hydro limit at m reach hydro limit at m

ost centralost central

QM2006, R. NouicerQM2006, S. A. Voloshin


18Differential v2, v2(pT) :PHENIX vs STAR (Au+Au)

• Non-flow effects are under controlNon-flow effects are under control– v2{4} v2{BBC} ~ v2{FTPC} < v2{2}

• Similar acceptance : BBC, FTPC

QM2006, S. A. Voloshin

STAR : Phys. Rev. Lett. 93, 252301 (2004)PHENIX : Preliminary


19v2(pT) in Cu+Cu

• Larger non-flow effects in smaller systemLarger non-flow effects in smaller system– Dominant non-flow is ~ O(1/N)

PHENIX

STAR preliminary (QM06, S. A. Voloshin)

v2{2}

v2{FTPC}

PHENIX : nucl-ex/0608033


20Higher order

• Non-zero vNon-zero v44 at RHIC at RHIC– v4 ~ (v2)2 (Ollitrault)

• vv44/(v/(v22))22 is a probe of ideal hydro behavior is a probe of ideal hydro behavior– N. Borghini and J.-Y. Ollitrault, Phys. Lett. B642, 227 (2006)

QM06, Y. Bai

QM05, H. Masui

STAR preliminary|| < 1.3


21v4/(v2)2 vs pT

• Experimentally, vExperimentally, v44/(v/(v22))22 ~ 1.2 - 1.5 ~ 1.2 - 1.5– Ideal hydro prediction v4/(v2)2 = 0.5

• Maximum non-flow contribution Maximum non-flow contribution

Star Preliminary


22Summary (i)

• The magnitude of vThe magnitude of v22 is as large as that from perfect fl is as large as that from perfect fluid hydrodynamics at RHICuid hydrodynamics at RHIC– 50 % increase from SPS– Hadron cascade cannot reprduce the magnitude of v2

• Eccentricity scalingEccentricity scaling– Consistent description of Au+Au and Cu+Cu v2 systematics

by participant eccentricity– Different conclusion from different experiments

• Non-flow effects are under control viaNon-flow effects are under control via– Large rapidity gap (PHENIX, STAR)– Multi-particle correlation (STAR)

• Higher order, vHigher order, v44

– Non-zero v4 is observed– v4/(v2)2 ~ 1 > 0.5 but systematic error is huge at high pT


23

Results (ii)identified hadrons


24“mT scaling” of v2

• vv22{BBC} for identified {BBC} for identified

hadronshadrons

• At low pAt low pTT, m, mTT scaling scaling

of vof v22

– Radial flow leads mass ordering of v2

• Meson-Baryon groupiMeson-Baryon grouping at intermediate png at intermediate pTT

– Quark coalescence, recombination


25NCQ scaling of v2

• NCQ scaling indicate tNCQ scaling indicate the collective flow evolhe collective flow evolves in quark level ves in quark level

• Number of Constituent Quark scaliNumber of Constituent Quark scaling by quark coalescence / recombing by quark coalescence / recombination modelnation model

• AssumptionAssumption– Exponential pT spectra

– Narrow momentum spread (-function)

– Common v2 for light quarks (u, d, s)

R. J. Fries, et., al, Phys. Rev. C68, 044902 (2003)V. Greco, et., al, Phys. Rev. C68, 034904 (2003)


26Multi-strange hadrons

• Why ?Why ? and are less affec

ted by hadronic interactions

– Hadronic interactions at a later stage do not produce enough v2

Y. Liu et., al, J. Phys. G32, 1121 (2006)

J. H. Chen et., al, Phys. Rev. C74, 064902 (2006)


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QM06, A. Taranenko

STAR preliminary200 GeV Au+Au SQM06, M. Oldenburg

Multi-strange hadrons meson v2 is mmeson v2 is m

ore consistent wiore consistent with meson vth meson v22 than than baryon vbaryon v22

• Show sizable vShow sizable v22

– Collectivity at pre-hadronic stage, s-quark flow


28Universal scaling of v2

• Substantial elliptic flow sigSubstantial elliptic flow signals are observed for a varnals are observed for a variety of particles species at iety of particles species at RHICRHIC


29Universal scaling of v2

At mid-rapidityAt mid-rapidity


30Summary (ii)

• Mass ordering at low pMass ordering at low pTT – Predicted by hydrodynamics (radial flow effect)

• At intermediate pAt intermediate pTT, NCQ scaling holds a variet, NCQ scaling holds a variet

y of particles speciesy of particles species– Indication of light quark (u, d, s) collectivity at pre-

hadronic stage

• Universal vUniversal v22 motivated by perfect fulid hydrod motivated by perfect fulid hydrod

ynamics is observed for both mesons and barynamics is observed for both mesons and baryons over a broad range of kinetic energy, ceyons over a broad range of kinetic energy, centrality via NCQ scalingntrality via NCQ scaling


31

Back up


32Flow measurements

• 2 main types of methods2 main types of methods– “Event plane” method

• J.-Y. Ollitrault, Phys. Rev. D48, 1132 (1993)• A. M. Poskanzer and S. A. Voloshin, Phys. Rev. C58, 16

71 (1998)

– Multi-particle correlation method• N. Borghini, P. M. Dinh, J.-Y. Ollitrault, Phys. Rev. C63 0

54906 (2000); Phys. Rev. C64, 054901 (2001)• R. S. Bhalerao, N. Borghini, J.-Y. Ollitrault, Nucl. Phys. A

727, 373 (2003); Phys. Lett. B580, 157 (2004)

• Different sensitivity to “non-flow” effectsDifferent sensitivity to “non-flow” effects– Correlations unrelated to the reaction plane, ex. jet

s, resonance decays etc …


33Non-flow effects from Jets (i)

• Nucl-ex/0609009Nucl-ex/0609009• ““Trigger” pTrigger” pTT : 2.5 < p : 2.5 < pTT < 4 GeV/c < 4 GeV/c• ““Associated” pAssociated” pTT : 1 < p : 1 < pTT < 2 GeV/c < 2 GeV/c • Background Au+Au events from HIJINGBackground Au+Au events from HIJING

– Checked to reproduce the charged hadron multiplicity in from PHOBOS

– v2 is implemented according to the PHENIX v2 measurement (nucl-ex/0608033)

• Di-jet pairs are generated from PYTHIADi-jet pairs are generated from PYTHIA


34Non-flow effects from Jets (ii)

• Fake vFake v22 for leading particles for leading particles– Fake v2 is negligible in BBC acceptance (3 < < 4)

• NOTENOTE– Results are not corrected event plane resolution


35Non-flow effect on v4

• Consider 3-particle correlationConsider 3-particle correlation

• Maximum non-flow contribute if (i, k) correlate Maximum non-flow contribute if (i, k) correlate non-flow and (j, k) correlate flownon-flow and (j, k) correlate flow

flowNon-flow


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Signal + BackgroundBackground

Before subtraction

After subtraction

Clear signal KK++KK--

– Typical S/N ~ 0.3

• Centrality 20 – 60 %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

anisotropic flow @ rhic

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