Centrarity Dependence

1. RIKEN-BNL and LBL and Nu Xu Model Masashi Kaneta • 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 Tch : Chemical freeze-out temperature mq : light-quark chemical potential ms : strangeness chemical potential gs : strangeness saturation factor Introduction • The 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 (m), and the strangeness saturation factor (gs). 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. • 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; • The strangeness is not fully equilibrated because gs is 0.5-0.8 [5,8,9] (if strangeness is in equilibration, gs=1 [1]; • The kinetic freeze-out (elastic scatterings cease) occurs at a lower temperature 100-120 MeV; • 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 - mB) 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. References Does it work well? • Yes!! • Demonstration • for 130 GeV Au+Au, <Npart>=317 • Three data set for fit • set (4) : p, K, p, L, K*, f, and X • set (5) : p, K, p, L, f, X, and W • set (6) : p, K, p, L, K*, f, X, and W Data 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> , ,, ,’, , 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)  Centrarity Dependence of Chemical Freeze-out in Au+Au Collisions at RHIC Summary • Tch, mq, ms seems to be flat in 130 and 200 GeV Au+Au collisions • Tch ~ 150-170MeV • mq ~ 10 MeV (small net Baryon density) • ms ~0 MeV (close to phase boundary) • There is a dependence of ratio combinations for the fit parameters • the deviation is <10% • gs increasing with <Npart> • Full strangeness equilibration only central Au+Au collisions at RHIC • Seems to be reached around <Npart>~100-150 Particle 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) p, K, and p • (2) p, K, p and L • (3) p, K, p, L, f, and X • (4) p, K, p, L, K*, f, and X • (5) p, K, p, L, f, X, and W • (6) p, K, p, L, K*, f, X, and W