Hadronization Mechanisms: Coalescence versus Fragmentation

1. ReCo Overview & Prospectives V. Greco BNL , 29 April 2005

2. baryon/meson pattern Result robust vs uncertainties • Overview:Early successes of Reco+Fragm. • pT spectra ( enh. B/M ratio, RAA , Rcp ) • Elliptic Flow (“scaling”) • Developments I:Extensions • Resonances (from QGP or hadron phase) • Wave function (Widths, Higher Fock state) • Insight on charm interaction • v4M/v4B , v1M/v1B • Charge Fluctuations • Developments II:Prospective • Jet-like Dynamical Correlations • Low pT (Energy, Entropy, # conservation) • Links to QCD Relation to EOS-WG Topics

3. Hadrons at RHIC pions protons PHENIX, nucl-ex/0212014 • Fragmentation p/p ~ 0.2 • Jet quenching should affect both PHENIX, nucl-ex/0304022 p0 suppression: evidence of jet quenching before fragmentation Fragmentation is not the dominant mechanism of hadronization at pT < 4-6GeV !?

4. Fragmentation: Parton spectrum • Leading parton pT ph= z pT according toa probability Dh(z) • z < 1, energy needed to create quarks • from vacuum Coalescence: B M • partons are already there • ph= n pT ,, n = 2,3 • to be close in phase space $ Coalescence vs. Fragmentation H Partonic Hydro behavior shifted at higher pT Even if eventually Fragmentationtakes over …

5. Phase-Space Coalescence fqinvariant parton distribution functionthermal (mq=0.3 GeV, ms=0.47 GeV) with radial flow (b=0.5) + quenched minijets (L/l = 3.5, mq=0.01GeV, ms=0.175 GeV) |Mqq->m|2 depends only on the phase space weighted by wave function; npQCD also encoded in the quark masses (gluon dressing), mq=0.3 GeV, ms=0.475 GeV. fHhadron Wigner function Dx = 1/Dp ~ 0.85 fm coalescence radius parameter

6. TAMU implementation T=170 MeV ET ~ 730 GeV b(r)~ 0.5 r/R T ~ 170 MeV quenched soft hard V ~ 900 fm-3 e ~ 0.8 GeVfm-3 dS/dy ~ 4800 L/l=3.5 P. Levai et al., NPA698(02)631 Coalescence Integral solved in a 3D geometry, with radial flow space-momentum correlation (important to fix bulk parton distribution) Locally v1, u1 … not small Coalescence on bulk matter consistent with hydro, experiments, ec

7. Meson & Baryon Spectra Au+Au @200AGeV (central) sh V. Greco et al., PRL90 (03)202302 PRC68(03) 034904 R. Fries et al., PRL90(03)202303 PRC68(03)44902 R. C. Hwa et al., PRC66(02)025205 • Proton suppression hidden by coalescence! ReCo dominates up to 4..6 GeV/c; fragmentation and energy loss takes over above.

8. Baryon/Meson ratio TAMU DUKE r-> pp OREGON DUKE

9. Coalescence scaling Enhancement of partonic v2 Duke Elliptic Flow v2,q from a fit to p data -> v2 p, K, L ... prediction D. Molnar and S.A. Voloshin, PRL91 (03) w.f. effect 5% B/M breaking (Dp~0.25 GeV) Large breaking if Dp >> (OSU, PRC68) Shape consistent with cascade (AMPT, MPC) To be seen, breaking of the scaling !

10. Effect of Resonances & wave function w.f. + resonance decay p from K & p * K, L, p …v2 not affected by resonances! p coal. moved towards p data V.G., C.M. Ko, PRC 70 (03)

11. Resonances II K* from QGP decays into a K with a v2 ~ to K directly produced • HG resonances: • hadron final stage, h-h rescattering • scaling with n=4 r (pT ) is determined by experiments and related to width of particles and cross section in the hadronic medium. C. Nonaka , PRC69, 31902 (2004) • Medium effects: • m* shift v2 of decay product No sensitive to resonance width (Final p spectra weak dependence) p’s from r Can we learn more via the analisis of resonances v2? Can we see evidence of chiral symmetry restoration?

