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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

3% uncertainty on trigger inefficiency 0.5-7 %

  • Uncertainty on simulation of paddle response <2 %


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

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


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

data: 0.615 +/- 0.061(preliminary)