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Feb 2007 Big Sky, Montana Nuclear Dynamics 2007 Conference Is There A Mach Cone?

Feb 2007 Big Sky, Montana Nuclear Dynamics 2007 Conference Is There A Mach Cone?. For the STAR Collaboration Claude Pruneau. Motivations/Goals Expectations/Models Search + Analysis Methods Data + Results Summary/Conclusions. Motivations . Mach Cone Concept/Calculations

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Feb 2007 Big Sky, Montana Nuclear Dynamics 2007 Conference Is There A Mach Cone?

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  1. Feb 2007Big Sky, MontanaNuclear Dynamics 2007 ConferenceIs There A Mach Cone? For the STAR Collaboration Claude Pruneau Motivations/Goals Expectations/Models Search + Analysis Methods Data + Results Summary/Conclusions

  2. Motivations Mach Cone Concept/Calculations Stoecker, Casalderry-Solana et al, Muller et al.; Ruppert et al., … Dip “Puzzle” in 2-Particle Correlations vs~0.33 pTtrig = 3.0-4.0 GeV/c; pTasso = 1.0-2.5 GeV/c ~1.1 rad Velocity Field Mach Cone • Other Scenarios • Cherenkov RadiationDremmer, Majumder, Koch, & Wang; Vitev • Jet Deflection (Flow) • Fries; Armesto et al.; Hwa See M. Horner’s talk at QM06 Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  3. 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 Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  4. Two Analysis Techniques Measure 1-, 2-, and 3-Particle Densities 3-particle densities = superpositions of truly correlated 3-particles, and combinatorial components. We use two approaches to extract the truly correlated 3-particles component • . Jet+Flow Subtraction Model: Cumulant technique: PROs Simple Definition Model Independent. Intuitive in concept Simple interpretation in principle. CONs Not positive definite Interpretation perhaps difficult. Model Dependent v2 and normalization factors systematics See J. Ulery & nucl-ex/0609017/0609016 See C. Pruneau, nucl-ex/0608002 Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  5. Mach Cone Search - Data set and cuts • p+p, d+Au, = 200 GeV used as reference. • Search For Mach Cone in Au + Au, = 200 GeV • Minimum bias, and Central Triggers Data Samples (Run 4) • Particle Cuts: Predicated by the observation of the “dip” • Jet tag (trigger) : 3 < pt < 4 GeV/c, ||<1 • Associates: 1 < pt < 2 GeV/c, ||<1 • Collision Centrality: • Estimated based on reference multiplicity in || < 0.5. Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  6. Measurement of 3-Particle Cumulant • Clear evidence for finite 3-Part Correlations • Observation of flow like and jet like structures. • Evidence for v2v2v4 contributions Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  7. 3-Cumulant vs. centrality Au + Au 80-50% 30-10% 10-0% Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  8. 3-Cumulant Sensitivity to Cone Signal Use a simple Jet + Cone toy model Jet: <N1>=1 per jet (3<pt<4 GeV/c) <N2>=2 per jet (1<pt<2 GeV/c) <Jet>/event ~ 0.27 Actual data have ~1 trigger/event Cone: <N2>=2 per jet (1<pt<2 GeV/c) Event Mult ~ 300 to 600. Cone Near Side Jet Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  9. 3-Cumulant Background: Jet x Flow Flowing Jet - Differential Attn. Rel. Reaction Plane Model: Jet Emission Rel. Reaction Plane with Finite v2. 2 particles from a jet 1 particle from the background (a.u.) Work in progress to assess the strength of this term in the cumulant and systematics. Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  10. “Jetty”signal 2-Part Correlation Δ Δ Flow background Δ12 Δ12 Δ12 Jet-Flow Subtraction Method Estimate/Remove JetBackground Hard-Soft Term See J. Ulery, nucl-ex/0609017/0609016 Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  11. Estimate/Remove Trigger  2-Background Soft-soft term Estimate/Remove Trigger  Background Flow Δ v2(1) v2(2)  v22 Δ Δ12 Δ v4 (1) v4 (2) + +v2(1)v2(2)v2(3)  v24 Δ12 v4=1.15v22 Δ12 Jet-Flow Subtraction Method (cont’d) Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  12. Jet - Flow Subtraction Method - System Size Dependence (1) Δ Δ Δ Δ12 Δ12 Δ12 d+Au pp Au+Au 50-80% (12+13)/2- (12-13)/2 Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  13. Jet - Flow Subtraction Method - System Size Dependence (1) Au+Au 30-50% Au+Au 0-10% Au+Au 10-30% Δ Δ Δ Δ12 Δ12 Δ12 (12+13)/2- (12-13)/2 Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  14. Deflected Jet + Cone Elongated Away Side Jet Cone Near Side Jet - Flow Subtraction Result in Au+Au - Triggered 0-12% 13 12 Diagonal and Off-diagonal structures are suggestive of conical emission at an angle of about 1.45 radians in central Au+Au. Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  15. 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 Yield and Systematics • 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 Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  16. Summary/Conclusions • 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. • 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 Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  17. Additional Material Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  18. 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 • v22 suppressed but finite • v22 cancellation possible with modified cumulant. Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  19. 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 Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  20. 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 Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  21. 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. Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  22. 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. Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  23. 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. Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  24. Background subtracted QM2005 Au+Au 0-10% most central What changed since QM05 • Increased data sample • Two Analysis Methods • Jet-Flow Background Method: • Improved efficiency corrections • Reduce the number of free parameters Example  Acceptance Correction Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

  25. Cone Yield vs. Collision Centrality Away Cone Deflected Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007

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