Dave Kettler for the STAR Collaboration Hot Quarks Estes Park, CO August, 2008

1. Universal Centrality and Collision Energy Trends for v2 Measurements From 2D Angular Correlations Dave Kettler for the STAR Collaboration Hot Quarks Estes Park, CO August, 2008

2. Agenda • Overview of correlation analysis • 62 and 200 GeV 2D angular correlations • Fit components • v2 trends on centrality and energy Two-Particle Correlations

3. Au-Au Collisions at STAR • Potentially hundreds of tracks • Massive amount of data • Subtle signal One Event How do we get a human-interpretable signal out while preserving as much information as possible? Two-Particle Correlations

4. Autocorrelations I Step-by-step procedure One event described by a probability distribution r which is sampled by observed particles On azimuth for single event: Single-particle distribution: histogram Two-particle distribution: measure tracks in TPC Define: Project two-particle distribution to difference variable ‘sample’ probability distribution with observed particles Loop over all particle pairs, make a histogram of their angular difference: for large N Exact same form as the autocorrelation in conventional signal analysis Two-Particle Correlations

5. Autocorrelations II • What does a single event angular distribution look like? • Global v2 structure? • Varying substructure (minijets, resonances, momentum cons., etc) • Properties of the autocorrelation: • Translation Invariance: • Summations: varies event by event for better statistics need many events Average the autocorrelations, not single-particle distributions • Standard (event plane) v2 analysis: • Line up single-particle distributions according to reaction plane • Reaction plane is estimated from particles in the event. Subject to nonflow effects We measure all structure Two-Particle Correlations

6. Multivariable Correlations LS US hD hS 2D Angular Autocorrelation t fD fS p-p 200 GeV Minijets? If the structure is all in the difference variable then you can project without loss of information No trigger Later consider 6D space: Make use of hD dependences of different structures Two-Particle Correlations

7. Correlation Measure ρ(p1,p2)= 2 particle density in momentum space ρsibling(p1,p2) Event 1 ρreference(p1,p2) Event 2 Start with a standard definition in statistics: Pearson’s Correlation Coefficient Δρas a histogram on bin (a,b): ε = bin width, converts density to bin counts measures number of correlated pairs per final state particle Normalize Two-Particle Correlations

8. proton-proton 200 GeV Au-Au Data Analyzed 1.2M minbias 200 GeV Au+Au events; included all tracks with pt > 0.15 GeV/c,|η| <1, fullφ note: 38-46% not shown 84-93% 74-84% 64-74% 55-64% 46-55% φΔ ηΔ 18-28% 9-18% 28-38% 5-9% 0-5% φΔ ηΔ STAR Preliminary M. Daugherity We observe the evolution of several correlation structures from peripheral to central Au+Au CI=LS+US Two-Particle Correlations

9. 62 GeV Au-Au Data Analyzed 13M 62 GeV Au+Au minbias events; included all tracks with pT > 0.15 GeV/c, |η| < 1, full φ note: 37-46% not shown 84-95% 75-84% 65-75% 56-65% 46-56% 18-28% 28-37% 9-18% 5-9% 0-5% STAR Preliminary M. Daugherity A similar evolution appears but with quantitative differences compared to the 200 GeV data. CI=LS+US Two-Particle Correlations

10. Proton-Proton Components yt2 yt1 p-p transverse correlations p-p axial correlations φΔ ηΔ soft component semi-hard component STAR Preliminary φΔ φΔ ηΔ ηΔ Longitudinal Fragmentation: 1D Gaussian onηΔ HBT peak at origin, LS pairs only Minijets: 2D Gaussian at origin plus broad away-side peak: -cos(φΔ) Two-Particle Correlations

11. Fit Function (5 easy pieces) Same-side “Minijet” Peak, 2D gaussian Away-side -cos(φ) Proton-Proton fit function STAR Preliminary “soft” “hard” = + φΔ φΔ φΔ ηΔ ηΔ ηΔ dipole longitudinal fragmentation 1D gaussian HBT, e+e- 2D exponential cos(2φΔ) • Au-Au fit function • Use proton-proton fit function + cos(2φΔ) quadrupole term (~flow). • This gives the simplest possible way to describe Au+Au data. quadrupole Note: from this point on we’ll include entire momentum range instead of using soft/hard cuts φΔ ηΔ Two-Particle Correlations

12. Quadrupole Centrality Systematics star preliminary star preliminary transform primary 2D measurements 2D autocorrelation model fits dashed curves: all have common shape – amplitudes follow linear dependence on Two-Particle Correlations

13. Quadrupole Energy Systematics per-particle  per-pair star preliminary RHIC quadrupole AGS SPS Bevalac low-x glue nucleon hydro saturation? RHIC SPS AGS squeezeout Bevalac A new QCD phenomenon at RHIC? Two-Particle Correlations

14. A-A Eccentricity point-like objects acting at a distance point-like nucleon structure N-N minbias: interacting spheres Optical Glauber parametrization • Minbias N-N interactions are not point-like objects acting at a distance • The W-S distribution may better describe low-x glue we use the optical Glauber eccentricity Two-Particle Correlations

15. Universal Centrality and Energy Trends star preliminary star preliminary is this hydro-inspired format relevant to data? universal trends represent all A-A systems for energies above 12 GeV quadrupole represented by initial conditions (b, s1/2); no medium properties, EoS, viscosity, hydro v2e does not describe data Two-Particle Correlations

16. Same-side 2D gaussian – binary scaling Peak Amplitude Peak η Width Peak φ Width STAR Preliminary STAR Preliminary STAR Preliminary 200 GeV 62 GeV constant widths peripheral central small increase before transition Gaussian parameters Statistical and fitting errors as shown Systematic error is 9% of correlation amplitude Binary scaling: Kharzeev and Nardi model STAR Preliminary Note the absence of a transition point in the quadrupole: v2 & elliptic flow M. Daugherity L. Ray Deviations from binary scaling represent new physics unique to heavy ion collisions Two-Particle Correlations

17. Conclusions • Simultaneous measurement of quadrupole (~flow) and other structures (~nonflow) • Depending on centrality, 20-100% of naïvely measured v2 (uncorrected v2{2}, 1D projections, etc) appears to be due to ‘nonflow’ • Minijet peak scales with binary collisions until a transition point, then increases dramatically • The quadrupole component has no equivalent transition • Accurate quadrupole measurements reveal simple trends on b and s1/2, no dependence on EoS Two-Particle Correlations