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New Perspectives on Measurements of 2- and 3- Particle Correlations

New Perspectives on Measurements of 2- and 3- Particle Correlations. Claude A. Pruneau Wayne State University Detroit, MI, USA. Beyond the disappearance of Away-Side Jets. Au+Au 0-10% STAR preliminary. J ö r n Putschke, et al., STAR, Quark Matter 2006.

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New Perspectives on Measurements of 2- and 3- Particle Correlations

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

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

  3. “Reappearance” of the away side jet STAR Phys. Rev. Lett. 97 (2006) 162301 8 < pt(trig)<15 • “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. C. Pruneau, Wayne State

  4. Armesto et al, PRL 93 (2004), nucl-ex/0405301 Theoretical Scenarios - Ridge • Parton radiates energy before fragmenting and couples to the longitudinal flow • Gluon bremsstrahlung of hard-scattered parton • Parton shifted to lower pt • 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) 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., … vs~0.33 Velocity Field Mach Cone ~1.1 rad • Other Scenarios • Cherenkov RadiationMajumder, Koch, & Wang; Vitev • Jet Deflection (Flow) • Fries; Armesto et al.; Hwa 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? C. Pruneau, Wayne State

  7. Some Key Features of Charged Particle Jets T. Affolder, et al (CDF) PRD 65 (2002) 092002. Average number of particles vs Jet pt (for particles with pt>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 C. Pruneau, Wayne State

  8. Au+Au 0-10% ridge yield pt,assoc. > 2 GeV STAR preliminary  Some Key Features of the Near-Side Ridge Jörn Putschke et al., STAR , Quark Matter 2006, Shanghai “large energy” 4 < pt,trigger < 6 GeV 6 < pt,trigger < 10 GeV “wide” “stronger in central coll.” STAR preliminary “jet” slope ridge slope inclusive slope • Ridge persists up to highest trigger pt  correlated or collocated to jet production and ~ independent of trigger pt. • 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 Npart. C. Pruneau, Wayne State

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

  10. Back-to-back Jets “in vacuum” Away-side broadening Mach Cone Away-side deflection & flow Mach Cone & Deflection Kinematical Signatures  Relative Angles Definition 13 2 12 1  Angular Range 0 - 360o 13 3 1: 3 < pt < 4 GeV/c (Jet Tag) 2,3: 1 < pt < 2 GeV/c, 0   12 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 • . Jet+Flow Subtraction Model: Cumulant technique: Simple Definition Model Independent. PROs Intuitive in concept Simple interpretation in principle. Not positive definite Interpretation perhaps difficult. Model Dependent v2 and normalization factors systematics CONs See C. Pruneau, PRC See J. Ulery & nucl-ex/0609017/0609016 C. Pruneau, Wayne State

  12. Azimuthal Flow Particle Distribution Relative to Reaction Plane 2- Cumulants Reducible 2nd order in v 3- Cumulants Irreducible 3rd order in v • 3-Cumulant Flow Dependence : • Irreducible v2v2v4 contributions • Must be modeled and manually subtracted • vn2 suppressed. C. Pruneau, Wayne State

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

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

  16. Jet - Flow Cross Term - A toy Model • Jet-Flow correlation arises from finite eccentricity of medium + differential absorption+quenching. • A simple model… Jet Profile: Jet Flow: Background Flow: 3-Cumulant: 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 v2v2v4 contributions C. Pruneau, Wayne State

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

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

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

  21. Conical Search Summary • 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 v2v2, v4v4, and v2v2v4 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 v2 and details of the model. • Observe Structures Consistent with Conical emission in central collisions C. Pruneau, Wayne State

  22. Cone and Ridge Puzzles Summary • Ridge • Carries a large amount of particles and energy (high pt particles) • Not very sensitive to the trigger particle pt. • Strength grows with increasing centrality. • “Cone” • Seen in 2-part correlations for many pt ranges • Strong yield and also carry substantial energy in 2-part. • 3-Part signal still not clear. Not seen/strong in cumulant. • Medium Effect? • Ridge+Cone artifacts of the way we measure correlations? • What About Radial Flow? • Can radial flow affect jets? 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 M.Daugherity, et al., STAR, hep-ph/0506172 away-side – ΦΔ ~ π PYTHIA p+p, sqrt(s)=200 GeV Trigger: 3 < pt < 20 GeV/c Associate: 1 < pt < 2 GeV/c p+p same-side C. Pruneau, Wayne State

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

  26. Toy Model to Study the Effect of Radial Flow on Jet-like Structures, C.P., S. Gavin, S. Voloshin • Basic Hypothesis: Matter produced in A+A @ RHIC is subject to large collective flow. STAR, Phys. Rev. Lett. 92 (2004) 112301 Blastwave Fits to Spectra Large Velocities ! • 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. C. Pruneau, Wayne State

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

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

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

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

  31. PYTHIA p+p @ sqrt(s)=200 GeV; 3<pt<20 && 1<pt<2 =0.3 =0.4 =0.5 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? C. Pruneau, Wayne State

  33. Additional Material C. Pruneau, Wayne State

  34. Some Properties of Cumulants • Cumulants are not positive definiteThe number of particles in a bin varies e-by-e: ni = <ni> + ei Cumulant for Poisson Processes (independent variables) are null Cumulant for Bi-/Multi-nomial Processes ~ 1/Mn-1 (independent variables, but finite multiplicity) Where M is a reference multiplicity 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: 3- Particle Density: Product of Single Particle Densities: 2-Cumulant: 3-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/Mn-1. Enables Separation of Jet (Mach Cone) and Flow Background. 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. C. Pruneau, Wayne State

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

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

  39. PYTHIA p+p @ sqrt(s)=200 GeV; 3<pt<20 && 2<pt<3 =0.1 =0.2 C. Pruneau, Wayne State

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

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

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

  43. PYTHIA p+p @ sqrt(s)=200 GeV; 3<pt<20 && 2<pt<3 =0.1 =0.2 C. Pruneau, Wayne State

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

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