R. Lacey, SUNY Stony Brook PHENIX Measurements of Correlations at RHIC 1 National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) for the PHENIX Collaboration Arkadiy Taranenko The 15H International Conference on STRANGENESS IN QUARK MATTER (SQM 2015) JINR, Dubna, Russia, 6-11/07/2015

R. Lacey, SUNY Stony Brook Correlations Measurements at PHENIX 2 1)Introduction 2)Methods : V n measurements and HBT 3)System size and beam energy dependence of correlations 4)Correlations 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

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)

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, (2010) V n (EP): Phys.Rev.Lett. 107 (2011)  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= GeV/c.  No evidence for significant η-dependent non-flow contributions from di-jets for pT= GeV/c. Systematic uncertainty : event plane: 2-5% for v2 and 5-12% for v3. arXiv: , arXiv: arXiv: arXiv:

R. Lacey, SUNY Stony Brook = 0.39 GeV/c broader width smaller HBT radius 5 PHENIX: 3D 2π HBT correlation functions q = p 2 – p 1 k T = |p T2 + p T1 |/2 arXiv: [nucl-ex] arXiv: D Gaussian fits -Bertsch-Pratt coord. -LCMS (p 1z +p 2z =0) -Coulomb Corrected

R. Lacey, SUNY Stony Brook comparison of PHENIX & STAR HBT radii STAR data from arXiv: [nucl-ex] agreement between PHENIX and STAR data sets sizable extension in m T range from the combined data sets combine the data sets to construct excitation functions for HBT radii 6 Comparison of PHENIX vs STAR 3D 2π HBT Radii arXiv: [nucl-ex]

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? 7 Centrality dependence of v2 in CuCu/AuAu collisions at GeV 5 σ x & σ y  RMS widths of density distribution  Geometric fluctuations included  Geometric quantities constrained by multiplicity density.

R. Lacey, SUNY Stony Brook 8 Acoustic viscous modulation of v n Staig & Shuryak Phys.Rev. C84(2011) Collective Flow is acoustic Scaling expectations: v n is related to v 2 System size dependence n 2 dependence Initial Geometry characterized by many shape harmonics (ε n )  drive v n Roy A. Lacey et al, Phys.Rev.Lett. 112 (2014) 8; arXiv:

R. Lacey, SUNY Stony Brook 9 - Viscous Hydrodynamics Slope parameter β″ is nearly the same for Au+Au at GeV, but shows change from Au+Au to Cu+Cu at 200 GeV. Bigger viscous damping in smaller systems / different beam energy dependence? PRL112, (2014)

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

R. Lacey, SUNY Stony Brook 11 v 3 in 200 GeV Cu+Au vs Cu+Cu/Au+Au 11Phys.Rev. C84 (2011) The observed system size independence of v3 Is expected from the similar values of ɛ 3 Simultaneus measurements of v2 and v3  Crucial constraint for η/s

R. Lacey, SUNY Stony Brook geometric scaling of HBT radii in HI collisions S i are slopes from linear fits arXiv: [nucl-ex] 12

R. Lacey, SUNY Stony Brook q Expansion dynamics from HBT radii emission lifetime expansion radius for small m T emission duration expansion rate From the literature: ZPC 39, 69 (1988) PRL 74, 4400 (1995) PRL 75, 4003 (1995) NPA 608, 479 (1996) PRC 53, 918 (1996) 13 HBT radii = initial size + expansion + position-momentum correlations for central collisions, the initial-state Gaussian radius is

R. Lacey, SUNY Stony Brook nonmonotonic behavior with a maximum in emission duration  and corresponding minimum in expansion rate in this beam energy range. These characteristic non-monotonic patterns signal a suggestive change in the reaction dynamics arXiv: [nucl-ex] 14

R. Lacey, SUNY Stony Brook GeV 19.6 GeV39 GeV 62.4 GeV 200 GeV 2.76 TeV Scaling properties of flow Lacey et. al, Phys.Rev.Lett. 112 (2014) Phys.Rev. C91 (2015) 6, Karpenko, Iu.A.

