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

Claude Pruneau, for the STAR Collaboration, Nucl. Dyn Dip “Puzzle” in Dip “Puzzle” in 2-Particle Correlations p T trig = GeV/c; p T asso = 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

Claude Pruneau, for the STAR Collaboration, Nucl. Dyn Relative Angles Definition  12  13 Angular Range 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

Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 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/ See J. Ulery & nucl-ex/ /

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

Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 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

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

Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 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

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

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

Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 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

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

Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 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%

Claude Pruneau, for the STAR Collaboration, Nucl. Dyn  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

Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 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

Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 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

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

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

Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 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

Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 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

Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 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 Particle Density: 3-Cumulant: Enables Separation of Jet (Mach Cone) and Flow Background.

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

Claude Pruneau, for the STAR Collaboration, Nucl. Dyn 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 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

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