1. HI:C 07 - Montreal C. Pruneau, Wayne State 1 New Perspectives on Measurements of 2- and 3- Particle Correlations Claude A. Pruneau Wayne State University Detroit, MI, USA

2. HI:C 07 - Montreal C. Pruneau, Wayne State 2 Beyond the disappearance of Away-Side Jets 3<p t,trigger <4 GeV p t,assoc. >2 GeV Jörn Putschke, et al., STAR, Quark Matter 2006 Mark Horner, et al., STAR, Quark Matter 2006 p T,trig = 3.0-4.0 GeV/c; p T,asso = 1.0-2.5 GeV/c Au+Au 0-10% STAR preliminary Near-Side Ridge Away-Side Dip

3. HI:C 07 - Montreal C. Pruneau, Wayne State 3 “Reappearance” of the away side jet STAR Phys. Rev. Lett. 97 (2006) 162301 “Progressive” re-appearance of the away-side jet with increasing trigger pt in central Au+Au. Away-side yield vary with “system” size or collision centrality Yield dramatically suppressed rel. to d+Au. Associated yield on the near side is independent of centrality. 8 < p t (trig)<15

4. HI:C 07 - Montreal C. Pruneau, Wayne State 4 Theoretical Scenarios - Ridge  Parton radiates energy before fragmenting and couples to the longitudinal flow  Gluon bremsstrahlung of hard-scattered parton  Parton shifted to lower p t  Radiated gluon contributes to broadening  near-side jet also looses energy (finite pathlength)!  Medium heating + Parton recombination  Chiu & Hwa Phys. Rev. C72:034903,2005)  Recombination of thermal partons only indirectly affected by hard scattering  not part of the jet  Radial flow + trigger bias  Voloshin nucl-th/0312065, S. A. Voloshin, Nucl. Phys. A749, 287 (2005) Armesto et al, PRL 93 (2004), nucl-ex/0405301

5. HI:C 07 - Montreal C. Pruneau, Wayne State 5 Theoretical Scenarios - Away Side Dip Mach Cone Concept/Calculations Stoecker, Casalderry-Solana et al, Muller et al.; Ruppert et al., … Velocity Field Mach Cone Other Scenarios Cherenkov Radiation Majumder, Koch, & Wang; Vitev Jet Deflection (Flow) Fries; Armesto et al.; Hwa v s ~0.33 ~1.1 rad

6. HI:C 07 - Montreal C. Pruneau, Wayne State 6 Talk Outline Can the ridge and the dip be caused by jet - medium interactions, I.e. jet energy loss ? Is there a Mach Cone? Explore the role of radial flow. –Could radial flow “explain” both the ridge and dip structures?

7. HI:C 07 - Montreal C. Pruneau, Wayne State 7 T. Affolder, et al (CDF) PRD 65 (2002) 092002. Average number of particles vs Jet p t (for particles with p t >0.5 GeV/c, |  |<1, R=0.7) Estimates: Jet p ~ 7 GeV Yield in 3-4 GeV/c: ~0.45 Yield in 1-2 GeV/c: ~1 Jet p ~ 10 GeV Yield in 3-4 GeV/c: ~0.35 Yield in 1-2 GeV/c: ~1.5 Some Key Features of Charged Particle Jets

8. HI:C 07 - Montreal C. Pruneau, Wayne State 8 Some Key Features of the Near-Side Ridge Au+Au 0-10% STAR preliminary p t,assoc. > 2 GeV ridge yield  STAR preliminary “jet” slope ridge slope inclusive slope “wide” “stronger in central coll.” 4 < p t,trigger < 6 GeV 6 < p t,trigger < 10 GeV Ridge persists up to highest trigger p t  correlated or collocated to jet production and ~ independent of trigger p t. Ridge Spectrum ~ “bulk-like”, NOT “jet-like”. Ridge energy quite large - roughly a few GeV. Ridge comparable in Au+Au and Cu+Cu at same N part. “large energy” Jörn Putschke et al., STAR, Quark Matter 2006, Shanghai

9. HI:C 07 - Montreal C. Pruneau, Wayne State 9 Mark Horner, et al., STAR, Quark Matter 2006 More Key Features of the Near- and Away-Side Structures Near-side Jet+Ridge Near-side Jet Only Away-side

