Centrality Dependence of the Balance Function in Pb–Pb Collisions (NA49)

P. E. ChristakoglouHEP 2003

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Centrality Dependence of the Balance Function in Pb–Pb Collisions (NA49)

P. CHRISTAKOGLOU – M. FARANTATOSA. PETRIDIS – M. VASSILIOU

UNIVERSITY OF ATHENS


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OUTLINE

Introduction – Balance Function definition

NA49 setup

Toy model analysis

Analysis of pp@158 GeV Stability of results

Analysis of PbPb@158 AGeV Stability of results Centrality dependence

Summary

Future Plans


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MOTIVATION

Motivated by the idea that hadrons are locally produced in charge – anticharge pairs.

We can measure separation of balancing charges.

Early pairs separate due to longitudinal expansion.

Later pairs are correlated at small Δy.

Can signal delayed hadronization.


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BALANCE FUNCTION DEFINITION

The Balance function is defined as a correlation in y of oppositely charged particles, minus the correlation of same charged particles, normalized to the total number of particles.

)P,N(

)P,|P,N()P,|P,N()P,N(

)P,|P,N()P,|P,N(21

)P|B(P1

1212

1

121212

where P2: relative rapidityP1: anywhere in the detector

1)P|B(P2P

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EVENTSlstatistica N

1σ

22

21

N

ΔΔ

N

ΔΔB

Normalization:

Statistical Errors:

Error in Balance Function:

Ref:• Bass-Danielewicz-Pratt, Phys. – Rev.Lett.85, 2000• D. Drijard et al, Nucl. Phys. B(155), 1979


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Balance Functions (B.F) – How they work?

(b, p2 |a, p1) N (b, p2 | a, p1)

N (a, p1)

(b, p2 |a, p1) : is the conditional probability of observing a particle of type b in bin p2 given the existence of a particle of type a in bin p1

Both terms are summed over all events , though pairs involve particles of the same event.


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The overall width of the Balance Function (B.F.) in relative rapidity is a combination of the thermal spread and the effect of diffusion.

Due to cooling the width falls with time (σtherm).

The effect of diffusion stretches the B.F. (σδn).

If the hadronization occurred at early times then the effect of collisions is to broaden the B.F.

On the other hand late stage hadronization suggests narrower B.F.

PROPERTIES OF B.F. ‘S WIDTH


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ANALYSIS STEPS

Toy model analysis

Analysis of pp@158 GeV data – 500K Events

Analysis of mixed pp@158 GeV data – 500k Events

Analysis of PbPb@158 AGeV data – 700K EventsCentrality Dependence Study – 6 Centrality Bins

Analysis of mixed PbPb@158 AGeV data


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Multiplicity Dependence Equal number of positive & negative

particles. For each run this number is

increased , starting from 100 to 600 total particles with a step of 100 (50 pos. & 50 neg.).

We analyze the whole interval of the input distribution.

TOY MODEL ANALYSIS

During all steps of the toy model analysis we used Gaussian distributions as an input in order to simulate the pseudo – rapidity distributions according to NA49 data.


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Net charge Dependence Fixed number of total particles

(400). For each run the net charge is

increased , starting from 40 to 200. The number of positive particles is

always bigger than that of the negative particles.

We analyze the whole interval of the distribution.Correlation Dependence

Fixed number of total particles (400). For each run , equal number of positive and

negative particles is doped symmetrically around the mean of the input distribution.

The distributions of the correlated particles are also Gaussians with a much narrower width.

For each run the number of the correlated particles is increased , starting from 20 to 80.

We analyze in the interval mean ± 1.2 (symmetrically around the mean ).


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Correlation Width Dependence Fixed number of total particles (400). Fixed number of correlated particles (60). The distributions of the correlated particles

are also Gaussians. For each run the width of the distributions

of the correlated particles is increased.


Constant Ratio Multiplicity that is increased in each run. Number of correlated particles is also

increased in each run. The distributions of the correlated particles

are also Gaussians with a fixed width (narrower than the initial input).

The ratio of correlated particles over uncorrelated is constant.



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NA49 SETUP


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NA49 PbPb@158 AGeV Event


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pp @ 158 GeV

SELECTION CRITERIAEvent Level Cuts: Those cuts are imposed in order to reduce a possible contamination from non target collisions. Cuts on vertex coordinates x , y , z:,

Δx = 1.0 cm | x0 = 0 cm,

Δy = 1.0 cm | y0 = 0 cm,

Δz = 3.0 cm | z0 = -580.0 cm Number of tracks > 2 At least one positive and one negative track per event.

Track Level Cuts: Those cuts are imposed in order to reduce the contamination of particles from secondary interactions , weak decays etc. Cuts on the extrapolated distance of the closest approach (impact parameter) of

the particle at the vertex plane and other quality cuts.

Δxxx 0

Δzzz 0

Δyyy 0

1.0cmby 2.0cmbx


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Balance function for pp@158 GeV real and mixed data


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Comparison of the two previous balance functions


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pp@158 GeV – Stability check


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PbPb @ 158 AGeV

SELECTION CRITERIAEvent Level Cuts: Those cuts are imposed in order to reduce a possible contamination from non target collisions. Cuts on vertex coordinates x , y , z:,

Δx = 1.0 cm | x0 = 0 cm,

Δy = 1.0 cm | y0 = 0 cm,

Δz = 3.0 cm | z0 = -578.9 cm Number of tracks > 50 At least one positive and one negative track per event.

