IntroductionIntroductionThe statistical model approach is established by analysis of particle

ratios of the high energy heavy ion collisions in GSI-SIS to CERN-SPS energy [1-7] and elementary collisions (e+e-, pp, and pp) [8,9]. The model describes the particle

ratios by the chemical freeze-out temperature (Tch), the chemical potential (), and

the strangeness saturation factor (s). Many feature of the data imply that a large

degree of the chemical equilibration may be reached both at AGS and SPS energies excepting strangeness hadrons. There are the four most important results.

1.At high energy collisions the chemical freeze-out (inelastic collisions cease) occurs at about 150-170 MeV and it is `universal' to both elementary and the heavy ion collisions;

2.The strangeness is not fully equilibrated because s is 0.5-0.8 [5,8,9]

(if strangeness is in equilibration, s=1 [1];

3.The kinetic freeze-out (elastic scatterings cease) occurs at a lower temperature 100-120 MeV;

4.The compilation of the freeze-out parameters [10] in the heavy ion collisions in the energy range from 1 - 200 A·GeV shows that a constant energy per particle

<E>/<N> ~ 1 GeV can reproduce the behavior in the temperature-potential (Tch

- B) plane [10].

We have many hadron yields and ratios including multi-strange hadrons as a

function of centrality in Au+Au collisions at sNN = 130 and 200 GeV at RHIC. They

allow us to study centrality dependence of chemical freeze-out at RHIC energy.

ModelModel• Based on Ref[11] and used in Ref.[12-14]• Density of particle i is

• Compute particle densities for resonances (mass<1.7GeV)

• And then we can obtain particle ratios to compare data

• Resonances in this model are:

Qi : 1 for u and d, -1 for u and d

si : 1 for s, -1 for s

gi : spin-isospin freedom

mi : particle mass

ch : Chemical freeze-out temperatureq : light-quark chemical potentials : strangeness chemical potentials : strangeness saturation factor

, , , , ’, , f0(980) , a0 (980), h1(1170), b1 (1235), a1 (1260), f2(1270), f1 (1285), (1295), (1300), a2(1320),

f0(1370), (1440), (1420), f1 (1420), (1450), f0 (1500), f1 (1510), f2’(1525), (1600), 2(1670), (1680),

3(1690), fJ(1710), (1700)

K, K*, K1(1270), K1(1400), K*(1410), K0*(1430), K2*(1430), K*(1680)

p, n, N(1440), N(1520), N(1535), N(1650), N(1675), N(1680), N(1700)

(1232), (1600), (1620), (1700)

, (1450), (1520), (1600), (1670), (1690)

, (1385), (1660), (1670)

, (1530), (1690)

Data from RHIC experimentsData from RHIC experiments•Now we have many set of data for dN/dy and ratios from RHIC experiments

•However, the centrality bin selection is not the same among experiments

•We need to adjust ratios as a function of “common” centrality to combine all of data for centrality dependence of chemical freeze-out

– Assumption• dN/dy is linearly scaled by <Npart>

• Actually, the data looks like that dependence

– Select one set of centrality bins• interpolate dN/dy for the centrality as a function of <Npart>

Particle combinations for the fitParticle combinations for the fit•The chemical freeze-out parameter seems to be sensitive to combination of particle ratios as discussed in Ref.[14]

•Hence we checked the following six combinations of particle ratios for the fit:

(1) , K, and p(2) , K, p and (3) , K, p, , , and (4) , K, p, , K*, , and (5) , K, p, , , , and (6) , K, p, , K*, , , and

Does it work well?Does it work well?•Yes!!•Demonstration

–for 130 GeV Au+Au, <Npart>=317

–Three data set for fit•set (4) : , K, p, , K*, , and •set (5) : , K, p, , , , and •set (6) : , K, p, , K*, , , and

SummarySummary• Tch, q, s seems to be flat in 130 and 200 GeV Au+Au

collisions– Tch ~ 150-170MeV

– q ~ 10 MeV (small net Baryon density)

– s ~ 0 MeV (close to phase boundary)

• There is a dependence of ratio combinations for the fit parameters– the deviation is <10%

• s increasing with <Npart>• Full strangeness equilibration only central Au+Au collisions at RHIC

• Seems to be reached around <Npart>~100-150

ReferencesReferences