10. HI:C 07 - Montreal C. Pruneau, Wayne State 10 Relative Angles Definition 1 2 3  12  13 Angular Range 0 - 360 o 1: 3 < pt < 4 GeV/c (Jet Tag) 2,3: 1 < pt < 2 GeV/c, Mach Cone & Deflection Kinematical Signatures  13  12 0   Back-to-back Jets “in vacuum” Away-side broadening Away-side deflection & flow Mach Cone

11. HI:C 07 - Montreal C. Pruneau, Wayne State 11 QM06 - STAR - Analysis Techniques Measure 1-, 2-, and 3-Particle Densities 3-particle densities = superpositions of truly correlated 3-particles, and combinatorial components. Star uses two approaches to extract the truly correlated 3-particles component 1)Cumulant technique: 2)Jet+Flow Subtraction Model: Simple Definition Model Independent. Intuitive in concept Simple interpretation in principle. PROs CONs Not positive definite Interpretation perhaps difficult. Model Dependent v 2 and normalization factors systematics –.–. See C. Pruneau, PRCSee J. Ulery & nucl-ex/0609017/0609016

12. HI:C 07 - Montreal C. Pruneau, Wayne State 12 Azimuthal Flow Particle Distribution Relative to Reaction Plane 2- Cumulants Reducible 2 nd order in v Irreducible 3 rd order in v 3- Cumulants 3-Cumulant Flow Dependence : Irreducible v 2 v 2 v 4 contributions Must be modeled and manually subtracted v n 2 suppressed.

13. HI:C 07 - Montreal C. Pruneau, Wayne State 13 Two Illustrative Models :  1 =  2 =  3 =10 o ;   =0 o No deflection Random Gaussian Away-Side Deflection  1 =  2 =  3 =10 o ;   =30 o Di-Jets: Mach Cone  mach (a)  12  1 3  mach (b)  mach

14. HI:C 07 - Montreal C. Pruneau, Wayne State 14 Example: 2-particle Decay: 2-Cumulant Maxwell Boltzman, T=0.2 GeV Isotropic Emission/Decay of rho-mesons, with pion background. 3-Particle Density contains 2-body decay signals. 2-Body Signal Not Present in 3-cumulant. Suppression of 2-part correlations with 3-cumulant Many resonances, e.g.  0 s , N*, … contribute to the soft-soft term, and likely to the hard-soft as well.

15. HI:C 07 - Montreal C. Pruneau, Wayne State 15 Conical Emission Sensitivity/Efficiency Correction Jet + Mach Cone Model –On average, the jet includes 1 high pt particle, 2 low pt particles –On average, the “cone” includes 2 low pt particles, –Cone angle fixed at 70 degrees and width of 0.2 radians. Finite Efficiency Simulation

16. HI:C 07 - Montreal C. Pruneau, Wayne State 16 Jet - Flow Cross Term - A toy Model Jet Profile: Jet Flow: Background Flow: 3-Cumulant: Jet-Flow correlation arises from finite eccentricity of medium + differential absorption+quenching. A simple model…

17. HI:C 07 - Montreal C. Pruneau, Wayne State 17 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

18. HI:C 07 - Montreal C. Pruneau, Wayne State 18 3-Cumulant vs. centrality Au + Au 80-50%30-10%10-0%

19. HI:C 07 - Montreal C. Pruneau, Wayne State 19 Two-Component Model Analysis Au+Au 0-12% No Jet Flow  12  13 (  12 +  13 )/2-  (  12 -  13 )/2 Au+Au 0-12%  12 (  12 -  13 )/2 (  12 +  13 )/2-   13 Nominal Model: Used “reaction plane” v2 estimates Used Zero Yield at 1 rad for normalizations “Systematics” Estimates: Vary v 2 in range: v 2 {2} - v 2 {4} Vary point of normalization Turn Jet-Flow background term on/off

20. HI:C 07 - Montreal C. Pruneau, Wayne State 20 Mach Cone  * Three particle correlation True 3PC jet correlations Deflected Jet  * PHENIX Preliminary Data is consistent with the presence of a Mach Cone away-side jet but does not rule out small contributions from other topologies. PHENIX simulation Real data Chun Zhang, et al. PHENIX, QM06

