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

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

1.Chemical analysis Multiplicities or ratios of hadrons

are nicely fitted with statistical distributions.

parameters : Tch , B,ch , s,ch , s

= Tch at RHIC energy is close to the phase transition temperature to

QGP.

= The hadrons are chemically frozen out just after the

hadronization.

= s close to 1, and the strangeness is nearly equilibrated.

chi Te /)(

Analysis 1.

2. Thermal analysis

The slopes of pt spectra are well explained with expanding

fireball model when absolute magnitude for each hadrons is

arbitrary adjusted .

parameters : Tth , B,th , s,th ,

= The success of thermal analysis (pt < 2GeV/c) is the evidence of

the radial expansion.

thi Tupe /)(

Analysis 2.

J. Adams et al. [STAR Collaboration] 2004, Phys. Rev. Lett. 92 112301

1. The temperatures of the two analysis are different, Tch Tth.

2. 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

Cooper-Frye Formula

H. Dobler, J. Sollfrank, U. Heinz, P. L. B457,353(1999)J. D. Bjorken, Phys. Rev. D Vol. 27, 1F. Cooper and G. Frye, Phys. Rev. D 10, 140(1974)

For an ellipsoidally expanding fireball

Blast-wave model

Hadron yields, slopes and magnitude of mt spectra of various hadrons can be simultaneously explained within a single model.

Consistent way of analyzing both the ratios and pt spectrum

Nith is fixed.

Calculate chemical potential of each particles mi from Ni

th.

Thermal freeze-out Find thermal freeze out parameters to fit mt spectra using i.Resonance contribution should be included.

Tch Tth

Chemical freeze out: Number of each particles is fixed.

Chemical analysis

Total Particle Number

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.

Transverse Mass Spectrum

Chemical Potential from particle ratios fixed at Tch.

Thermal analysis

Hadron ratios at chemical freeze-out time

Strength of two freeze-out model

1.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.

2.Two freeze-out model can explain ratios of hadrons , transverse momentum spectrum of each hadrons without arbitrary normalizations and rapidity distribution of charged hadrons.

Results of chemical analysis

Tch=173.4 MeV

B=18.5 MeV

s=7.9 MeV

s=0.986

2/n=1.4

Tch=173.9 MeV

B=26.4 MeV

s=6.0 MeV

s=1.01

2/n=0.12

Result of thermal analysis

Tth=121.1 MeV

=126.4 MeV

max=5.0

0=1.03

s=0.986

2/n=5.3

Result of rapidity distribution

Tth=121.1 MeV

=126.4 MeV

max=5.0

0=1.03

s=0.986

Conclusion

1. In an 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.

I’ll give you chance which you can give me the LHC data(rapidity, Pt, ratios of particles).

Contact to me : choi3over4@korea.com

Thanks ! ^.*

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]