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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

Andrzej Olszewski, IFJ Kraków

for PHOBOS Collaboration

“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

- 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 ModelAu+Au

b(fm)

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

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

- 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 UncertaintiesCentrality 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

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

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

Paddles

Paddlemean

Participants

Npart

Determination of NpartDivide full sample into equal bins of different centrality

Signal in Paddles

Event MC

Glauber geometry

Derive properties of centrality parameters in each bin

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

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 NpartSummary

- 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

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.

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

stot Nhadron + NCoulomb

Measurement of cross section ratiosstot= 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)

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