1. 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

2. Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007 2 Dip “Puzzle” in Dip “Puzzle” in 2-Particle Correlations p T trig = 3.0-4.0 GeV/c; p T asso = 1.0-2.5 GeV/c See M. Horner’s talk at QM06 Motivations Mach Cone Concept/Calculations Stoecker, Casalderry-Solana et al, Muller et al.; Ruppert et al., … Velocity Field Mach Cone Other Scenarios Cherenkov Radiation Dremmer, Majumder, Koch, & Wang; Vitev Jet Deflection (Flow) Fries; Armesto et al.; Hwa v s ~0.33 ~1.1 rad

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

4. 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 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, nucl-ex/0608002 See J. Ulery & nucl-ex/0609017/0609016

5. 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 < p t < 4 GeV/c, |  |<1 Associates: 1 < p t < 2 GeV/c, |  |<1 Collision Centrality: Estimated based on reference multiplicity in |  | < 0.5.

6. 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 v 2 v 2 v 4 contributions

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

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

9. 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 v 2. 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.

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

11. Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007 11 Estimate/Remove Trigger  2-Background Soft-soft term Δ   Δ  12 Jet-Flow Subtraction Method (cont’d) Estimate/Remove Trigger  Background Flow v 2 (1) v 2 (2)  v 2 2 v 4 (1) v 4 (2) + +v 2 (1)v 2 (2)v 2 (3)  v 2 4 Δ   Δ  12 Δ   Δ  12 v 4 =1.15v 2 2

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

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

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

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

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

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

18. Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 2007 18 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 2 2 suppressed but finite v 2 2 cancellation possible with modified cumulant.

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

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

21. 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: 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.

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

23. 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.

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

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