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

2. N. N. Ajitanand RHIC-AGS20082 Outline Formation of the QGP medium Probing the QGP medium Medium modification of jets Experimental 3-particle studies Conclusions and Outlook

3. N. N. Ajitanand RHIC-AGS20083 Cue from Lattice QCD: Phase Transition Energy density required for QGP formation Necessary to create ε > 0.6 – 1.0 GeV/fm 3 in heavy ion collisions Necessary to create ε > 0.6 – 1.0 GeV/fm 3 in heavy ion collisions

4. N. N. Ajitanand RHIC-AGS20084 PRL87, 052301 (2001) Central collisions peripheral collisions time to thermalize the system (  0 ~ 0.2 - 1 fm/c)  Bjorken  ~ 5 - 15 GeV/fm 3 ~ 35 – 100 ε 0 Extrapolation From E T Distributions Achieved Energy Density is Well Above the Predicted Value for the Phase Transition Predicted Value for the Phase Transition Achieved Energy Density is Well Above the Predicted Value for the Phase Transition Predicted Value for the Phase Transition 200 GeV Au+Au Collisions studies at RHIC!

5. N. N. Ajitanand RHIC-AGS20085 Quark scaling of v2 indicates flow sets in at the partonic stage Strong quenching observed for high pt hadrons hydro-like flow observed Conclusion : Strongly Interacting State of matter produced in 200 GeV Au + Au called sQGP Conclusion : Strongly Interacting State of matter produced in 200 GeV Au + Au called sQGP

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

7. N. N. Ajitanand RHIC-AGS20087 Jet Study via 2-particle azimuthal Correlations Associated low pT particle pT High pT particle Correlation Function N(pT)

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

9. N. N. Ajitanand RHIC-AGS20089 Simulation Test of Jet Recovery using ZYAM Di-jet faithfully recovered Normal Jet Shapeabnormal Jet Shape Line : Input Jet Correlation Squares : Extracted Jet Correlation Caution : Jet recovery very sensitive to v2 Need to assess error in v2 estimation very carefully Open symbols : v2 Closed symbols : 0.95 v2

10. N. N. Ajitanand RHIC-AGS200810 200 GeV Au+Au : Hadron Jet Shapes Jet-pair distributions resulting from decomposition show significant modification Jet-pair distributions resulting from decomposition show significant modification PRL 97, 052301 (2006) 200 GeV Au+Au 1<pT<2.5 vs 2.5<pT<4.0

11. N. N. Ajitanand RHIC-AGS200811 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

12. N. N. Ajitanand RHIC-AGS200812 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)

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

14. N. N. Ajitanand RHIC-AGS200814 Hydrodynamic Mach-Cone 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. Cloud formed by a plane breaking the sound barrier. Betz QM08

15. 15 Renk, Ruppert, Phys. Rev. C76, 014908 (2007) Mach-Cone and Flow Renk, Ruppert, Phys. Lett. B646 19 (2007) Rapidity distribution and longitudinal flow affects the observed 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.

16. 16 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. J. Ruppert & B. Müller, Phys. Lett. B618 (2005) 123 Parallel Perpendicular Current Density

17. N. N. Ajitanand RHIC-AGS200817 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. Poynting Vector shock-wave diffusion wake Bullet at 2.45c s Gubser, Pufu, Yarom arXiv:0706.4307v1 (2007)

18. N. N. Ajitanand RHIC-AGS200818 Čerenkov Gluon Radiation Gluons radiated by superluminal partons. Angle is dependent on emitted momentum. Koch, Majumder, Wang PRL 96 172302 (2006) Čerenkov angle vs emitted particle momentum p (GeV/c)

19. 19 Experimental 3-particle Studies from STAR and PHENIX

20. N. N. Ajitanand RHIC-AGS200820 STAR 3- Particle Cumulant Analysis Measure 1-, 2-, and 3-Particle Densities 3-particle densities = superpositions of truly correlated 3-particles, and combinatorial components. Cumulant technique: Simple Definition Model Independent. PROs CONsNot positive definite Interpretation perhaps difficult. Pruneau, nucl-ex/0608002

21. 21 Measurement of 3-Particle Cumulant Clear evidence for finite 3-Part Correlations Observation of flow like and jet like structures. Evidence for v 2 v 2 v 4 contributions

22. N. N. Ajitanand RHIC-AGS200822 STAR 3- Particle Azimuthal Correlation Analysis Jet+Flow Subtraction : Intuitive in concept Simple interpretation in principle. Model Dependent v 2 and normalization factors systematics Ulery QM08 PROs CONs

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

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

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

26. N. N. Ajitanand RHIC-AGS200826 STAR Associated P T Dependence No significant p T dependence of observed emission angle. –Consistent with Mach-cone –Inconsistent with simple Čerenkov radiation 0.5<p T Assoc <0.751<p T Assoc <1.5 2<p T Assoc <3

27. N. N. Ajitanand RHIC-AGS200827 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 v 2 and details of the model. Observe Structures Consistent with Conical emission in central collisions STAR Summary/Conclusions

28. 28 PHENIX 3-particle Analysis 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<p T Trig <4 GeV/c 1<p T Assoc <2.5 GeV/c **  * Trigger Plane Normal to Trigger Near Side Away Side **  * Near-Side  * =  Au+Au 10-20 % Ajitanand QM08,HP06, IWCF’06

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

30. N. N. Ajitanand RHIC-AGS200830 PHENIX SIM Test of Harmonic removal Jet+Harmonic ZYAM gives good Jet Recovery Input Jet Harmonic removed Jet Correlation = Total Correlation – a0*(Harmonic Correlation) “ao” is adjusted till Jet Correlation surface goes to zero at its minimum (ZYAM )

31. 31 Blue : Input Red : Recovered True 3P correlations successfully recovered (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 Test of (2+1) removal (2+1) processes successfully removed Flat Correlation Surface (offset added)

32. N. N. Ajitanand RHIC-AGS200832 3-particle Correlations without harmonic removal PHENIX Preliminary Data Most central shows jet dominated landscape with strong away side modification 10-20 % 0-5 %5-10 % 20-40 %40-60 %60-90 %

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

34. N. N. Ajitanand RHIC-AGS200834 Data Simulated Deflected jet Simulated Mach Cone The data validates the presence of a Mach Cone away-side jet but does not rule out contributions from other topologies. Total 3P jet correlations True 3P jet correlations Azimuthal Sections

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

36. 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 –p T 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. N. N. Ajitanand RHIC-AGS200837 Outlook New data and detectors will allow for: –Higher statistics will allow for systematic studies of both trigger (RP aligned) and associated p T 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 c s and EOS.