21. HI:C 07 - Montreal C. Pruneau, Wayne State 21 Use 3 Particle Azimuthal Correlations. Identification of correlated 3-particle from jet and predicted Mach cone is challenging task. Must eliminate 2-particle correlation combinatorial terms. Must remove flow background - including v 2 v 2, v 4 v 4, and v 2 v 2 v 4 contributions. Use two approaches: Cumulant & Jet - Flow Subtraction Model Cumulant Method Unambiguous evidence for three particle correlations. Clear indication of away-side elongated peak. Finite Sensitivity: No evidence for Cone signal 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 Conical Search Summary

22. HI:C 07 - Montreal C. Pruneau, Wayne State 22 Cone and Ridge Puzzles Summary l Ridge l Carries a large amount of particles and energy (high pt particles) l Not very sensitive to the trigger particle pt. l Strength grows with increasing centrality. l “Cone” l Seen in 2-part correlations for many pt ranges l Strong yield and also carry substantial energy in 2-part. l 3-Part signal still not clear. Not seen/strong in cumulant. l Medium Effect? l Ridge+Cone artifacts of the way we measure correlations? l What About Radial Flow? l Can radial flow affect jets?

23. HI:C 07 - Montreal C. Pruneau, Wayne State 23 Observations from p+p… Di-jets are only back-to-back in the transverse plane, non in rapidity. In eta-phi space, this leads to a ridge-like structure at  in p+p PYTHIA p+p, sqrt(s)=200 GeV Trigger: 3 < p t < 20 GeV/c Associate: 1 < p t < 2 GeV/c M.Daugherity, et al., STAR, hep-ph/0506172 same-side away-side – Φ Δ ~ π p+p

24. HI:C 07 - Montreal C. Pruneau, Wayne State 24 Effect of Radial Flow on Resonances C. P., PRC 74, 064910 (2006), e-Print Archive: nucl-ex/0608002 (a)0.01 < p t (  o ) < 0.1 GeV/c, p t (  ) < 0.2 GeV/c; (b)0.1 0.3 GeV/c, p t (2) < 0.2 GeV/c (c)0.1 < p t (  o ) < 0.5 GeV/c, p t (  ) < 0.2 GeV/c (d)0.6 0.2 GeV/c, p t (2) < 0.2 GeV/c (e)1.5 0.2 GeV/c, p t (2) < 0.2 GeV/c.; (f)5.5 < p t (  o ) < 10. GeV/c, p t (  ) < 2.0 GeV/c. Rho-decays at Finite Temperature

25. HI:C 07 - Montreal C. Pruneau, Wayne State 25 Effect of Transverse Radial Flow on “Clusters” S. Voloshin, e.g. nucl-ex/05 Based on the blast wave model.

26. HI:C 07 - Montreal C. Pruneau, Wayne State 26 Large velocities, if applicable to jets or entire pp events, or string fragmentation can lead to dramatic changes in the correlation functions. So… let’s try boosting pp PYTHIA events at selected radial velocities in random transverse/radial directions. Work Hypothesis: Maximum Coupling Between Flow and Jets. No diffusion or Attenuation. Toy Model to Study the Effect of Radial Flow on Jet-like Structures, C.P., S. Gavin, S. Voloshin STAR, Phys. Rev. Lett. 92 (2004) 112301 Large Velocities ! Blastwave Fits to Spectra Basic Hypothesis: Matter produced in A+A @ RHIC is subject to large collective flow.

27. HI:C 07 - Montreal C. Pruneau, Wayne State 27 How does this work? Effect of Radial Flow on Jet-like Structures  >0 A+A participant region p+p collision (in vacuum) p+p boosted by high  radial flow: focusing p+p boosted by low  radial flow: focusing + deflection

28. HI:C 07 - Montreal C. Pruneau, Wayne State 28 PYTHIA p+p @ sqrt(s)=200 GeV; 3<p t <20 && 1<p t <2  =0.1  =0.2

29. HI:C 07 - Montreal C. Pruneau, Wayne State 29  =0.3  =0.4  =0.5 PYTHIA p+p @ sqrt(s)=200 GeV; 3<p t <20 && 1<p t <2 “Dip” “Suppression”

30. HI:C 07 - Montreal C. Pruneau, Wayne State 30 PYTHIA p+p @ sqrt(s)=200 GeV; 3<p t <20 && 1<p t <2  =0.1  =0.2 3-cumulants

