The Geometry of Hadronization in Au-Au Collisions at s NN 1/2 = 130 and 200 GeV

1. The Geometry of Hadronization in Au-Au Collisions at sNN1/2 = 130 and 200 GeV Studied with Two-Particle, Charge-Dependent Number Fluctuations and Correlations R. L. Ray The University of Texas at Austin For the STAR Collaboration QM 2004 Poster Session

2. Abstract: QM 2004 Poster Session

3. - + Introduction: In high energy proton-proton collisions color string fragmentation is subject to local charge and momentum conservation. These symmetries lead to charge ordering seen in jet fragmentation, and local transverse momentum conservation seen in high energy elementary collisions. Semi-hard scattering “minijet” In relativistic heavy ion collisions we measure the effects of the hot, dense medium on known processes such as this. We also study how these known processes affect, or probe the medium in order to measure its properties. To do so we measure non-statistical fluctuations and large momentum scale correlations taking advantage of STAR’s large acceptance; interpretation is in terms of short-range dynamical responses. QM 2004 Poster Session

4. Measuring Correlations & Particle Pair Density Ratio: Event 1 Count number of sibling pairs in all events in each bin in (f1-f2) vs (h1-h2) Azimuthal angle f Event 2 Similarly, count number of mixed pairs from different events in each bin in (f1-f2) vs (h1-h2) Normalize using total number of sibling and mixed event pairs. *(Ratios formed using similar events, then r’s summed over all events.) Pseudorapidity h QM 2004 Poster Session

5. Data Selection and Cuts: Collision system: • Central (15%) trigger (210k events after event cut) • Minimum-bias trigger (124k events after event cut) • 0.15 < pt < 2 GeV • |h|<1.3 • full 2p azimuth • Centrality bins Pair cuts correct for track splitting and merging, and remove most of HBT/Coulomb correlations Event ordering on vertex position and multiplicity QM 2004 Poster Session

6. CI CD  US= LS ( + +, - - ) ( + -,- + ) Constructing Charge Dependent Correlations- Like- and Unlike-sign Combinations: Project to form “joint autocorrelations” LS US f1  f2 fD= f1- f2 h1  h2 hD=h1-h2 No correlation structure along sum direction; projections onto difference variables f1-f2 and h1-h2 preserve information; provides compact representation. STAR Preliminary Charge-Independent Charge-Dependent QM 2004 Poster Session

7. conservation Correlations for p+p at 200 GeV on fD,hD STAR Preliminary dE/dx electron cut charge conservation Autocorrelations reveal peak structures near fD=0,hD=0 superimposed on signals due to charge & p conservation. Effects of charge conservation stronger for unlike-sign than like-sign QM 2004 Poster Session

8. Correlation Structures in pp CD – the reference: Local charge conservation; charge ordering azimuthal symmetry Local momentum conservation Quantum interference STAR Preliminary (gamma conversion electron contamination) QM 2004 Poster Session

9. peripheral central Charge-Dependent (LS-US) Correlations for Au-Au at 130 GeV: fD hD STAR Preliminary hD fD (Another view of same data.) Development of 2D symmetric correlation shape and increased amplitude. QM 2004 Poster Session

10. Fit CD correlations with a model: (extrapolation range assumed) STAR Preliminary Deduced rms widths versus multiplicity and path length n, where: QM 2004 Poster Session

11. Summary of 130 GeV Au-Au CD Correlations: • Large-amplitude CD two-particle number correlations are observed on fD,hDmomentum space. • CD joint autocorrelations show strong centrality dependencies of correlation structure: amplitude increases and saturates, widths decrease along both hD and fD. • Results suggest a trend from 1D string fragmentation to 2D surface emission: a drastic change in the Hadronization Geometry in central Au-Au collisions. • This points to the growth of an Opaque Medium in central collisions. These correlations were measured by the direct, pair-ratio method. But correlations can be obtained another way… QM 2004 Poster Session

12. Obtaining the CD auto-correlations from non-statistical fluctuations, or variance excess – A Complementary Method: • Based on the integral relationship between autocorrelations and variance excess in the measure quantity, i.e. net charge in the present application. • Avoids the normalization ambiguities inherent in density ratio analyses within finite acceptance and allows measurement of very large scale correlations which exceed the acceptance scale. • Numerically much faster than summing over pairs. • Facilitates study of canonical suppression, or charge conservation effects, in finite acceptance < 4p and participant nucleon number fluctuation effects. • This method is applied to Au-Au collisions at sNN1/2 = 200 GeV. QM 2004 Poster Session

13. Event-wise net charge fluctuations: We measure variances: where for purely statistical fluctuations In general N can be a conserved quantity such as charge, baryon number, etc. but, due to finite acceptance for the measurement, fluctuates from event-to-event. Here we measure net charge: NQ = N+- N- where N+ and N-are the number of positive and negative particles in the acceptance for each event. QM 2004 Poster Session

14. Relation to autocorrelation: Variance excess at some scale integrates over auto-correlation: which is approximated with discrete sums for data, The autocorrelations are obtained from the measured variance excess via inversion of this integral equation. Straightforward inversion results in a noise dominated autocorrelation. The standard way to get useful solutions is to impose a smoothing constraint on the autocorrelation using Tikhonov regularization. fD scale integral l df dh hD k References: http://www.phy.aukland.ac.nc/Staff/smt/453707SC.html http://www.samsi.info/inverse.html http://www.iop.org/EJ/journal/0266-5611 http://venda.uku.fi/research/FIPS QM 2004 Poster Session

15. Data (CD): • Canonical suppression causes linear • decrease in Ds2 with scale. • Trend from central to peripheral Au-Au • continues in pp with decreasing multiplicity. STAR Preliminary 200 GeV AuAu 200 GeV pp QM 2004 Poster Session

16. Invert -- autocorrelations (CD): • Strong small scale correlations for central Au-Au, • decreasing strength for more peripheral data. • Local charge conservation evident. • Peripheral Au-Au and high multiplicity pp • have similar shapes. 200 GeV pp 200 GeV Au-Au STAR Preliminary QM 2004 Poster Session

17. Compare CD and CI autocorrelations from inversion method: 200 GeV AuAu Using Using STAR Preliminary CD CI • Momentum conservation in both at fD = p with additional v2 (flow) in CI. • Elongation in same-side CI hD peak, but narrowing in CD. • Narrowing in both CI and CD same-side peaks for fD. QM 2004 Poster Session

18. Relation of CD hD autocorrelation to Balance function: BF depends on acceptance (Dh) and pseudorapidity difference variables Acceptance function: Canonical suppression due to total charge conservation for finite, <4p acceptance Two-particle, charge-dependent autocorrelation 0 Dh |h1-h2| • Balance function width depends on acceptance range and • both the width and amplitude of the CD autocorrelation; • interpretation in terms of correlation width is ambiguous. • Observed reduction in BF width (Phys. Rev. Lett. 90, 172301 (2003) ) with increased centrality is consistent with the observed • increase in correlation amplitude. QM 2004 Poster Session

19. Possible interpretation is that these data are consistent with correlated pairs escaping from an opaque medium - reduced mean free path - escape probability falls exponentially (smaller power) with opening angle Alternative hypothesis: e.g. distortion of opening-angle distribution by large radial flow Study changing geometry of hadronization - from 1D string fragmentation  2+D surface emission in A-A, which is an open issue in QCD phenomenology Comparisons with Hijing and RQMD in progress Summary of CD Correlations on (f1-f2) vs (h1-h2): QM 2004 Poster Session