P. E. Christakoglou HEP Centrality Dependence of the Balance Function in Pb–Pb Collisions (NA49) P. CHRISTAKOGLOU – M. FARANTATOS A. PETRIDIS – M. VASSILIOU UNIVERSITY OF ATHENS

P. E. Christakoglou HEP OUTLINE Introduction – Balance Function definition NA49 setup Toy model analysis Analysis of GeV  Stability of results Analysis of AGeV  Stability of results  Centrality dependence Summary Future Plans

P. E. Christakoglou HEP 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.

P. E. Christakoglou HEP 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. where P 2 : relative rapidity P 1 : anywhere in the detector 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

P. E. Christakoglou HEP Balance Functions (B.F) – How they work? : is the conditional probability of observing a particle of type b in bin p 2 given the existence of a particle of type a in bin p 1 Both terms are summed over all events, though pairs involve particles of the same event.

P. E. Christakoglou HEP 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 (σ therm ). The effect of diffusion stretches the B.F. (σ δn ). 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

P. E. Christakoglou HEP ANALYSIS STEPS Toy model analysis Analysis of GeV data – 500K Events Analysis of mixed GeV data – 500k Events Analysis of AGeV data – 700K Events Centrality Dependence Study – 6 Centrality Bins Analysis of mixed AGeV data

P. E. Christakoglou HEP 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.

P. E. Christakoglou HEP 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 ).

P. E. Christakoglou HEP 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. We analyze in the interval mean ± 1.2 (symmetrically around the mean ). 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. We analyze in the interval mean ± 1.2 (symmetrically around the mean ).

P. E. Christakoglou HEP NA49 SETUP

P. E. Christakoglou HEP NA49 AGeV Event

P. E. Christakoglou HEP GeV SELECTION CRITERIA Event 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 | x 0 = 0 cm, Δy = 1.0 cm | y 0 = 0 cm, Δz = 3.0 cm | z 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.

P. E. Christakoglou HEP Balance function for GeV real and mixed data

P. E. Christakoglou HEP Comparison of the two previous balance functions

P. E. Christakoglou HEP GeV – Stability check

P. E. Christakoglou HEP AGeV SELECTION CRITERIA Event 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 | x 0 = 0 cm, Δy = 1.0 cm | y 0 = 0 cm, Δz = 3.0 cm | z 0 = 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.

P. E. Christakoglou HEP CENTRALITY DEFINITION BinE 0 Range (Gev)N part 10 – – – – – – Ref: Glenn Cooper Thesis

P. E. Christakoglou HEP Balance functions for different centralities

P. E. Christakoglou HEP AGeV – Stability of B.F ‘s width

P. E. Christakoglou HEP Balance functions for all veto bins – Mixed data

P. E. Christakoglou HEP Centrality Dependence

P. E. Christakoglou HEP STAR PRELIMINARY RESULTS

P. E. Christakoglou HEP 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 GeV real and mixed data (reference point).  Analysis of 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.

P. E. Christakoglou HEP OUTLOOK Centrality dependence – Need for MC data for 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).

P. E. Christakoglou HEP CERN – SPS Acceleration of 208 Pb nuclei in LINAC3 (LINear Accelerator). Ions 208 Pb 53+ go through PSB (PS – Booster)  94 AMeV Ions 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 (~10 5 Pb ions/sec). Target with 1% interaction length  end up with 10 3 events/sec. Events with large nuclear overlap  10 events/sec (30 events/spill) 4 weeks / year running period  5x10 6 events.

P. E. Christakoglou HEP TPC – NA49 CHARACTERISTICS OF NA49 TPC TPC :VTPCMTPC HEIGHT (cm)72129 LENGTH (cm) WIDTH (cm) DRIFT LENGTH (cm)66115

P. E. Christakoglou HEP GAS – RESOLUTIONS VTPC : The gas mixture is NeCO 2 (90:10) (high particle density) MTPC : The gas mixture is ArCO 2 CH 4 (90:5:5) (lower particle density) Momentum resolution :

P. E. Christakoglou HEP CALORIMETERS Ring Calorimeter: To measure E T – 240 parts, 10 rings radially and 24 sectors azimuthally.  E – M: 16 layers Pb – scintillators  Hadronic: 20 layers Fe – scintillators Veto Calorimeter: To measure E L – Trigger on central events.  E – M:  Hadronic:

P. E. Christakoglou HEP DETERMINATION OF EVENT CENTRALITY Estimate of b by fraction of Cross Section A simple, model independent estimate of in each centrality sample is made assuming for an event sample increases monotonically with increasing b, so that: where dσ/dE o is the measured E o 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(E o ) is given by:

P. E. Christakoglou HEP Estimate of N part from spectra Within each centrality sample, an estimate of N part 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 :