Centrality Measurements

1. Centrality Measurements • Participant-Spectator model of high energy • nucleus-nucleus collisions • Motivation for centrality dependent measurements • Model uncertainties in centrality determination • Methods of centrality determination in collider experiment PHOBOS • Summary Andrzej Olszewski, IFJ Kraków for PHOBOS Collaboration

2. “Spectators” “Participants” “Spectators” l b impact Centrality: Participants vs. Spectators • Presence of particles with properties typical for fragmentation process among products of nuclear interaction led to formulation of the participant-spectator model • The collision geometry (i.e. the impact parameter) determines the number of nucleons that participate in the collision

3. Nucleon density • Independent collisions of participating nucleons. • Only several % of collisions happens at small impact parameter. (r) RA a r(fm) Centrality distribution % cross section Au+Au Glauber Model Au+Au b(fm)

4. Contemporary Models • Glauber geometry • Superposition of elementary • nucleon-nucleon collisions • + rescattering • Scaling hypotheses • Properties of elementary • collisions may depend on • centrality • Saturation • Jet quenching • Hard/soft collisions Kolb P.F., hep-ph/0103234

5. Npart Npart Precision in Model Tests • Changing size of nuclei and • studying inclusive samples • samples with large dispersion Construction of event samples • Selecting events by centrality • full range of centrality conditions, small dispersions

6. <Npart>/<Npart>Hijing • Optical approximation > 10% difference compared to exact, or Monte Carlo results for peripheral collisions • Nucleon: point like, extended • modifies density distribution • < 5% difference • Woods-Saxon parameters • from charge distribution, • Nucleon-Nucleon • cross-section estimation • < 2% difference Npart Glauber Model Uncertainties

7. Centrality in PHOBOS Neutral „spectators” Zero-degreeCalorimeter Zero-degreeCalorimeter “Participants” Neutral „spectators” Produced Particles • Many things scale with Npart: • Transverse Energy • Particle Multiplicity • Particle Spectra Paddle detectors

8. Experimental Measures of Centrality ZDCmean NSi Paddlemean Paddlemean Signal in Paddles anti-correlated with number of spectators Signal in Paddles correlated with multiplicity of produced particles

9. Data MC 50% most central ZDC a.u. Modelling Experiment • Hijing particle production • + event shape • Geant detector simulations • + detector resolution • Hijing geometry • Scaling Nspect Nneutrons • Fit to experimental width of • energy fluctuations in ZDC’s

10. MC Paddles Paddlemean Participants Npart Determination of Npart Divide full sample into equal bins of different centrality Signal in Paddles Event MC Glauber geometry Derive properties of centrality parameters in each bin

11. Experimental Precision • Average value of centrality parameters is not sensitive to the quantity on which the selection cut was performed • The dispersion of centrality distribution changes with the quantity on which the selection cut was performed (Npart)/<Npart> <Npart> % cross-section % cross-section

12. 3% uncertainty on trigger inefficiency 0.5-7 % • Uncertainty on simulation of paddle response <2 % D(Npart) Total systematic error Total systematic error on Npart DNpart/Npart Variation of cross section +3% Variation of cross section +3% Simulation of paddle response Simulation of smearing Npart Systematic Uncertainties of Npart

13. Summary • We need precision measurements of centrality dependent processes • to understand physics phenomena in nuclear matter at high density. • High granularity and precision of measurements is achieved by using • samples of selected events with close centrality properties. • Uncertainties in Glauber model calculations affect both theoretical • and experimental results. • Results shown as a function of centrality (fraction of cross-section) are least sensitive to Glauber model uncertainties of centrality determination • Number of participating nucleons and N-N collisions is sensitive to details of Glauber calculations, so same type calculations must be used when comparing results using these numbers • Optical approximation should be avoided, since it provides incorrect results in A-A collisions

14. Summary • Experimental errors in determination of average properties of centrality • parameters are dominated currently by uncertainties in the fraction of • cross-section measured. • The biases coming from the use of experimental quantities for centrality • selection cuts are comparatively small. • The changing precision (dispersion) of event selection with the use of • different experimental signals may have to be taken into account in the • future, when other sources of systematic errors will get reduced.

15. The End

16. Ben Hao, nucl-th/0108003 Definition of Participating Nucleon • Definition of what counts as participating nucleon may differ widely among Monte Carlo models • (In)elastic scattering of nucleons on other nucleons or produced particles may be or may not be included in counting • Do not mix these estimates with results of a pure Glauber model calculations

17. shadron Nhadron stot Nhadron + NCoulomb Measurement of cross section ratios stot= shadron + sCoulomb theoretical predictions: 10.92 = 6.92 + 4.0barn measurement (trigger): Ntot = N(paddles) + N(exclusiveZDC) s = N / L g shadron/ stottheory: 0.636 +/- 0.032(Nucl.Instr.Meth.A 417(1998)1) data: 0.615 +/- 0.061(preliminary)