Quark Coalescence at RHIC

1. Quark Coalescence at RHIC Che-Ming Ko Texas A&M University • Introduction • Quark coalescence Baryon/meson ratio Hadron elliptic flows and quark number scaling Effect of resonance decays Charm flow Higher-order anisotropic flows • Coalescence in transport model • Exotica (pentaquark baryon) • Entropy problem • Summary Thanks to: Chen, Greco, Levai, Rapp

2. Coalescence model in heavy ion collisions • Extensively used for light clusters production • First used for describing hadronization of QGP by Budapest group • Currently pursued by Oregon: Hwa, Yang (PRC 66 (02) 025205), ……… Duke-Minnesota: Bass, Nonaka, Meuller, Fries (PRL 90 (03) 202303; PRC 68 (03) 044902 ) Ohio and Wayne States: Molnar, Voloshin (PRL 91 (03) 092301; PRC 68 (03) 044901) Texas A&M: Greco, Levai, Rapp, Chen, Ko (PRL (03) 202302; PRC 68 (03) 034904) • Most studies are schematic, based on parametrized QGP parton distributions • Study based on parton distributions from transport models has been developed by TAMU group (PRL 89 (2002) 152301; PRC 65 (2002) 034904 ) and is now also pursued by D. Molnar (nucl th/0406066)

3. PRL 90, 202102 (2003); PRC 68, 034904 (2003) Coalescence model Number of hadrons with n quarks and/or antiquarks Spin-color statistical factor e.g. Quark distribution function Coalescence probability function For baryons, Jacobi coordinates for three-body system are used.

4. Monte-Carlo method Introduce quark probabilities Pq(i) according to their transverse momentum and spatial distributions Allow to treat all quarks on same footing

5. Thermal QGP Power-law minijets Choose T=170 MeV quenched soft hard L/l=3.5 Parton transverse momentum distributions Consistent with data (PHENIX) P. Levai et al., NPA 698 (02) 631

6. Other inputs or assumptions • Minijet fragmentation via KKP fragmentation functions • Gluons are converted to quark-antiquark pairs with equal probabilities in all flavors. • Quark-gluon plasma is given a transverse collective flow velocity of β=0.5 c, so partons have an additional velocity v(r)=β(r/R). • Minijet partons have current quark masses mu,d=10 MeV, ms=175 MeV, while QGP partons have constituent quark masses mu,d=300 MeV, ms=475 MeV. • Use same coalescence radiifor all hadrons, i.e., Δx=0.85 fm and Δp=0.24 GeV.

7. Pion and proton spectra Au+Au @ 200AGeV (central) Similar results from other groups Oregon: parton distributions extracted from pion spectrum Duke group: no resonances and s+h but use harder parton spectrum

8. Baryon/meson ratios coalescence BM fragmentation Quark coalescence enhances baryons production at intermediate transverse momentum

9. Elliptic flows Quark v2 extracted from pion and kaon v2 using coalescence model

10. Naïve quark coalescence model Only quarks of same momentum can coalescence, i.e., Δp=0 Quark transverse momentum distribution Meson elliptic flow Quark number scaling of hadron v2 (except pions): Baryon elliptic flow same for mesons and baryons

11. Effects due to wave function and resonance decays Effect of resonance decays Wave function effect Wave fun.+ res. decays

12. Charm spectra D meson J/ψ Charm quark T=0.72 GeV T=0.35-0.50GeV Bands correspond to flow velocities between 0.5 and 0.65 NJ/ψ =2.7 . 10-3 NJ/ψ =0.9 . 10-3

13. S. Kelly,QM04 Charmed meson elliptic flow V2 of electrons Greco, Rapp, Ko, PLB595 (04) 202

14. Effect of higher-order parton anisotropic flows Kolb, Chen, Greco, Ko, PRC 69 (2004) 051901 Including 4th order quark flow Meson elliptic flow Baryon elliptic flow

15. Higher-order anisotropic flows Data can be described by a multiphase transport (AMPT) model Parton cascade Data

16. A multiphase transport model Lin, PaL, Zhang, Li &Ko, PRC 61, 067901 (00); 64, 041901 (01) • Initial conditions: HIJING • Parton evolution: ZPC • Hadronization: Lund string model for default AMPT • Coalescence model for string melting scenario • Hadronic scattering: ART String melting: PRC 65, 034904 (02); PRL 89, 152301 (02) • Convert hadrons from string fragmentation into quarks and antiquarks • Evolve quarks and antiquarks in ZPC • When stop interacting, combine nearest quark and antiquark to • meson, and nearest three quarks to baryon, • Hadron flavors are determined by quarks’ invariant mass

17. Quark elliptic flows from AMPT • pT dependence of charm quark v2 is different from that of light quarks • At high pT, charm quark has similar v2 as light quarks • Charm elliptic flow is also sensitive to parton cross sections

18. Pseudorapidity dependence of v1 and v2 • String melting describes data near mid-rapidity (||<1.5) • At large rapidity (||>3), hadronic picture works better

19. Θ+production in heavy ion collisions Chen, Greco, Ko, Lee and Liu, nucl-th/0308006 Quark coalescence model with quark distribution function and Theta+ Wigner function Take σ=0.86 fm (RΘ~0.9 fm) gives NΘ~0.64, reduced to 0.19 by relativistic correction and sensitive to the Θ+ wave function Compare to ~ 0.9 (Randrup, PRC 68) and ~ 0.4 (Letessier et al, PRC 68) from statistical model

20. Entropy For non-relativistic system For g→π assuming mg=mπ 70% decrease Coalescence model 16% decrease But energy is not conserved ΔE/E~ 18% Need to take into account binding effect.

21. Summary • Hadronization via parton coalescence seems to work well in understanding observed hadron yields and transverse momentum spectra as well as their elliptic flows. • Coalescence of minijet partons with partons from QGP is an alternative mechanism for hadronization of minijet partons. • Incorporation of parton coalescence in transport models is useful. For QGP partons, it has already been included in the AMPT model (Lin et al., PRC 65, 034904 (2002); PRL 89, 152301 (2002)). Need to include minijet partons as well.