R. Lacey, SUNY Stony Brook 16 Collective Effects in Small Systems: LHC and RHIC: p+Pb, d+Au Mass ordering of PID v2 in p+Pb (ALICE,CMS) and d+Au (PHENIX) Multiparticle correlations: CMS, ATLAS, ALICE Long-range correlations: double ridge : CMS, ATLAS, ALICE, PHENIX,STAR Scaling relations: p+Pb vs Pb+Pb: CMS,ATLAS

R. Lacey, SUNY Stony Brook Geometric scaling of HBT radii arXiv: [nucl-ex] HBT radii scale with initial transverse size for both p(d)+A and A+A collisions larger slope corresponds to larger expansion rate for LHC data final-state rescattering effects are important in p(d)+A collisions also 17

R. Lacey, SUNY Stony Brook Long range correlation in d+Au/ 3 He+Au 18 Ridges are seen on both Au-going and 3 He-going sides | Δ| > 2.75 : MPC – hadron correlations

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 19 PHENIX Plan to study more systems | Δ| > 2.75 : Event plane method

R. Lacey, SUNY Stony Brook 20 PHENIX Plan to study more systems 2013: d+Au at 200 GeV 2014: 3 He+Au ( with high multiplicity trigger) 2015: p+p, p+Au, p+Al ( with high multiplicity trigger) 2016: interested in beam energy scan for p+Au or d+Au collisions ( 20, 39, 62, 200 GeV) Schenke

R. Lacey, SUNY Stony Brook 21 v 2 of Identified charged hadrons Au+Au/Cu+Cu at 200 GeV arXiv:

R. Lacey, SUNY Stony Brook 22 v 2, v 3, v 4 of Identified charged hadrons Au+Au at 200 GeV arXiv:

R. Lacey, SUNY Stony Brook 23 Scaling Properties of Vn Flow at 200 GeV arXiv:  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

R. Lacey, SUNY Stony Brook 24 arXiv: , arXiv: arXiv: arXiv: 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 e-Print: arXiv: arXiv: Comparison with LHC ALICE Pb+Pb at 2.76 TeV : charged pions

R. Lacey, SUNY Stony Brook 25 arXiv: , arXiv: arXiv: arXiv: PHENIX ALICE:: arXiv: arXiv: Comparison with LHC ALICE Pb+Pb at 2.76 TeV : (anti)protons apply blueshift to RHIC data

R. Lacey, SUNY Stony Brook 26 arXiv: , arXiv: arXiv: arXiv: Difference in kaons between RHIC and LHC looks complicated, especially the difference between charged and neutral kaons at LHC. PHENIX ALICE: CERN-PH-EP e-Print: arXiv: arXiv: Comparison with LHC ALICE Pb+Pb at 2.76 TeV : kaons

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 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 From HBT radii in symmetric HI collisions:  Nonmonotonic behavior in this beam energy range of emission duration and expansion rate  change in expansion dynamics in this energy range 27

R. Lacey, SUNY Stony Brook 28 Backup Slides

R. Lacey, SUNY Stony Brook 29 Possible signals In the vicinity of a phase transition or the CEP anomalies in the space-time dynamics can enhance the time-like component of emissions. v 1 and HBT measurements are invaluable probes Dirk Rischke and Miklos Gyulassy Nucl.Phys.A608: ,1996 Dirk Rischke and Miklos Gyulassy Nucl.Phys.A608: ,1996 In the vicinity of a phase transition or the CEP, the sound speed is expected to soften considerably. H. Stoecker, NPA 750, 121 (2005) Collapse of directed flow

R. Lacey, SUNY Stony Brook Ye Olde HBT formulae Formerly used to understand dynamics before era of multi-stage models, assumptions too restrictive 30 Chapman, Scotto, Heinz, PRL (95) Makhlin, Sinyukov, ZPC (88) (R 2 out -R 2 side ) sensitive to emission duration empirical fit just as effective Anticipate extended emission duration with 1 st order transition

R. Lacey, SUNY Stony Brook 31 Scaling properties of flow

R. Lacey, SUNY Stony Brook 32 Recent PHENIX publications on flow at RHIC: 1) 2) Recent PHENIX publications on flow at RHIC: 1) Systematic Study of Azimuthal Anisotropy in Cu+Cu and Au+Au Collisions at 62.4 and 200 GeV: arXiv: ) Measurement of the higher-order anisotropic flow coefficients for identified hadrons in Au+Au collisions at 200 GeV : arXiv:

R. Lacey, SUNY Stony Brook 33 Flow in symmetric colliding systems : Cu+Cu vs Au+Au 33 Phys.Rev.Lett. 107 (2011) 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

R. Lacey, SUNY Stony Brook 34 A B  Geometric fluctuations included  Geometric quantities constrained by multiplicity density. Phys. Rev. C 81, (R) (2010) arXiv: σ x & σ y  RMS widths of density distribution Geometric quantities for scaling Geometry Roy A. Lacey, Stony Brook University, QM2014