1. R. Lacey, SUNY Stony Brook PHENIX Measurements of Anisotropic Flow in Heavy-Ion Collisions at RHIC Energies 1 Nuclear Chemistry Group, SUNY Stony Brook, NY for the PHENIX Collaboration Arkadiy Taranenko The 2nd International Conference on the Initial Stages in High-Energy Nuclear Collisions, Napa Valley, California, 3-7/12/2014

2. R. Lacey, SUNY Stony Brook PHENIX V n Measurements at RHIC 2 1)Introduction 2)Methods / flow and non-flow 3)System size dependence of anisotropy? 4)Azimuthal anisotropy in small systems: d+Au and 3 He+Au at 200GeV 5)PID V n results and hadronization at RHIC 6)PID V 2 results: comparison with LHC 7)Conclusions and Outlook 22 33 44

3. R. Lacey, SUNY Stony Brook PHENIX Flow Measurements : Methods 3 Correlate hadrons in central Arms with event plane (RXN, etc) (I) (II)  ∆φ correlation function for EP N - EP S  ∆φ correlation function for EP - CA Central Arms (CA) |η’| < 0.35 (particle detection) ψ n RXN (|  |=1.0~2.8) MPC (|  |=3.1~3.7) BBC (|  |=3.1~3.9) From 2012: - FVTX (1.5<|  |<3)

4. R. Lacey, SUNY Stony Brook PHENIX Flow Measurements : Methods 4 ψ n RXN (|  |=1.0~2.8) MPC (|  |=3.1~3.7) BBC (|  |=3.1~3.9) Phys. Rev. Lett. 105, 062301 (2010) V n (EP): Phys.Rev.Lett. 107 (2011) 252301  Good agreement between V n results obtained by event plane (EP) and two- particle correlation method (2PC)  No evidence for significant η-dependent non-flow contributions from di-jets for pT=0.3-3.5 GeV/c.  No evidence for significant η-dependent non-flow contributions from di-jets for pT=0.3-3.5 GeV/c. Systematic uncertainty : event plane: 2-5% for v2 and 5-12% for v3. arXiv:1412.1038, arXiv:1412.1043arXiv:1412.1038arXiv:1412.1043

5. R. Lacey, SUNY Stony Brook 5 Recent PHENIX publications on flow at RHIC: 1) 2) Recent PHENIX publications on flow at RHIC: 1) Systematic Study of Azimuthal Anisotropy in Cu+Cuand Au+Au Collisions at 62.4 and 200 GeV: arXiv:1412.1043 2) Measurement of the higher-order anisotropic flow coefficients for identified hadrons in Au+Au collisions at 200 GeV : arXiv:1412.1038 5

6. R. Lacey, SUNY Stony Brook Eccentricity scaling is broken and v2/ ɛ depends on the Knudsen number K=λ/ Ṝ, where λ is the mean free path and Ṝ is the transverse size of the system. How viscous damping depends on the size of the colliding system / beam energy? 6 Centrality dependence of v2 in CuCu/AuAu collisions at 62.4-200 GeV 5 σ x & σ y  RMS widths of density distribution  Geometric fluctuations included  Geometric quantities constrained by multiplicity density.

7. R. Lacey, SUNY Stony Brook 7 - Viscous Hydrodynamics Slope parameter β″ is nearly the same for Au+Au at 62.4-200 GeV, but shows change from Au+Au to Cu+Cu at 200 GeV. Bigger viscous damping in smaller systems / different beam energy dependence? PRL112, 082302(2014)

8. R. Lacey, SUNY Stony Brook 8 Flow in symmetric colliding systems : Cu+Cu vs Au+Au 8 Phys.Rev.Lett. 107 (2011) 252301 Strong centrality dependence of v 2 in AuAu, CuCu Weak centrality dependence of v 3 Scaling expectation: Simultaneus measurements of v2 and v3  Crucial constraint for η/s

9. R. Lacey, SUNY Stony Brook 9 Centrality/Pt dependence of v 2, v 3 in 200 GeV Cu+Au 9 - Clear centrality dependence of v 2 - No Significant centrality dependence of v 3  Same centrality dependence as seen in symmetric collisions: Au+Au and Cu+Cu

10. R. Lacey, SUNY Stony Brook 10 v 2, in 200 GeV Cu+Au vs Cu+Cu/Au+Au 10 Phys.Rev. C84 (2011) 067901 The observed system size dependence of v2: AuAu>Cu+Au>CuCu originate from the differences in initial ɛ 2

