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N. N. Ajitanand Nuclear Chemistry, SUNY Stony Brook 27 May 2008 AGS-RHIC Workshop 2008

Three Particle Correlations. N. N. Ajitanand Nuclear Chemistry, SUNY Stony Brook 27 May 2008 AGS-RHIC Workshop 2008. Outline. Formation of the QGP medium Probing the QGP medium Medium modification of jets Experimental 3-particle studies Conclusions and Outlook.

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N. N. Ajitanand Nuclear Chemistry, SUNY Stony Brook 27 May 2008 AGS-RHIC Workshop 2008

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  1. Three Particle Correlations N. N. Ajitanand Nuclear Chemistry, SUNY Stony Brook 27 May 2008 AGS-RHIC Workshop 2008

  2. Outline • Formation of the QGP medium • Probing the QGP medium • Medium modification of jets • Experimental 3-particle studies • Conclusions and Outlook N. N. Ajitanand RHIC-AGS2008

  3. Cue from Lattice QCD: Phase Transition Energy density required for QGP formation Necessary to create ε > 0.6 – 1.0 GeV/fm3 in heavy ion collisions N. N. Ajitanand RHIC-AGS2008

  4. PRL87, 052301 (2001) Extrapolation From ET Distributions peripheral collisions Central collisions time to thermalize the system (t0 ~ 0.2 - 1 fm/c) eBjorken~ 5 - 15 GeV/fm3 ~ 35 – 100 ε0 200 GeV Au+Au Collisions studies at RHIC! Achieved Energy Density is Well Above the Predicted Value for the Phase Transition N. N. Ajitanand RHIC-AGS2008

  5. Strong quenching observed for high pt hadrons Conclusion : Strongly Interacting State of matter produced in 200 GeV Au + Au called sQGP hydro-like flow observed Quark scaling of v2 indicates flow sets in at the partonic stage N. N. Ajitanand RHIC-AGS2008

  6. Jets are a natural probe of the Medium Finally partons fragment, (possibly) outside the medium Scattered partons propagate through the medium radiating gluons and interacting with partons of the medium In relatvistic heavy ion collisions hard parton-parton processes occur early

  7. pT Jet Study via 2-particle azimuthal Correlations High pT particle N(pT) Associated low pT particle Correlation Function N. N. Ajitanand RHIC-AGS2008

  8. Two source model gives : Correlation Flow Jet ZYAM : Zero Yield At Minimum Sets a0 It is necessary to decompose the correlation function to obtain the Jet Function! vary a0 till condition is satisfied Correlation Jet H(v2) Obtain using BBC Reaction Plane Large η gap minimizes non-flow effects Ajitanand et.al. Phys. Rev. C 72, 011902 (2005)

  9. Simulation Test of Jet Recovery using ZYAM Di-jet faithfully recovered Normal Jet Shape abnormal Jet Shape Line : Input Jet Correlation Squares : Extracted Jet Correlation Open symbols : v2 Closed symbols : 0.95 v2 Caution : Jet recovery very sensitive to v2 Need to assess error in v2 estimation very carefully N. N. Ajitanand RHIC-AGS2008

  10. 200 GeV Au+Au : Hadron Jet Shapes PRL 97, 052301 (2006) 200 GeV Au+Au 1<pT<2.5 vs 2.5<pT<4.0 Jet-pair distributions resulting from decomposition show significant modification N. N. Ajitanand RHIC-AGS2008

  11. Medium modification of jets : Expectations • Mach-cone in HIC first introduced in 1970s by Hofmann, Stöcker, Heinz, Scheid and Greiner. • Away-side structure in 2-particle correlations renewed interest. • Conical emission is a possible explanation for shape: • Mach-cone shock waves • Čerenkov gluon radiation • Other explanations suggested: • Large angle gluon radiation • Defected jets • deflected by radial flow • path-length dependent energy loss N. N. Ajitanand RHIC-AGS2008

