Hadronization of a QGP via recombination Kang Seog
Hadronization of a QGP via recombination Kang Seog Lee Chonnam National University • Introduction – recombination model • Dynamic recomination calculation : Hydrodynamic evolution of QGP + + Hadronization via recombination in mixed phase + Hadronic rescattering by URQMD • Results • Summary and Outlook collaborators: • S. Bass • B. Müller • C. Nonaka
Recombination : long history High Energy Physics Phenomenology: • K. P. Das & R. C. Hwa, Phys. Lett. B 68, 459 (1977) Quark-Antiquark Recombination in the Fragmentation Region Ø description of leading particle effect • T. Ochiai, Prog. Theo. Phys. 75, 1184 (1986) • E. Braaten, Y. Jia & T. Mehen, Phys. Rev. Lett. 89, 122002 (2002) • R. Rapp & E. V. Shuryak, Phys. Rev. D 67, 074036 (2003) Heavy-Ion Phenomenology: • T. S. Biro, P. Levai & J. Zimanyi, Phys. Lett. B 347, 6 (1995) ALCOR: a dynamical model for hadronization Ø yields and ratios via counting of constituent quarks • R. C. Hwa & C. B. Yang, Phys. Rev. C 66, 025205 (2002) • R. Fries, B. Mueller, C. Nonaka & S. A. Bass, Phys. Rev. Lett. 90 • R. Fries, B. Mueller, C. Nonaka & S. A. Bass, Phys. Rev. C 68, 044902 (2003) • V. Greco, C. M. Ko and P. Levai, Phys. Rev. Lett. 90 Anisotropic flow: • S. Voloshin, QM 2002, nucl-ex/020014 • Z. W. Lin & C. M. Ko, Phys. Rev. Lett 89, 202302 (2002) : AMPT • D. Molnar & S. Voloshin, nucl-th/0302014 Jin-Hui Chen’s talk
Recombination+Fragmentation Model R. J. Fries, C. Nonaka, B. Mueller & S. A. Bass, PRL 90 202303 (2003) ; PRC 68, 044902 (2003) basic assumptions: • at low pt, the quarks and antiquark spectrum is thermal and they recombine into hadrons locally “at an instant”: Ø features of the parton spectrum are shifted to higher pt in the hadron spectrum • at high pt, the parton spectrum is given by a p. QCD power law, partons suffer jet energy loss and hadrons are formed via fragmentation of quarks and gluons
Hadron Spectra I
Elliptic Flow: Recombination vs. Fragmentation • high pt: v 2 for all hadrons merge, since v 2 from energy-loss is flavor blind Ø charged hadron v 2 for high pt shows universal & limiting fragmentation v 2 Ø quark number scaling breaks down in the fragmentation domain
Parton Number Scaling of v 2 • in leading order of v 2, recombination predicts: P. Soerensen, UCLA & STAR @ SQM 2003 Ø smoking gun for recombination Ø measurement of partonic v 2 !
Hadron Ratios vs. pt
Model QGP and hydrodynamic expansion initial state pre-equilibrium hadronic phase and freeze-out hadronization QGP • hydrodynamic evolution - C. Nonaka • reasonable for a perfect fluid Hadronization via recombination • recombination Hadronic rescattering • URQMD - S. Bass
Recombination of thermal quarks I • wave functions are best know in the light cone frame. • for a thermal distribution:
Recombination of thermal quarks II • hadronization hypersurface : mixed phase • Energy conservation during the recombination Ø For a cell at hadronization, hadronization where QGP phase. is the energy available for is the volume fraction of • In a hydrodynamic cell, i, hadronization rate in is proportional to direction
Recombination of thermal quarks III • depends only on the quark masses and is independent of hadron mass. • Since baryons. , there are 4 cases for mesons and 8 cases for Ø Inside a group, relative abundances are assumed to be (Ci : degeneracy factors) e. g.
Recombination of thermal quarks IV • After hadronization, hadronic rescattering is simulated by URQMD !
Results & Comparison to Data • • hadron spectra hadron ratios – coming soon RAA – coming soon elliptic flow – coming soon
Summary & Outlook Hadronization of a QGP via Recombination: • Hydrodynamic evolution of a QGP until mixed phase - reasonable for a perfect fluid • hadronization via quark recombination - quark number scaling of elliptic flow, … • hadronic rescattering by URQMD - different chemical and thermal freeze-out No problem of freeze-out prescription !!! issues to be addressed in the future: • results are coming soon. • comparison with statistical hadronization • combine with viscous hydrodynamics or parton cascade
Statistical Model vs. Recombination • in the Statistical Model, the hadron distribution at freeze-out is given by: • If , recombination is identical to SM!
Parton Number Scaling of Elliptic Flow • in the recombination regime, meson and baryon v 2 can be obtained from the parton v 2 in the following way: Øneglecting quadratic and cubic terms, one finds a simple scaling law:
Recombination: Pro’s & Con’s Pro’s: • for exponential parton spectrum, recombination is fragmenting parton: more effective than ph = z p, z<1 fragmentation • baryons are shifted to higher pt than mesons, for same recombining partons: quark distribution p 1+p 2=ph Ø understand behavior of protons! Con’s: • recombination violates entropy conservation • gluons at hadronization need to be converted
- Slides: 25