11. R. Lacey, SUNY Stony Brook 11 v 3 in 200 GeV Cu+Au vs Cu+Cu/Au+Au 11 Phys.Rev. C84 (2011) 067901 The observed system size independence of v3 Is expected from the similar values of ɛ 3

12. R. Lacey, SUNY Stony Brook Long range correlation in d+Au/ 3 He+Au 12 Ridges are seen on both Au-going and 3 He-going sides

13. R. Lacey, SUNY Stony Brook The v 2 and v 3 in 3 He+Au The v 2 of 3 He+Au is similar to that of d+Au A clear v 3 signal is observed in 0- 5% 3 He+Au collisions 13

14. R. Lacey, SUNY Stony Brook The v 2 of  and p in d+Au Mass ordering for identified hadron is observed in both d+Au and p+Pb ---- consistent with hydrodynamic flo w 14

15. R. Lacey, SUNY Stony Brook 15 v 2 of Identified charged hadrons Au+Au/Cu+Cu at 200 GeV arXiv:1412.1043

16. R. Lacey, SUNY Stony Brook 16 v 2, v 3, v 4 of Identified charged hadrons Au+Au at 200 GeV arXiv:1412.1038

17. R. Lacey, SUNY Stony Brook 17 Scaling Properties of Vn Flow at 200 GeV arXiv:1412.1038  NCQ-scaling holds well for v 2,v 3,v 4 below 1GeV in KE T space, at 200GeV v n is related to v 2

18. R. Lacey, SUNY Stony Brook 18 arXiv:1412.1038, arXiv:1412.1043arXiv:1412.1038arXiv:1412.1043 V2(pt) shape if very similar for charged pions between RHIC/LHC: 10-14% difference The difference in eccentricities between : ɛ 2(PbPb at 2.76TeV) and ɛ 2(Au+Au at 200 GeV) will increase the difference by 5-7%. PHENIX ALICE: CERN-PH-EP-2014-104 e-Print: arXiv:1405.4632 arXiv:1405.4632 Comparison with LHC ALICE Pb+Pb at 2.76 TeV : charged pions

19. R. Lacey, SUNY Stony Brook 19 arXiv:1412.1038, arXiv:1412.1043 arXiv:1412.1038arXiv:1412.1043 PHENIX ALICE:: arXiv:1405.4632 arXiv:1405.4632 Comparison with LHC ALICE Pb+Pb at 2.76 TeV : (anti)protons apply blueshift to RHIC data

20. R. Lacey, SUNY Stony Brook 20 arXiv:1412.1038, arXiv:1412.1043arXiv:1412.1038arXiv:1412.1043 Difference in kaons between RHIC and LHC looks complicated, especially the difference between charged and neutral kaons at LHC. PHENIX ALICE: CERN-PH-EP-2014-104 e-Print: arXiv:1405.4632 arXiv:1405.4632 Comparison with LHC ALICE Pb+Pb at 2.76 TeV : kaons

21. R. Lacey, SUNY Stony Brook Summary V 2 and V 3 studied in different colliding systems: Au+Au/Cu+Cu and Cu+Au: –Similar magnitudes and trends observed both v2 and v3, independent of system –Viscous damping effects appear to be larger for smaller systems The ridge is observed in d+Au and 3 He+Au. –Similar magnitudes observed for v2 – v 3 signal observed for 3 He+Au –Mass ordering observed; splitting less than observed at LHC The v n of identified charged hadrons presented as a function of pT and centrality –Mass ordering for all harmonics at all centralities studied –Measurements can be scaled by generalized quark number scaling 21

22. R. Lacey, SUNY Stony Brook 22 Backup Slides

23. R. Lacey, SUNY Stony Brook 23 A B  Geometric fluctuations included  Geometric quantities constrained by multiplicity density. Phys. Rev. C 81, 061901(R) (2010) arXiv:1203.3605 σ x & σ y  RMS widths of density distribution Geometric quantities for scaling Geometry Roy A. Lacey, Stony Brook University, QM2014

24. R. Lacey, SUNY Stony Brook 24 PHENIX Flow Measurements : Event Plane Resolution

25. R. Lacey, SUNY Stony Brook 25 centrality (%) n=2 RXN n=3 RXN n=4 RXN n=2 MPC n=3 MPC  n = 200GeV Au+Au PHENIX Preliminary PHENIX Flow Measurements : Event Plane Resolution ψ n RXN (|  |=1.0~2.8) MPC (|  |=3.1~3.7) BBC (|  |=3.1~3.9) Overall good event plane resolution for V n measurements and study beam energy dependence of the flow.

