# Presentation: 380715

## 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

## 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.

## 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 ...

## 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

##  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 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)

## 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 *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.

## 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)

## Two-Particle Hadron Spectra

- mT 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 RTO and RTS
- contribution of time is ignored for RTO
- in the strong transverse flow limit, all “size” parameters have 1/sqrt(mT) dependence

## 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

## Two-Particle Hadron Spectra

- Cascade Model Calculation
- Decomposition of coordinate
- zH 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 zH can be made:
- L is a trivial factor (if time is longer then size is larger)
- the length of homogeneity measured with rapidity LH contains all dynamical effects
- L and LH can be calculated with cascade model data

## 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 LH 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

## Three-Particle Hadron Spectra

- Three-Particle Interferometry
- Relation between C3 and C2
- For a chaotic particle emission source:
- For the two-particle correlation function *C*2, the phase information of Fij does not survive.
- For the three-particle correlation function *C*3, the phase information survive as the phase factor cos.

## 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)

## 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 s 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 *C*3 is made.