1 Anisotropic RHIC Hiroshi Masui / Univ. of Tsukuba Feb./11/2007 RHIC 高エネルギー原子核反応の物理研究会、 RHIC 現象論松本合宿

Feb/11/2007H. Masui / Univ. of Tsukuba 2 Outline IntroductionIntroduction –Anisotropic flow, eccentricity ResultsResults –Several scaling relations have been observed especially for elliptic flow Eccentricity scaling Scaling of higher order anisotropy m T and NCQ scaling of elliptic flow SummarySummary

Feb/11/2007H. Masui / Univ. of Tsukuba 3 Definition & Terminology

Feb/11/2007H. Masui / Univ. of Tsukuba 4 Anisotropic 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 Reaction plane X Z Y PxPx PyPy PzPz

Feb/11/2007H. Masui / Univ. of Tsukuba 5 Observables Particle azimuthal distributions by Fourier expansionParticle azimuthal distributions by Fourier expansion –Odd harmonics (v 1, v 3, …) vanish at mid-rapidity in symmetric collision v 2 = “Elliptic Flow”v 2 = “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/11/2007H. Masui / Univ. of Tsukuba 6 Methods Event plane methodMulti-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 (decrease) 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, (2000); Phys. Rev. C64, (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/11/2007H. Masui / Univ. of Tsukuba 7 Event plane method Brackets denote average over all events and all particles,  k n is “event plane resolution”Brackets denote average over all events and all particles,  k n is “event plane resolution” w (weight) is chosen to maximize the event plane resolution (ex. p T, multiplicity etc)w (weight) is chosen to maximize the event plane resolution (ex. p T, multiplicity etc) –The best weight is v n itself 

Feb/11/2007H. Masui / Univ. of Tsukuba 8 Event PHENIX Event plane Beam-Beam Counter (BBC), |  | ~ 3 - 4Event plane Beam-Beam Counter (BBC), |  | ~ Large rapidity gap between measured particles (  ~ 0) and event plane  Reduce non-flow effectsLarge rapidity gap between measured particles (  ~ 0) and event plane  Reduce non-flow effects –di-jet contribution is negligible (nucl-ex/ )

Feb/11/2007H. Masui / Univ. of Tsukuba 9 Multi-particle correlation Non-flow effects contribute orderNon-flow effects contribute order –1/N in 2-particle correlation –1/N 3 in 4-particle correlation 2-particle correlation 4-particle correlation

Feb/11/2007H. Masui / Univ. of Tsukuba 10 Terminology  std : standard eccentricity  std : standard eccentricity –Spatial anisotropy in coordinate space  part  : Participant eccentricity  part  : Participant eccentricity –Effect from the fluctuations in the positions of participant nucleons v 2 {EP 2 } : v 2 with respect to the 2 nd harmonic Event Planev 2 {EP 2 } : v 2 with respect to the 2 nd harmonic Event Plane –v 2 {BBC} : v 2 {EP 2 } by BBC in PHENIX –v 2 {FTPC} : v 2 {EP 2 } by Forward-TPC in STAR –v 2 {EP}(AA-pp) : Modified event plane method v 2 {n} : v 2 from n-th particle cumulantsv 2 {n} : v 2 from n-th particle cumulants v 4 {n} : v 4 from n-th particle cumulantsv 4 {n} : v 4 from n-th particle cumulants

Feb/11/2007H. Masui / Univ. of Tsukuba 11 Eccentricity : definition Participant eccentricity in a given event is defined by the axes (x’, y’)Participant eccentricity in a given event is defined by the axes (x’, y’) –  …  denote average over all participant nucleons and events in the same impact parameter –{…} denote the average over all participants in one collision event

Feb/11/2007H. Masui / Univ. of Tsukuba 12 Eccentricity vs centrality Fluctuations lead significant increase of eccentricity at most central and peripheralFluctuations lead significant increase of eccentricity at most central and peripheral

Feb/11/2007H. Masui / Univ. of Tsukuba 13 Results (i) non-identified hadrons

Feb/11/2007H. Masui / Univ. of Tsukuba 14 Integrated v 2 ~ 50 % increase from SPS to RHIC~ 50 % increase from SPS to RHIC Hadron cascade underestimate the magnitude of v 2 at RHICHadron cascade underestimate the magnitude of v 2 at RHIC –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, (2003) STAR : Nucl. Phys. A715, 45c, (2003). PHENIX : Preliminary. PHOBOS : nucl-ex/ (2006) QM2005, H. Masui RQMD

