1. Jan. 13, 2004QM 2004 Poster Session1 The Geometry of Hadronization in Au-Au Collisions at s NN 1/2 = 130 and 200 GeV Studied with Two-Particle, Charge-Dependent Number Fluctuations and Correlations R. L. Ray For the STAR Collaboration The University of Texas at Austin

2. QM 2004 Poster Session2 Abstract:

3. QM 2004 Poster Session3 +- 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. 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. Introduction: Semi-hard scattering “minijet”

4. QM 2004 Poster Session4 Measuring Correlations & Particle Pair Density Ratio: Azimuthal angle  Pseudorapidity  Event 1 Event 2 Count number of sibling pairs in all events in each bin in (      vs      Similarly, count number of mixed pairs from different events in each bin in (      vs      Normalize using total number of sibling and mixed event pairs. *(Ratios formed using similar events, then r’s summed over all events.)

5. QM 2004 Poster Session5 Event ordering on vertex position and multiplicity Centrality bins  0.15 < p t < 2 GeV   |<1.3  full 2  azimuth Central (15%) trigger (210k events after event cut) Minimum-bias trigger (124k events after event cut) Data Selection and Cuts: Collision system: Pair cuts correct for track splitting and merging, and remove most of HBT/Coulomb correlations

6. QM 2004 Poster Session6       Constructing Charge Dependent Correlations- Like- and Unlike-sign Combinations: STAR Preliminary        LS US =  CI CD         LSUS Project to form “joint autocorrelations” No correlation structure along sum direction; projections onto difference variables     and     preserve information; provides compact representation. Charge-Independent Charge-Dependent

7. QM 2004 Poster Session7 Correlations for p+p at 200 GeV on  ,   dE/dx electron cut Effects of charge conservation stronger for unlike-sign than like-sign Autocorrelations reveal peak structures near      superimposed on signals due to charge & p conservation. conservation STAR Preliminary charge conservation

8. QM 2004 Poster Session8 Correlation Structures in pp CD – the reference: Local charge conservation; charge ordering Local momentum conservation Quantum interference (gamma conversion electron contamination) STAR Preliminary azimuthal symmetry

9. QM 2004 Poster Session9 Charge-Dependent (LS-US) Correlations for Au-Au at 130 GeV:  Development of 2D symmetric correlation shape and increased amplitude.  centralperipheral   STAR Preliminary (Another view of same data.)

10. QM 2004 Poster Session10 Fit CD correlations with a model: STAR Preliminary Deduced rms widths versus multiplicity and path length, where: (extrapolation range assumed)

11. QM 2004 Poster Session11 Summary of 130 GeV Au-Au CD Correlations: Large-amplitude CD two-particle number correlations are observed on      momentum space. CD joint autocorrelations show strong centrality dependencies of correlation structure: amplitude increases and saturates, widths decrease along both   and  . 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…

12. QM 2004 Poster Session12 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 < 4  and participant nucleon number fluctuation effects. This method is applied to Au-Au collisions at s NN 1/2 = 200 GeV.

13. QM 2004 Poster Session13 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: N Q = N +  N  where N + and N   are the number of positive and negative particles in the acceptance for each event.

14. QM 2004 Poster Session14 Relation to autocorrelation: Variance excess at some scale integrates over auto-correlation: k l scale integral     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. which is approximated with discrete sums for data, 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

15. QM 2004 Poster Session15 200 GeV AuAu  Canonical suppression causes linear decrease in  2 with scale.  Trend from central to peripheral Au-Au continues in pp with decreasing multiplicity. Data (CD): 200 GeV pp STAR Preliminary

16. QM 2004 Poster Session16 200 GeV Au-Au  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. Invert -- autocorrelations (CD): 200 GeV pp STAR Preliminary

17. QM 2004 Poster Session17 200 GeV AuAu STAR Preliminary Compare CD and CI autocorrelations from inversion method:  Momentum conservation in both at    with additional v 2 (flow) in CI.  Elongation in same-side CI   peak, but narrowing in CD.  Narrowing in both CI and CD same-side peaks for   Using CDCI

18. QM 2004 Poster Session18 Relation of CD   autocorrelation to Balance function: BF depends on acceptance (  ) and pseudorapidity difference variables Acceptance function: Canonical suppression due to total charge conservation for finite, <4  acceptance Two-particle, charge-dependent autocorrelation  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.      0 

19. QM 2004 Poster Session19 Summary of CD Correlations on (     ) vs (     ): 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