1. One-, Two- and Three-Particle Hadron Spectra Recent Results from CERN/SPS Experiment NA44 Atsushi Sakaguchi (Osaka University) for the NA44 Collaboration NBI I.G. Bearden, H. Boggild, J.J. Garhoje, A.G. Hansen and O. Hansen LANL J. Boissevain, D.E. Fields, H. van Hecke, J. Simon-Gillo, W. Sondheim, J.P. Sullivan and N. Xu Columbia J.R. Dodd, M. Leltchouk, A. Medvedev, M. Potekhin and W.J. Willis Nantes B. Erazmus, G. Paic and J. Pluta Hiroshima S. Esumi, K. Kaimi, M. Kaneta, N. Maeda, S. Nishimura, H. Ohnishi, T. Sugitate and Y. Sumi CERN C.W. Fabjan, A. Franz, B. Holzer, P. Hummel, R. Malina, F. Piuz, G. Poulard, M. Spegel and D.S. Zachary Boskovic Institute, Zagreb D. Ferenc and A. Ljubicic Ohio State D. Hardtke, T.J. Humanic, R. Jayanti, S.U. Pandey and D. Reichhold SUNY, Stony Brook B.V. Jacak and M. Kopytine Lund B. Lorstad and J. Schmidt-Sorensen Texas A&M M. Murray and K. Wolf BNL V. Polychronakos Osaka A. Sakaguchi

2. One-Particle Hadron Spectra Transverse Mass (m T ) Spectra Based on Hydrodynamical Model For a thermalized particle emission source with an expansion, the m T inverse slope (apparent temperature T APP ) is a mixture of the freeze-out temperature T FO and the effect of the expansion. The effect of the expansion is simply parameterized with the transverse flow velocity v T. For 3 dimensionally expanding system with cylindrical symmetry (T.Csörgo and B.Lörstad, PR C54 (1996) 1390) Blast wave model (3D isotropic expansion model) gives similar relation in the p T <<m limit. Systematic studies of the m T inverse slope can provide information of both the freeze-out temperature T FO and the transverse flow velocity v T.

3. One-Particle Hadron Spectra Mass systematics of the m T inverse slope gives freeze-out temperature T FO around 140 MeV transverse flow velocity v T increases with system size Beyond the Simple Picture Underlying picture of this analysis is hadronic matter is thermalized traveling with common flow velocity v T freeze-out at the same time for all particle species This simple picture is very successful, but might be too simple in details. Example of anti-proton case...

4. One-Particle Hadron Spectra Particle Ratio Based on Thermal Model Ratio of particles generated in the heavy ion collisions is parameterized with the temperature T and the chemical potentials of quarks  q (q=u,d,s). Model assumptions: chemical equilibrium for u and d quarks at least relative chemical equilibrium for s quark strange neutrality to estimate the temperature T OK in full phase space for static source maybe OK for the HI collisions if net strangeness density is not large, and correction is possible if necessary

5. One-Particle Hadron Spectra Experimental Result From particle ratios in Pb+Pb collisions at 158AGeV (y=2.6) What does the result mean ? similar results as the S+A collisions at CERN/SPS and different from BNL/AGS results  s is small T is larger than T FO For more details “Kaon and Proton Ratios from Central Pb+Pb Collisions at the CERN SPS (NA44)”, Masashi Kaneta in the parallel session Hadron(H1) in Tuesday afternoon (NA44 Preliminary)

6. Two-Particle Hadron Spectra Two-Particle Interferometry Two-Particle Interferometry in Heavy Ion Collisions Two-particle interferometry is a good tool to study the space-time structure of the source function. The “size” parameter of the particle interferometry is a measure of the length of homogeneity R HO, which has contributions from the geometrical size R G and the thermal length R TH. The space-momentum correlation in the heavy ion collisions at CERN/SPS energy is characterized: scaling like rapid expansion in the longitudinal direction flow in the transverse direction The two-particle interferometry can see the effect of the space- momentum correlation clearly in the longitudinal direction, and can study the flow effect in the transverse direction.