Feb/11/2007H. Masui / Univ. of Tsukuba 15 Eccentricity scaling (i) Assume  = k  v 2Assume  = k  v 2 A Glauber model estimate of  givesA Glauber model estimate of  gives –k = 3.1  0.2 v 2 scales with  and the scaled v 2 values are independent of the system sizev 2 scales with  and the scaled v 2 values are independent of the system size  Scale invariance of ideal hydrodynamics  Scale invariance of ideal hydrodynamics nucl-ex/

Feb/11/2007H. Masui / Univ. of Tsukuba 16 Eccentricity scaling (ii) Scaling of v 2 /  part  in Cu+Cu and Au+AuScaling of v 2 /  part  in Cu+Cu and Au+Au Participant eccentricity is relevant geometric quantity for generating elliptic flowParticipant eccentricity is relevant geometric quantity for generating elliptic flow PRL: nucl-ex/ PRC C72, R (2005) PHOBOS Collaboration PRL: nucl-ex/ Cu+Cu 200 GeV Au+Au 200 GeV Statistical errors only

Feb/11/2007H. Masui / Univ. of Tsukuba 17 Eccentricity scaling (iii) Linear increase from SPS to RHICLinear increase from SPS to RHIC Eccentricity scaling of v 2 reach hydro limit at most centralEccentricity scaling of v 2 reach hydro limit at most central QM2006, R. NouicerQM2006, S. A. Voloshin

Feb/11/2007H. Masui / Univ. of Tsukuba 18 Differential v 2, v 2 (p T ) : PHENIX vs STAR (Au+Au) Non-flow effects are under controlNon-flow effects are under control –v 2 {4}  v 2 {BBC} ~ v 2 {FTPC} < v 2 {2} Similar acceptance : BBC, FTPC QM2006, S. A. Voloshin STAR : Phys. Rev. Lett. 93, (2004) PHENIX : Preliminary

Feb/11/2007H. Masui / Univ. of Tsukuba 19 v 2 (p T ) 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) v 2 {2} v 2 {FTPC} PHENIX : nucl-ex/

Feb/11/2007H. Masui / Univ. of Tsukuba 20 Higher order Non-zero v 4 at RHICNon-zero v 4 at RHIC –v 4 ~ (v 2 ) 2 (Ollitrault) v 4 /(v 2 ) 2 is a probe of ideal hydro behaviorv 4 /(v 2 ) 2 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/11/2007H. Masui / Univ. of Tsukuba 21 v 4 /(v 2 ) 2 vs p T Experimentally, v 4 /(v 2 ) 2 ~ Experimentally, v 4 /(v 2 ) 2 ~ –Ideal hydro prediction v 4 /(v 2 ) 2 = 0.5 Maximum non-flow contributionMaximum non-flow contribution Star Preliminary

Feb/11/2007H. Masui / Univ. of Tsukuba 22 Summary (i) The magnitude of v 2 is as large as that from perfect fluid hydrodynamics at RHICThe magnitude of v 2 is as large as that from perfect fluid hydrodynamics at RHIC –50 % increase from SPS –Hadron cascade cannot reprduce the magnitude of v 2 Eccentricity scalingEccentricity scaling –Consistent description of Au+Au and Cu+Cu v 2 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, v 4Higher order, v 4 –Non-zero v 4 is observed –v 4 /(v 2 ) 2 ~ 1 > 0.5 but systematic error is huge at high p T

Feb/11/2007H. Masui / Univ. of Tsukuba 23 Results (ii) identified hadrons

Feb/11/2007H. Masui / Univ. of Tsukuba 24 “m T scaling” of v 2 v 2 {BBC} for identified hadronsv 2 {BBC} for identified hadrons At low p T, m T scaling of v 2At low p T, m T scaling of v 2 –Radial flow leads mass ordering of v 2 Meson-Baryon grouping at intermediate p TMeson-Baryon grouping at intermediate p T –Quark coalescence, recombination

