Centrality measurements
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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.

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Centrality measurements
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

Centrality participants vs spectators





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

Glauber m odel

Nucleon density

  • Independent collisions of participating nucleons.

  • Only several % of collisions happens at small impact parameter.





Centrality distribution

% cross section


Glauber Model



Contemporary m odels
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

Precision in model tests



Precision in Model Tests

  • Changing size of nuclei and

  • studying inclusive samples

    • samples with large dispersion



event samples

  • Selecting events by centrality

    • full range of centrality conditions, small dispersions

Glauber model uncertainties


  • 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


Glauber Model Uncertainties

Centrality in phobos
Centrality in PHOBOS

Neutral „spectators”




Neutral „spectators”

Produced Particles

  • Many things scale with Npart:

    • Transverse Energy

    • Particle Multiplicity

    • Particle Spectra

Paddle detectors

Experimental m easures of c entrality
Experimental Measures of Centrality





Signal in Paddles

anti-correlated with

number of spectators

Signal in Paddles correlated with multiplicity of produced particles

Modelling e xperiment




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

Determination of n part






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

Experimental p recision
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



% cross-section

% cross-section

Systematic u ncertainties of n part


Total systematic error

Total systematic error on Npart


Variation of cross section +3%

Variation of cross section +3%

Simulation of paddle response

Simulation of smearing


Systematic Uncertainties of Npart


  • 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


  • 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.

Definition of participating nucleon

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

Measurement of cross section ratios

s hadron 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


shadron/ stottheory: 0.636 +/- 0.032(Nucl.Instr.Meth.A 417(1998)1)

data: 0.615 +/- 0.061(preliminary)