7. Two-Particle Hadron Spectra Conventions Reference Frame Longitudinal Center of Mass System (LCMS) is used. The LCMS is approximately the frame moving with the source in the longitudinal direction. Parameterization The correlation function C 2 is parameterized as follows: Coulomb Correction Coulomb wave integration: 2  and 2 K data analysis in the Pb+Pb collisions standard Gamow correction: 2  and 2K data analysis in the S+A collisions (about a few % systematic deviation)

8. Two-Particle Hadron Spectra m T Dependence Based on Hydrodynamical Model The interferometric parameters in the lowest order are estimated as follows:  FO is freeze-out time finite geometrical size effect is included in R TO and R TS contribution of time is ignored for R TO in the strong transverse flow limit, all “size” parameters have 1/sqrt(m T ) dependence

9. Two-Particle Hadron Spectra Multiplicity Dependence Simple Model of Freeze-out The “size” parameters R of the particle interferometry is believed to have a multiplicity dependence: This is coming from a condition of the freeze-out at a constant density. Multiplicity Dependence Data from NA44 semi-central events (  /  TOTAL ~15%) for the S+A and Pb+Pb collisions at y=3.7 minimum-bias data for the S+A collisions at y=3.7

10. Two-Particle Hadron Spectra Cascade Model Calculation Decomposition of coordinate  z H is the length of homogeneity in the z (beam) direction  L is the longitudinal proper time and  L is the longitudinal space-time rapidity This is a purely mathematical decomposition. Decomposition of the length of homogeneity  z H can be made:  L is a trivial factor (if time is longer then size is larger) the length of homogeneity measured with rapidity  L H contains all dynamical effects  L and  L H can be calculated with cascade model data

11. Two-Particle Hadron Spectra From NA44 Data The multiplicity dependence of the “size” parameters from particle interferometry is weaker than the prediction of the simple freeze- out model (dN/dy) 1/3. Cascade Model Results Cascade model calculation suggests:  L is proportional to (dN/dy) 1/3 the length of homogeneity measured in rapidity  L H is decreasing as dN/dy increases Some dynamical effect is the origin of the weak multiplicity dependence. Possible Explanations Effect of growth of the transverse flow with particle multiplicity Effect of finite geometrical size Non-equilibrium effect at low multiplicity

12. Three-Particle Hadron Spectra Three-Particle Interferometry Relation between C 3 and C 2 For a chaotic particle emission source: For the two-particle correlation function C 2, the phase information of F ij does not survive. For the three-particle correlation function C 3, the phase information survive as the phase factor cos .

13. Three-Particle Hadron Spectra Phase Calculation with NA44 Data The phase factor cos  can be calculated as follows: Results from C 3 and C 2 of pion for the S+Pb collisions at 200AGeV This is the first trial to get the phase information cos  experimentally. For more details “Three Pion Correlations in Heavy-Ion Collisions at the CERN SPS (NA44)”, Janus Schmidt-Sorensen in the parallel session Hadron(H3) in Thursday afternoon (NA44 Preliminary)

14. Summary One-Particle Hadron Spectra Picture of Evolution of Hadronic Matter A simple expansion picture with a few parameters (T FO and v T ) is successful to understand the the hadron m T spectra. Systematical difference of the m T inverse slope between anti-proton and proton shows a small breaking of the simple picture. The m T inverse slopes of deuteron, anti-deuteron and triton are consistent with the mass systematics. Chemical Parameters Small  s and T>T FO Two-Particle Hadron Spectra Expansion Effects in Particle Correlation R L shows clear 1/sqrt(m T ) dependence m T dependence of R TO and R TS favors rapid transverse flow v T >0.4c Freeze-out Model and Particle Correlation Multiplicity dependence of “size” parameters is weaker than (dN/dy) 1/3 presumably due to some dynamical effects. Three-Particle Hadron Spectra Source Function and Phase The first trial of getting phase information in C 3 is made.