Feb/11/2007H. Masui / Univ. of Tsukuba 25 NCQ scaling of v 2 NCQ scaling indicate the collective flow evolves in quark levelNCQ scaling indicate the collective flow evolves in quark level Number of Constituent Quark scaling by quark coalescence / recombination modelNumber of Constituent Quark scaling by quark coalescence / recombination model AssumptionAssumption –Exponential p T spectra –Narrow momentum spread (  - function) –Common v 2 for light quarks (u, d, s) R. J. Fries, et., al, Phys. Rev. C68, (2003) V. Greco, et., al, Phys. Rev. C68, (2003)

Feb/11/2007H. Masui / Univ. of Tsukuba 26 Multi-strange hadrons Why ?Why ? –  and  are less affected by hadronic interactions –Hadronic interactions at a later stage do not produce enough v 2 Y. Liu et., al, J. Phys. G32, 1121 (2006) J. H. Chen et., al, Phys. Rev. C74, (2006)

Feb/11/2007H. Masui / Univ. of Tsukuba 27 QM06, A. Taranenko STAR preliminary 200 GeV Au+Au SQM06, M. Oldenburg Multi-strange hadrons  meson v2 is more consistent with meson v 2 than baryon v 2  meson v2 is more consistent with meson v 2 than baryon v 2 Show sizable v 2Show sizable v 2 –Collectivity at pre-hadronic stage, s-quark flow

Feb/11/2007H. Masui / Univ. of Tsukuba 28 Universal scaling of v 2 Substantial elliptic flow signals are observed for a variety of particles species at RHICSubstantial elliptic flow signals are observed for a variety of particles species at RHIC

Feb/11/2007H. Masui / Univ. of Tsukuba 29 Universal scaling of v 2 At mid-rapidity

Feb/11/2007H. Masui / Univ. of Tsukuba 30 Summary (ii) Mass ordering at low p TMass ordering at low p T –Predicted by hydrodynamics (radial flow effect) At intermediate p T, NCQ scaling holds a variety of particles speciesAt intermediate p T, NCQ scaling holds a variety of particles species –Indication of light quark (u, d, s) collectivity at pre- hadronic stage Universal v 2 motivated by perfect fulid hydrodynamics is observed for both mesons and baryons over a broad range of kinetic energy, centrality via NCQ scalingUniversal v 2 motivated by perfect fulid hydrodynamics is observed for both mesons and baryons over a broad range of kinetic energy, centrality via NCQ scaling

Feb/11/2007H. Masui / Univ. of Tsukuba 31 Back up

Feb/11/2007H. Masui / Univ. of Tsukuba 32 Flow 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, 1671 (1998) –Multi-particle correlation method N. Borghini, P. M. Dinh, J.-Y. Ollitrault, Phys. Rev. C (2000); Phys. Rev. C64, (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. jets, resonance decays etc …

Feb/11/2007H. Masui / Univ. of Tsukuba 33 Non-flow effects from Jets (i) Nucl-ex/ Nucl-ex/ “Trigger” p T : 2.5 < p T < 4 GeV/c“Trigger” p T : 2.5 < p T < 4 GeV/c “Associated” p T : 1 < p T < 2 GeV/c“Associated” p T : 1 < p T < 2 GeV/c Background Au+Au events from HIJINGBackground Au+Au events from HIJING –Checked to reproduce the charged hadron multiplicity in  from PHOBOS –v 2 is implemented according to the PHENIX v 2 measurement (nucl- ex/ ) Di-jet pairs are generated from PYTHIADi-jet pairs are generated from PYTHIA

Feb/11/2007H. Masui / Univ. of Tsukuba 34 Non-flow effects from Jets (ii) Fake v 2 for leading particlesFake v 2 for leading particles –Fake v 2 is negligible in BBC acceptance (3 <  < 4) NOTENOTE –Results are not corrected event plane resolution

Feb/11/2007H. Masui / Univ. of Tsukuba 35 Non-flow effect on v 4 Consider 3-particle correlationConsider 3-particle correlation Maximum non-flow contribute if (i, k) correlate non-flow and (j, k) correlate flowMaximum non-flow contribute if (i, k) correlate non-flow and (j, k) correlate flow flowNon-flow

Feb/11/2007H. Masui / Univ. of Tsukuba 36 Signal + Background Background Before subtraction After subtraction Clear  signal   K + K -   K + K - –Typical S/N ~ 0.3 Centrality 20 – 60 %Centrality 20 – 60 % –S/N is good –Event plane resolution is good –Separation of v 2 between meson and baryon is good –Magnitude of v 2 do not vary very much