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Feb/11/2007H. Masui / Univ. of Tsukuba 3 Definition & Terminology
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1
Anisotropic Flow@ RHIC
Hiroshi Masui / Univ. of TsukubaHiroshi Masui / Univ. of TsukubaFeb./11/2007Feb./11/2007
RHICRHIC 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 observed especially for elliptic flow
• Eccentricity scaling• Scaling of higher order anisotropy• mT and NCQ scaling of elliptic flow
• SummarySummary
Feb/11/2007 H. Masui / Univ. of Tsukuba
3
Definition& Terminology
Feb/11/2007 H. Masui / Univ. of Tsukuba
4Anisotropic Flow• What ?What ?
– Azimuthally anisotropic emission 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
Reacti
on pl
ane
X
Z
Y
Px
Py Pz
Feb/11/2007 H. Masui / Univ. of Tsukuba
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)
Feb/11/2007 H. Masui / Univ. of Tsukuba
6MethodsEvent 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
Feb/11/2007 H. Masui / Univ. of Tsukuba
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 res
olution (ex. polution (ex. pTT, multiplicity etc), multiplicity etc)– The best weight is vn itself
Feb/11/2007 H. Masui / Univ. of Tsukuba
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)
Feb/11/2007 H. Masui / Univ. of Tsukuba
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
Feb/11/2007 H. Masui / Univ. of Tsukuba
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 nucleons
• vv22{{EPEP22} : v} : v22 with respect to the 2 with respect to the 2ndnd harmonic harmonic EEvent vent PPlanelane– 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
Feb/11/2007 H. Masui / Univ. of Tsukuba
11Eccentricity : definition• Participant eccentricity in a giveParticipant eccentricity in a give
n 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
Feb/11/2007 H. Masui / Univ. of Tsukuba
12Eccentricity vs centrality
• Fluctuations lead significant increase of Fluctuations lead significant increase of eccentricity at most central and peripheraleccentricity at most central and peripheral
Feb/11/2007 H. Masui / Univ. of Tsukuba
13
Results (i)non-identified hadrons
Feb/11/2007 H. Masui / Univ. of Tsukuba
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 R at R
HICHIC– 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
Feb/11/2007 H. Masui / Univ. of Tsukuba
15Eccentricity scaling (i)• Assume Assume = k = k v v22
• A Glauber model estimA Glauber model estimate of ate of gives gives – k = 3.1 0.2
• vv22 scales with scales with and the and the scaled vscaled v22 values are in values are independent of the systedependent of the system sizem size
Scale invariance of idScale invariance of ideal hydrodynamicseal hydrodynamics
nucl-ex/0608033
Feb/11/2007 H. Masui / Univ. of Tsukuba
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 relevant 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
Feb/11/2007 H. Masui / Univ. of Tsukuba
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
Feb/11/2007 H. Masui / Univ. of Tsukuba
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
Feb/11/2007 H. Masui / Univ. of Tsukuba
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
Feb/11/2007 H. Masui / Univ. of Tsukuba
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
Feb/11/2007 H. Masui / Univ. of Tsukuba
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
Feb/11/2007 H. Masui / Univ. of Tsukuba
22Summary (i)• The magnitude of vThe magnitude of v22 is as large as that from perfect flui is as large as that from perfect flui
d hydrodynamics at RHICd 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
Feb/11/2007 H. Masui / Univ. of Tsukuba
23
Results (ii)identified hadrons
Feb/11/2007 H. Masui / Univ. of Tsukuba
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
Feb/11/2007 H. Masui / Univ. of Tsukuba
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 (-functi
on)– 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)
Feb/11/2007 H. Masui / Univ. of Tsukuba
26Multi-strange hadrons• Why ?Why ?
and are less affected 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)
Feb/11/2007 H. Masui / Univ. of Tsukuba
27
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
Feb/11/2007 H. Masui / Univ. of Tsukuba
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
Feb/11/2007 H. Masui / Univ. of Tsukuba
29Universal scaling of v2
At mid-rapidityAt mid-rapidity
Feb/11/2007 H. Masui / Univ. of Tsukuba
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 variety 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 hydrodynamics 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
Feb/11/2007 H. Masui / Univ. of Tsukuba
31
Back up
Feb/11/2007 H. Masui / Univ. of Tsukuba
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 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)
• Different sensitivity to “non-flow” effectsDifferent sensitivity to “non-flow” effects– Correlations unrelated to the reaction plane, ex. jet
s, resonance decays etc …
Feb/11/2007 H. Masui / Univ. of Tsukuba
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
Feb/11/2007 H. Masui / Univ. of Tsukuba
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
Feb/11/2007 H. Masui / Univ. of Tsukuba
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
Feb/11/2007 H. Masui / Univ. of Tsukuba
36
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