  12. Conical Emission • Mach-cone: • Shock waves excited by a supersonic parton. • Can be produced in different theories: • Hydrodynamics • H. Stöcker et al. (Nucl.Phys.A750:121,2005) • J. Casalderra-Solana et. al. (Nucl.Phys.A774:577,2006) • T. Renk & J. Ruppert (Phys.Rev.C73:011901,(2006)) • Colored plasma • J. Ruppert & B. Müller (Phys.Lett.B618:123,2005) • AdS/CFT • S. Gubser, S. Pufu, A. Yarom. (arXiv:0706.4307v1, 2007) • Čerenkov Gluon Radiation: • Radiation of gluons by a superluminal parton. • I.M. Dremin (Nucl. Phys. A750: 233, 2006) • V. Koch et. al. (Phys. ReV. Lett. 96, 172302, 2006) • A. Majumdar Hard Probes 2006 • Parton Cascade • G. L. Ma et. al. (Phys. Lett. B647, 122, 2007) N. N. Ajitanand RHIC-AGS2008

  13. Trigger M M Away-side Mach-Cone • Mach angle depends on speed of sound in medium • T dependent • Angle independent of associated pT. PNJL Model Mikherjee, Mustafa, Ray Phys. Rev. D75 (2007) 094015

  14. Renk, Ruppert, Phys. Lett. B646 19 (2007) Mach-Cone and Flow • Rapidity distribution and longitudinal flow affects theobserved angle and width. • Transverse flow affects shape of 3-particle correlation. • signal at ~1 GeV/c ~9x larger if flow and shockwave aligned than if perpendicular. Renk, Ruppert, Phys. Rev. C76, 014908 (2007)

  15. Betz QM08 Hydrodynamic Mach-Cone Cloud formed by a plane breaking the sound barrier. • Energy radiated from the parton is deposited in collective hydrodynamic modes. • Strength of the correlation dependent on source term which is not fundamentally derived. • Similar to jet creating a sonic boom in air. N. N. Ajitanand RHIC-AGS2008

  16. Parallel Colored Modes • QCD analog of charged particle in plasma from QED. • Mach-cone is longitudinal modes excited in quantum plasma by a supersonic parton. • Colored sound. • Černkov gluon radiation is the transverse mode excited by superluminal parton in the plasma. Current Density Perpendicular J. Ruppert & B. Müller, Phys. Lett. B618 (2005) 123

  17. Poynting Vector Ads/CFT • Mach cone with strong diffusion wake from heavy quarks. • Mach cone with no diffusion wake for quarkonium. • No need to add a source term. • Done in infinitely massive limit. Gubser, Pufu, Yarom arXiv:0706.4307v1 (2007) Bullet at 2.45cs diffusion wake N. N. Ajitanand RHIC-AGS2008 shock-wave

  18. Čerenkov Gluon Radiation Čerenkov angle vs emitted particle momentum • Gluons radiated by superluminal partons. • Angle is dependent on emitted momentum. Koch, Majumder, Wang PRL 96 172302 (2006) p (GeV/c) N. N. Ajitanand RHIC-AGS2008

  19. Experimental 3-particle Studies from STAR and PHENIX

  20. STAR 3- Particle Cumulant Analysis Pruneau, nucl-ex/0608002 Measure 1-, 2-, and 3-Particle Densities 3-particle densities = superpositions of truly correlated 3-particles, and combinatorial components. Cumulant technique: PROs Simple Definition Model Independent. CONs Not positive definite Interpretation perhaps difficult. N. N. Ajitanand RHIC-AGS2008

  21. Measurement of 3-Particle Cumulant • Clear evidence for finite 3-Part Correlations • Observation of flow like and jet like structures. • Evidence for v2v2v4 contributions

  22. STAR 3- Particle Azimuthal Correlation Analysis Ulery QM08 Jet+Flow Subtraction : PROs Intuitive in concept Simple interpretation in principle. CONs Model Dependent v2 and normalization factors systematics N. N. Ajitanand RHIC-AGS2008

  23. near near near Medium Medium Medium away away away di-jets deflected jets Conical Emission Azimuthal 3-Particle Correlations

  24. STAR Results d+Au Cu+Cu 0-10% pp Au+Au 10-30% Au+Au 0-12% Au+Au 50-80%

  25. Conical emission peaks STAR Projections and Angle ZDC 0-12% Au+Au shows significant peaks in off-diagonal projection at: 1.38 ± 0.02 (stat.) ± 0.06 (sys.) radians