Track Level Cuts: Those cuts are imposed in order to reduce the contamination of particles from secondary interactions , weak decays etc. Cuts on the extrapolated distance of the closest approach (impact parameter) of

the particle at the vertex plane and other quality cuts.

Δxxx 0

Δzzz 0

Δyyy 0

0.3cmby 0.5cmbx


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CENTRALITY DEFINITION

Bin E0 Range (Gev)

Npart

1 0 – 9250 373

2 9250 – 14670 319

3 14670 – 21190 252

4 21190 – 26080 188

5 26080 – 29340 141

6 29340 – 40000 88

Ref:• Glenn Cooper Thesis


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Balance functions for different centralities


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PbPb@158 AGeV – Stability of B.F ‘s width


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Balance functions for all veto bins – Mixed data


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Centrality Dependence


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STAR PRELIMINARY RESULTS


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CONCLUSIONS

We ‘ve developed a method (Balance Function) that could possibly signal delayed hadronization.Toy model analysis : B.F independent on multiplicity. B.F independent on net charge. B.F depends on the number of correlations. B.F depends on the width of the distribution of the correlated particles.

Data analysis: Analysis of pp@158 GeV real and mixed data (reference point). Analysis of PbPb@158 AGeV real and mixed data – centrality dependence study:

B.F ‘s width decreases as we go from the most peripheral to the most central PbPb collisions.

The decrease is of the order of 12%. STAR results show the same effect as NA49 data. STAR ‘s decrease is of the order of 16%.

The decrease of B.F. ‘s width could be due to:Delayed hadronization compared with the characteristic 1 fm/c hadronization time.Strong transverse flow.Anomalously short diffusion of particles.Decay of resonances that have lifetimes similar to the proposed time of hadronization.


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OUTLOOK

Centrality dependence – Need for MC data for PbPb @ 158 AGeV in different centralities.

Study of Balance Function’s width dependence on the number of resonances that decay (M.C.).

Energy dependence – Analyze PbPb data for different energies .

System dependence – Study of Balance Function for different systems (CC – SiSi).


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CERN – SPS

Acceleration of 208Pb nuclei in LINAC3 (LINear Accelerator).Ions 208Pb53+ go through PSB (PS – Booster) 94 AMeVIons go through PS (Proton Synchrotron) 4.25 AGeV Ions go through SPS (Super Proton Synchrotron) e- are removed 158 AGeV

Every 20 sec 5 sec beam to deliver (~105 Pb ions/sec).Target with 1% interaction length end up with 103 events/sec .Events with large nuclear overlap 10 events/sec (30 events/spill)4 weeks / year running period 5x106 events.


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TPC – NA49

CHARACTERISTICS OF NA49 TPC

TPC : VTPC

MTPC

HEIGHT (cm) 72 129

LENGTH (cm) 260 384

WIDTH (cm) 200 384

DRIFT LENGTH (cm)

66 115


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GAS – RESOLUTIONS

VTPC : The gas mixture is NeCO2 (90:10) (high particle density)

MTPC : The gas mixture is ArCO2CH4 (90:5:5) (lower particle density)

Momentum resolution :

1-(GeV/c)PP 410730

).(


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CALORIMETERS

Ring Calorimeter: To measure ET – 240 parts , 10 rings radially and 24 sectors azimuthally. E – M: 16 layers Pb – scintillators

Hadronic: 20 layers Fe – scintillators

Veto Calorimeter: To measure EL – Trigger on central events. E – M:

Hadronic:

E

0.140.003

Eσ(E)

E

0.640.003

Eσ(E)

E

0.17E

σ(E)

E

0.740.03

Eσ(E)


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DETERMINATION OF EVENT CENTRALITY

Estimate of b by fraction of Cross Section

A simple , model independent estimate of <b> in each centrality sample is made assuming <Eo> for an event sample increases monotonically with increasing b , so that:

where dσ/dEo is the measured Eo spectrum and dσ/db is closely given by the geometrical cross – section 2πb since the probability of at least one nucleon – nucleon interaction is large. So b(Eo) is given by:

bE

dbdb

ddE

dE

d

00

00

0

''

''

21

0

00

0

01/

''

)(

E

dEdE

dEb


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Estimate of Npart from spectraWithin each centrality sample , an estimate of Npart can be obtained from the measurements of the and distributions along with model estimates of the yield of net neutrons and net hyperons .

The distributions are used to estimate the total strangeness carried by mesons. By strangeness conservation , this total should be compensated by the net strangeness carried by . It is assumed that is equal to so that the net strangeness carried by mesons is twice . Since Ξ and Ω- carry more than one strange quark , the net strangeness carried by the hyperons is given by :

Then in terms of measured quantities :

pp nn YY

pp

nnawhere

:

KK

KK

YY KK 00 KK KK

121 YYYYYY

YY

))(())(( KKppaN part 122

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Centrality Dependence of the Balance Function in Pb–Pb Collisions (NA49)