Recombinational Hadronization

1. Recombinational Hadronization Kang Seog Lee 李康錫 全南大學校 Chonnam National University collaborators: • S. Bass • B. Müller • C. Nonaka • Dynamic recombination calculation : Hydrodynamic evolution of QGP + + Hadronization via recombination +decays • Two freeze-out analysis of hadron production collaborators: • Suk Choi • U. Heinz

2. Recombination of quarks into hadrons R.J. Fries, C. Nonaka, B. Mueller & S.A. Bass, PRL 90 202303 (2003) ; PRC68, 044902 (2003) basic assumptions: • Quark-gluon plasma is formed during the relativistic heavy-ion collisions. Hadronization occurs by recombining thermal quarks. • Three main features of hadron production can be naturally explained. • pt spectra in the mid pt range – 4GeV • Quark number scaling of elliptic coefficient • Large baryon to meson ratio near pt – 4GeV

3. Hadron Spectra

4. Parton Number Scaling of v2 W.A. Zajc

5. Large p/pi ratio

6. hadronic phase and freeze-out QGP and hydrodynamic expansion initial state pre-equilibrium hadronization Hydrodynamic evolution of QGP with Recombinational Hadronization

7. Hadronization in the mixed phase • hadronization hypersurface : mixed phase • Energy conservation during the recombination • For a hydrodynamic cell at Tc at with velocity , is the energy available for hadronization, where . • The probability for a hadron to be formed is given by EdN/d3p. • EdN/d3p is given by recombination model or equilibrium distribution.

8. Probability for producing hadrons by recombination of quarks • wave functions are best known in the light cone frame. • thermal distribution:

9. Recombination of thermal quarks • depends only on the quark masses and is independent of hadron mass. • If , especially , then recombination model becomes thermal distrib. • If , then ! • This is why exp(-m/T) is missing in recomb. Model. Nucleons are equally abundant as pions. – One may have to put in e(-m/T) factor.

10. Equilibrium Hadronization • When quarks constituting a hadron are same, relative abundances are assumed to be : e.g. (Ci : degeneracy factor) • In thermal equilibrium hadronization,

11. Decay and Rescattering of hadrons • With Monte Carlo method, one can generate hadrons until all the energy of each hydrodynamic cell is converted into hadrons. Roughly 7000 – 11,000. • In order to compare with data, decay of high mass hadrons should be considered. - Done. • Effects from hadronic rescattering can be studied by UrQMD. - Need to be done.

12. Rapidity distribution In the recombination hadronization, baryons are produced abundantly leaving less energy for pion production. Same as the plot of available energy vs. rapidity of cell

13. Pion pt spectrum Hadronic decays are included but rescattering of hadrons are not considered. Effect from the rescatterng on the slope will be investigated.

14. Proton pt spectrum Additional e(-m/T) factor is needed to reduce the number of protons in the recombination hadronization.

15. K+ pt spectrum

16. Elliptic coefficient For elliptic flow more peripheral collision should be considered. At higher pt elliptic coefficient decreases back to 0 ?

17. Summary I Model for hadronization of a QGP using Monte Carlo method with probabilities from recombination model and statistical distribution has been developed. Thousands of hadrons are generated. dN/dy and pt spectra of various hadrons are measured. - Shape of dN/dy is OK. - Too many protons from recombination model. - Need additional exp(-m/T) factor. Any observables can be measured from the generated hadrons. – V2, HBT etc. Effect from hadronic rescattering will be investigated with URQMD.

18. Two freeze-out Analysis of Hadron Production 1. Chemical analysis of particle ratios 2. Thermal analysis of particle spectra 3. Two freeze-out model

19. Chemical Analysis of Hadron Ratios - chemical freeze-out • hadron yields & ratios can be fitted in the framework of a statistical model: Resonance contribution is important.

20. z Thermal Analysis of Pt Spectra • model based on:E. Schnedermann, J. Sollfrank, and U. Heinz, Phys. Rev. C 48, 2462 (1993), H. Dobbler and U. Heinz • parameters: thermal freeze-out temperature Tfo transverse flow rapidity ρ chemical potentials Resonance contribution should be considered.

21. Hadron spectra at low pt • Blastwave works well for wide array of different hadron flavors • best fit for T = 0.7 ± 0.2 and Tfo = 110  23 MeV in central collisions Resonance contribution by Sollfrank

22. Results of Chemical and thermal analysis

23. Two freeze-out model of hadron production After chem. f.o., numbers of particles are fixed, while further elastic collision between the particles of same kind makes the temperature decrease. Calculation of resonance contribution with Sollfrank’s

24. Thermal Analysis • model based on:H. Dobbler and U. Heinz • parameters: thermal freeze-out temperature Tfo transverse flow rapidity ρ , longitudinal flow rapidity radius R(z), overall constant V • are calculated from

25. Chemical Analysis Of Ratios

26. Mt spectra

27. Summary II • Two freeze-out scheme is applied to fit both the hardron ratios and transverse momentum spectra and found to give nice fits to both of them.