  26. STAR Associated PT Dependence 2<pTAssoc<3 0.5<pTAssoc<0.75 1<pTAssoc<1.5 • No significant pT dependence of observed emission angle. • Consistent with Mach-cone • Inconsistent with simple Čerenkov radiation N. N. Ajitanand RHIC-AGS2008

  27. STAR Summary/Conclusions • Cumulant Method • Unambiguous evidence for three particle correlations. • Clear indication of away-side elongated peak. • No evidence for Cone signal given flow backgrounds • Jet-Flow Background Method • Model Dependent Analysis • Cone amplitude sensitive to magnitude v2 and details of the model. • Observe Structures Consistent with Conical emission in central collisions N. N. Ajitanand RHIC-AGS2008

  28. Trigger Near-Side Plane Normal to Trigger * * * * *= Ajitanand QM08,HP06, IWCF’06 PHENIX 3-particle Analysis Au+Au 10-20 % Near Side • Polar coordinate system relative to trigger particle direction. • Natural coordinate system if jets are back-to-back in both  and . • * is angle from trigger. • * the angle between the two associated particles projected onto plane defined by trigger. • 2.5<pTTrig<4 GeV/c • 1<pTAssoc<2.5 GeV/c Away Side

  29. Simulated Mach Cone *=0 Simulations Simulated Deflected jet Simulations with PHENIX acceptance. Azimuthal Sections * *

  30. PHENIX SIM Test of Harmonic removal Jet+Harmonic Jet Correlation = Total Correlation – a0*(Harmonic Correlation) “ao” is adjusted till Jet Correlation surface goes to zero at its minimum (ZYAM ) Input Jet Harmonic removed ZYAM gives good Jet Recovery N. N. Ajitanand RHIC-AGS2008

  31. Blue : Input Red : Recovered Flat Correlation Surface (offset added) Test of (2+1) removal (2+1) correlations obtained taking 2P in event 1 and 1P from event 2 For data relative amounts of soft-soft and hard-soft correlations set by relative strengths of observed 2P correlations True 3P Correlations absent True 3P Correlations present (2+1) processes successfully removed True 3P correlations successfully recovered

  32. 3-particle Correlations without harmonic removal Data PHENIX Preliminary 60-90 % 40-60 % 20-40 % 5-10 % 0-5 % 10-20 % Most central shows jet dominated landscape with strong away side modification N. N. Ajitanand RHIC-AGS2008

  33. Jet Correlations Total 3-particle Jet Correlation Radial section True 3-particle Jet Correlation Strong away side modification in both total and true 3P Jet Correlations

  34. Simulated Mach Cone Azimuthal Sections Data Total 3P jet correlations Simulated Deflected jet True 3P jet correlations The data validates the presence of a Mach Cone away-side jet but does not rule out contributions from other topologies. N. N. Ajitanand RHIC-AGS2008

  35. Run 7 3-particle Correlations (~ 5 times Run 4 statistics) 200 GeV Au+Au Run 7 PHENIX Preliminary 0-5 % 5-10 % 10-20 % 60-90 % 40-60 % 20-40 % Analysis in progress

  36. Conclusions • Broadened and double-peaked away-side structure in 2-particle correlations. • Can be explained by conical emission or other physics mechanisms. • Mach-cone • Čerenkov gluon radion • PHENIX • shape consistent with Mach-cone simulation. • STAR • Evidence of conical emission of correlated hadrons at an observed angle of 1.38 radians • pT independence of the angle suggests Mach-cone emission • With the aid of theoretical models the extracted angle my provide information on the speed of sound of the medium and the equation of state.

  37. Outlook • New data and detectors will allow for: • Higher statistics will allow for systematic studies of both trigger (RP aligned) and associated pT • Helped by increased jet production at LHC • Jet reconstruction may reveal Mach cone in favorable cases • Identified particle results: • Mach-cone emission should have a mass dependence in correlation strength • Full azimuthal TOF detectors ALICE and STAR (upgrade) will provide good PID for these analyses. • Possible change in angle between SPS, RHIC, and LHC. • Different initial temperatures • Many theoretical investigations have been carried out. • More work is needed to understand what the data tells us about cs and EOS. N. N. Ajitanand RHIC-AGS2008

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