Suk Choi , Kang Seog Lee Chonnam National University

1. Two freeze-out modelfor the hadrons produced in the Relativistic Heavy-Ion Collisions.New Frontiers in QCD 28 Oct, 2011, Yonsei Univ., Seoul, Korea Suk Choi , Kang Seog Lee Chonnam National University

2. What can we know from particle spectra? Hadron yield : chemical freeze-out temperature baryon and strange chemical potential strange saturation factor Pt-spectra : thermal freeze-out temperature chemical potentials(baryon, strange,…) system size, transverse expansion velocity

3. Analysis 1. • Chemical analysis • Multiplicities or ratios of hadrons • are nicely fitted with statistical distributions. • parameters : Tch , mB,ch , ms,ch , gs • = Tch at RHIC energy is close to the phase transition temperature to QGP. • = The hadrons are chemically frozen out just after the hadronization. • = gs close to 1, and the strangeness is nearly equilibrated.

4. Analysis 2. 2. Thermal analysis Theslopes of pt spectra are well explained with expanding fireball model when absolute magnitude for each hadrons is arbitrary adjusted . parameters : Tth , mB,th , ms,th , b = The success of thermal analysis (pt < 2GeV/c) is the evidence of the radial expansion. J. Adams et al. [STAR Collaboration] 2004, Phys. Rev. Lett. 92 112301

5. ? • The temperatures of the two analysis are different, TchTth. • The magnitudes and slopes of transverse momentum spectra of various hadrons cannot be fitted simultaneously. • Chemical freeze-out occurs earlier at high temperature than thermal freeze-out. • The inelastic collisions becomes less frequent. • The numbers of each hadron species are no more changing thus kept fixed. • The system expand continuing with elastic collisions. U. Heinz, AIP conf. Proc. 602:281-292, 2001

6. Blast-wave model Cooper-Frye Formula For an ellipsoidally expanding fireball H. Dobler, J. Sollfrank, U. Heinz, P. L. B457,353(1999) J. D. Bjorken, Phys. Rev. D Vol. 27, 1 F. Cooper and G. Frye, Phys. Rev. D 10, 140(1974)

7. Consistent way of analyzing both the ratios and pt spectrum Chemical freeze out : Number of each particles is fixed. Nith is fixed. Calculate chemical potential of each particles mi from Nith.  Tch Tth Thermal freeze-out Find thermal freeze out parameters to fit mt spectra using i. Resonance contribution should be included. Hadron yields, slopes and magnitude of mt spectra of various hadrons can be simultaneously explained within a single model.

8. Chemical analysis Chemical Potential T>Tch : The hot and dense system is chemically equilibrated. T<Tch : All kind of hadrons are frozen out and the number of hadrons are fixed. Total Particle Number

9. Thermal analysis Transverse Mass Spectrum Chemical Potential from particle ratios fixed at Tch. Hadron ratios at chemical freeze-out time

10. Strength of two freeze-out model • Two freeze-out model causes a small errors but reduces the computation significantly since the coupled equations for the chemical potentials now reduces to independent equations. • Two freeze-out model can explain ratios of hadrons , transverse momentum spectrum of each hadrons without arbitrary normalizations and rapidity distribution of charged hadrons.

11. Results of chemical analysis Tch=173.9 MeV mB=26.4 MeV ms=6.0 MeV gs=1.01 c2/n=0.12 Tch=173.4 MeV mB=18.5 MeV ms=7.9 MeV gs=0.986 c2/n=1.4

12. Result of thermal analysis Tth=121.1 MeV mp-=126.4 MeV hmax=5.0 r0=1.03 gs=0.986 c2/n=5.3

13. Result of rapidity distribution Tth=121.1 MeV mp-=126.4 MeV hmax=5.0 r0=1.03 gs=0.986

14. Conclusion • Inan cylindrically expanding fireball model, both the hadron ratios, magnitude and slopes of the pt spectra at RHIC are described assuming two freeze-outs. 2. Particle pt and rapidity spectra are nicely fitted without arbitrary normalization. 3. We are eagerly waiting for LHC data to analyze.

15. Thanks ! ^.* I’ll give you chance which you can give me the LHC data (rapidity, Pt, ratios of particles). Contact to me : choi3over4@korea.com

16. Reference [1] K. S. Lee, U. Heintz, E. Schnedermann : Z. Phys. C - Particles and Fields 48(1990)525-541 [2] K. S. Lee, U. Heintz, Z. Phys. C43 (1989) 425-429 [3] H. Dobler, J. Sollfrank, U. Heintz , [nucl-th/9904018] [4] B. Pin-zhen, J Rafalski , [nucl-th/0507037] [5] J. D. Bjorken, Physical Review D Vol. 27, Num. 1, January(1983)140-151 [6] J. Sollfrank, P. Koch, U. Heintz, Z. Phys. Rev. Lett. 78. 2080(1997) [7] L. Landau, Izv. Akg. Nauk SSSR, 17, 51 (1953). [8] F. Cooper and G. Frye, Phys. Rev. D 10, 140(1974) [9] U. Heinz, AIP Conf. Proc. 602, 281 (2001), [hep-ph/0109006] [10] J. Adams et al. (STAR), Phys. Rev. Lett. 92 (2004) 112301[nucl-ex/0310004]. [11] J. Adams et al. (STAR), Phys. Lett. B 612 (2005) 181[nucl-ex/0406003]. [12] J. Adams et al. (STAR), Phys. Rev. C 71 (2005) 064902 [nucl-ex/0412019]. [13] A. Billmeier et al. (STAR), J. Phys. G 30 (2004) S363. [14] H. Zhang (STAR) [nucl-ex/0403010]. [15] O. Barannikova (STAR) [nucl-ex/0403014]. [16] Quark Gluon Plasma [17] STAR collaboration, Nucl. Phys. A757 : 102-183 (2005) [18] J. L. Klay et al.[E-0895] Collaboration], Phys. Rev. C 68, 054905(2003) [nucl-ex/0306033]