31. HI:C 07 - Montreal C. Pruneau, Wayne State 31  =0.3  =0.4  =0.5 PYTHIA p+p @ sqrt(s)=200 GeV; 3<p t <20 && 1<p t <2

32. HI:C 07 - Montreal C. Pruneau, Wayne State 32 Summary A+A Studies of 2- and 3- Particle Correlations reveal new “unforeseen” structures. While they are many theoretical interpretations, and predictions based on energy loss, the strengths of the structures are quite large, and put in question the notion they are produced by energy loss. No Clear/Robust (Model Independent) Evidence For Mach Cone Yet!! Explored the effect of Strong Radial Flow Using p+p events from PYTHIA. –2- and 3- particle correlations. –Radial Flow Induces Patterns in Azimuthal Correlations that are “similar” to Conical Emission. –Produces a “relocation” of the pp away side ridge to the near side. –Pros: Explains “simply” two phenomena at once. Explains the large particle/energy carried by the ridge. –Cons: Requires a strong acceleration field that otherwise leaves the intrinsic correlation “unchanged” –Many Open issues: Effects of Quenching, Diffusion, Momentum Conservation, Requires detailed modeling, and comparison with data. Handle of Early Time System Expansion?

33. HI:C 07 - Montreal C. Pruneau, Wayne State 33 Additional Material

34. HI:C 07 - Montreal C. Pruneau, Wayne State 34 Some Properties of Cumulants Cumulants are not positive definite The number of particles in a bin varies e-by-e: n i = +  i Cumulant for Poisson Processes (independent variables) are null Cumulant for Bi-/Multi-nomial Processes ~ 1/M n-1 (independent variables, but finite multiplicity) Where M is a reference multiplicity

35. HI:C 07 - Montreal C. Pruneau, Wayne State 35 More Properties of Cumulants Consider a Superposition of  =1,…, s processes Number of particles in a phi bin in a given event: 1- Particle Density: 2- Particle Density: Product of Single Particle Densities: 2-Cumulant: Cumulant of a sum of processes equals sum of cumulants + sum of covariances between these processes. If the processes are independent, these covariances are null. At fixed multiplicity, these covariances are of order 1/M n-1. 3- Particle Density: 3-Cumulant: Enables Separation of Jet (Mach Cone) and Flow Background.

36. HI:C 07 - Montreal C. Pruneau, Wayne State 36 Cumulant Method - Finite Efficiency Correction Use “singles” normalization to account for finite and non-uniform detection efficiencies. Example: Robust Observables verified for sufficiently large  ij differences.

37. HI:C 07 - Montreal C. Pruneau, Wayne State 37 PYTHIA p+p @ sqrt(s)=200 GeV; 3<p t <20 && 0.2<p t <1  =0.1  =0.2  =0. NO BOOST

38. HI:C 07 - Montreal C. Pruneau, Wayne State 38  =0.3  =0.4  =0.5 PYTHIA p+p @ sqrt(s)=200 GeV; 3<p t <20 && 0.2<p t <1

39. HI:C 07 - Montreal C. Pruneau, Wayne State 39 PYTHIA p+p @ sqrt(s)=200 GeV; 3<p t <20 && 2<p t <3  =0.1  =0.2

40. HI:C 07 - Montreal C. Pruneau, Wayne State 40 PYTHIA p+p @ sqrt(s)=200 GeV; 3<p t <20 && 2<p t <3  =0.4  =0.5  =0.3

41. HI:C 07 - Montreal C. Pruneau, Wayne State 41 PYTHIA p+p @ sqrt(s)=200 GeV; 3<p t <20 && 0.2<p t <1 3-cumulants  =0.1  =0.2 Yield normalized per bin (72x72)

42. HI:C 07 - Montreal C. Pruneau, Wayne State 42  =0.3  =0.5 PYTHIA p+p @ sqrt(s)=200 GeV; 3<p t <20 && 0.2<p t <1

43. HI:C 07 - Montreal C. Pruneau, Wayne State 43 PYTHIA p+p @ sqrt(s)=200 GeV; 3<p t <20 && 2<p t <3  =0.1  =0.2

44. HI:C 07 - Montreal C. Pruneau, Wayne State 44  =0.3  =0.4  =0.5 PYTHIA p+p @ sqrt(s)=200 GeV; 3<p t <20 && 2<p t <3