26. R. Lacey, SUNY Stony Brook Significant bias from near-side jet for |Δη|<0.5 Consistent for larger Δη at p T <4 GeV Deviation again for p T >4 GeV due to swing of recoil jet EP method ( |Δη|< 2.5 with EP from full FCAL: 3.3<||<4.8 ) 26 Effect of rapidity gap on V n measurements at LHC J. Jia [ ATLAS Collaboration ] QM 2011 ATLAS AN: http://cdsweb.cern.ch/record/1352458 8

27. R. Lacey, SUNY Stony Brook Significant bias from near-side jet for |Δη|<0.5 Consistent for larger Δη at p T <4 GeV Deviation again for p T >4 GeV due to swing of recoil jet EP method ( |Δη|< 2.5 with EP from full FCAL: 3.3<||<4.8 ) 27 Effect of rapidity gap on V n measurements at LHC J. Jia [ ATLAS Collaboration ] QM 2011 ATLAS AN: http://cdsweb.cern.ch/record/1352458 5

28. R. Lacey, SUNY Stony Brook 28 Differential v 2 (p T ): Comparison with STAR Multi-particle methods Ratio V 2 {STAR} / V 2 {PHENIX EP} < 1.0 for 4p cumulant and LYZ method. LYZ : Lee-Yang-Zeros Method Lee-Yang-Zeros Method 4p cumulant method

29. R. Lacey, SUNY Stony Brook 29 Elliptic Flow Measurements V 2 (p T, centrality) in PHOBOS/STAR/PHENIX TPC FTPC ZDC/SMD FTPC ZDC/SMD η Central Arms BBC/MPC ZDC/SMD |η| < 1.3 |η|<0.35 η 2.5 <|η|< 4.0|η| > 6.3 3.1<|η|<3.7 RXN |η| > 6.6 1.0<|η|<2.8 3.1<|η|<3.9 STAR PHENIX 2.05<|η|<3.2 η EP PHOBOS η = 0-1.6 29

30. R. Lacey, SUNY Stony Brook 30 Elliptic Flow of Charged Hadrons: Au+Au at 39-200 GeV No significant change in v 2 (p T ) for √s = 39 -200 GeV ! Precision Data

31. R. Lacey, SUNY Stony Brook 31 PHENIX: Extensive anisotropy Data Phys. Rev. Lett. 105, 062301 (2010) High precision double differential measurements Phys.Rev.C81:034907,2010 31

32. R. Lacey, SUNY Stony Brook 32 KE T /n q < 1GeV – soft physics Hydrodynamic flow Interplay soft-hard 3.0 < p T < 5 GeV/c ? Hard dominates: p T > 5 GeV/c 32

33. R. Lacey, SUNY Stony Brook PHENIX Preliminary KE T & n q scaling validated for v 2 as a function of centrality Flow scales across centrality PHENIX Preliminary 33

34. R. Lacey, SUNY Stony Brook 34 V 4 : A Small, But Sensitive Observable For Heavy Ion Collisions Do we have qualitative agreement ? Answer is : YES!!! J.Phys.G35:104105,2008,J.Phys.G36:064061,2009 PHENIX: QM 08, WWND 08, DNP 08, QM 09 STAR: WWND 09, QM 2009 STAR preliminary V 4 ~ k * (V 2 2 ) – very small signal 34

35. R. Lacey, SUNY Stony Brook 35 Are Flow Measurements at RHIC Reliable?: PHENIX / PHOBOS from PHOBOS QM06 proc. J. Phys. G34 S887 (2007)‏ EP{2}EP{1} η PHOBOS EP: 2.05<|η|<3.2 Overall good agreement between differential flow measurements EP: 1.0<|η|<2.8 EP: 3.1<|η|<3.7 35

36. R. Lacey, SUNY Stony Brook 36 Are Flow Measurements at RHIC Reliable?: PHENIX / STAR (2) For 0-20% central collisions STAR V 2 > PHENIX V 2 : Is rapidity gap in STAR TPC too small ? Need detailed comparison with STAR FTPC results (2.5 <|η|< 4.0 ) Do we have the same centrality definition between experiments?

37. R. Lacey, SUNY Stony Brook V 2 {EP} – standard EP method V 2 {EP 2 } – modified EP method EP-Star 37 Are Flow Measurements at RHIC Reliable?: PHENIX / STAR (1) Overall good agreement for mid-central collisions with STAR results obtained using modified EP method ( exclude |Δη|<0.5 )