Quark Coalescence at RHIC CheMing Ko Texas AM

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 1

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) 2

Coalescence model PRL 90, 202102 (2003); PRC 68, 034904 (2003) 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. 3

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

Parton transverse momentum distributions • Thermal QGP • Power-law minijets • Choose T=170 Me. V que nch e d soft hard L/l=3. 5 P. Levai et al. , NPA 698 (02) 631 Consistent with data (PHENIX) 5

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 Me. V, ms=175 Me. V, while QGP partons have constituent quark masses mu, d=300 Me. V, ms=475 Me. V. • Use same coalescence radii for all hadrons, i. e. , Δx=0. 85 fm and Δp=0. 24 Ge. V. 6

Pion and proton spectra Au+Au @ 200 AGe. V (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 7

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

Elliptic flows Quark v 2 extracted from pion and kaon v 2 using coalescence model 9

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 v 2 (except pions): Baryon elliptic flow same for mesons and baryons 10

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

Charm spectra Charm quark D meson J/ψ T=0. 72 Ge. V T=0. 35 -0. 50 Ge. V Bands correspond to flow velocities between 0. 5 and 0. 65 NJ/ψ =2. 7. 10 -3 NJ/ψ =0. 9. 10 -3 12

Charmed meson elliptic flow S. Kelly, QM 04 V 2 of electrons Greco, Rapp, Ko, PLB 595 (04) 202 13

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

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

A multiphase transport model Lin, Pa. L, 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 16

Quark elliptic flows from AMPT • p. T dependence of charm quark v 2 is different from that of light quarks • At high p. T, charm quark has similar v 2 as light quarks • Charm elliptic flow is also sensitive to parton cross sections 17

Pseudorapidity dependence of v 1 and v 2 • String melting describes data near mid-rapidity (| |<1. 5) • At large rapidity (| |>3), hadronic picture works better 18

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) 19 from statistical model

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. 20

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. 21