One-, Two- and Three-Particle Hadron Spectra Recent Results from CERN/SPS Experiment NA44

1. One-, Two- and Three-Particle Hadron SpectraRecent Results from CERN/SPS Experiment NA44 • 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 Atsushi Sakaguchi (Osaka University) for the NA44 Collaboration

2. One-Particle Hadron Spectra • Transverse Mass (mT) Spectra • Based on Hydrodynamical Model • For a thermalized particle emission source with an expansion, the mT inverse slope (apparent temperature TAPP) is a mixture of the freeze-out temperature TFO and the effect of the expansion. • The effect of the expansion is simply parameterized with the transverse flow velocity vT . • 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 pT<<m limit. • Systematic studies of the mT inverse slope can provide information of both the freeze-out temperature TFO and the transverse flow velocity vT.

3. One-Particle Hadron Spectra • Mass systematics of the mT inverse slope gives • freeze-out temperature TFO around 140 MeV • transverse flow velocity vT increases with system size • Beyond the Simple Picture • Underlying picture of this analysis is • hadronic matter is thermalized • traveling with common flow velocity vT • 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 mq (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 • ms is small • T is larger than TFO • 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 RHO, which has contributions from the geometrical size RG and the thermal length RTH. • 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 C2 is parameterized as follows: • Coulomb Correction • Coulomb wave integration: 2p and 2 K data analysis in the Pb+Pb collisions • standard Gamow correction: 2p and 2K data analysis in the S+A collisions (about a few % systematic deviation)

8. Two-Particle Hadron Spectra • mT Dependence • Based on Hydrodynamical Model • The interferometric parameters in the lowest order are estimated as follows: • tFO is freeze-out time • finite geometrical size effect is included in RTO and RTS • contribution of time is ignored for RTO • in the strong transverse flow limit, all “size” parameters have 1/sqrt(mT) 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 (s/sTOTAL~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 • DzH is the length of homogeneity in the z (beam) direction • tL is the longitudinal proper time and hL is the longitudinal space-time rapidity • This is a purely mathematical decomposition. • Decomposition of the length of homogeneity DzH can be made: • tL is a trivial factor (if time is longer then size is larger) • the length of homogeneity measured with rapidity DhLH contains all dynamical effects • tL and DhLH 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: • tL is proportional to (dN/dy)1/3 • the length of homogeneity measured in rapidity DhLH 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 C3 and C2 • For a chaotic particle emission source: • For the two-particle correlation function C2, the phase information of Fij does not survive. • For the three-particle correlation function C3, the phase information survive as the phase factor cosf.

13. Three-Particle Hadron Spectra • Phase Calculation with NA44 Data • The phase factor cosf can be calculated as follows: • Results from C3 and C2 of pion for the S+Pb collisions at 200AGeV • This is the first trial to get the phase information cosf 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 (TFO and vT) is successful to understand the the hadron mT spectra. • Systematical difference of the mT inverse slope between anti-proton and proton shows a small breaking of the simple picture. • The mT inverse slopes of deuteron, anti-deuteron and triton are consistent with the mass systematics. • Chemical Parameters • Small ms and T>TFO • Two-Particle Hadron Spectra • Expansion Effects in Particle Correlation • RL shows clear 1/sqrt(mT) dependence • mT dependence of RTO and RTS favors rapid transverse flow vT>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 C3 is made.