12. Polarized QGP? Global transverse polarization in the direction orthogonal to the reaction plane MECHANISM: qq collision carry an angular momentum that can be transferred to the spin due to spin-orbital coupling Z.T. Liang, X.N. Wang, PRL94,102301(05) 2p <- r Pq degree of quark polarization

13. Higher Fock State Costituent quark picture is a good description of hadron PDF as Q2 < 1 GeV2 (higher Fock state are suppressed) Still contribution from higher terms may not be negligible Is v2 scaling preserved? Standard higher twist w.f For narrow w.f. limit n Fock state, nn= # partons B. Muller, nucl-th0503003 Spectra are also not affected (at least pT >> m ) s = # of sea quark

14. Charmed elliptic flow Flow mass effect V2q from p, p, K, L Coalescence can predict v2D for v2c = 0 S. Kelly,QM04 V2 of electrons V.G. et al., PLB595 (04) 202

15. Charm in a sQGP Charm scatters with D hadronic (chiral restored) resonances in the QGP (Van Hees, Rapp, nucl-th/0412015) Isotropic cross section Fokker-Plank approach on a hydro bulk evolution Therm +flow At high pT even light quarks don’t thermalize ! Do heavy Flavor Equilibrate (strongly interact)?

16. What happens at lower energy? Without changing any coalescence parameter! Jet quenching from I. Vitev, PLB606, 303 (05) Balance between fragmentation (w quenching) and coalescence Uncertainties: amount of quenching, bulk properties (ET, mb,..), p fragmentation function p+/pincrease by 20% p-/pdecrease slight decrease V. G., C. Ko, I.Vitev, nucl-th/0412043

17. Jet-like Correlation Correlation in the parton distribution Source of correlation are jets: dump energy and partons into medium Factorized Ansatz • Gaussian correlations in azimuthal angle  and rapidity y: • S0=1 inside a Vc ( Vc ~const , Vc ~Npart ) • f0 =1 (weak pT dependence) • C0 and f0 fixed to fit data Different processes : F-F, SS-SS, F-SH, F-SS,SH-SH,SH-SS Recombination enhances correlations in the parton phase, ( ~ amplification of elliptic flow)

18. Numerical example Baryons Mesons F-F and SS-SS with C0=0.08, Vc~Npart. Large correlations from F-F, favoring baryon triggers. F-F and SS-SS with C0=0.08x100/Npart (Vc~const.) Lower associated yield when adding SS-SS without correlations (C0=0), especially for baryon triggers. F-SH (- only) v=0.5 • Compatibility with jet-like correlation • Microscopic theory desireable: - how much comes from gluon radiation - relative strength of different correlation source • Different pT window to constraint f0 from R. Fries, HQ04

19. What Can we say? • Constituent quark masses close in phase space hadronize to give • intermediate pT hadrons with the baryon/meson pattern observed at RHIC: • - pT spectra ( enh. B/M ratio, RAA , Rcp, absence of baryon quenching ) • Elliptic Flow (“scaling”) • Large D meson v2 • This is how QCD seems to work in a dense medium ( @ pq > 0.75 GeV) • Result robust against uncertainty in resonance decay, wave function (shape, presence of higher Fock state) • Connection to QCD - Chiral Symmetry - Confinement • Low pT - Energy conservation - Entropy conservation - Particle conservation Need further investigation • Evolution with beam energy (breakdown point?) • Jet-like Correlation • Non Zero Rapidity

20. From Fragmentation toReCo • Dilute system • High virtualities • Fragmentation: 1 parton has to hadronize (e+e-,pp,...AA) • With more partons around: multiple parton fragmentation (higher twist) (pp,pA,AA) • If phase space is filled with partons: recombine/coalesce them into hadrons! • Dense system • Low virtualities (AA) At very low pT most hadrons are formed via coalescence (Voloshin, NPA715 (03)) R. Fries,HQ04

21. Statistical modelNhadat Tc & from recombination Nquark C. Nonaka et al., nucl-th/0501028 Nhad = 507 (635) Nquark= 1125 (1377) STAR, PRC68 (2003) 44905 Bulk : Charge Fluctuations Neglecting: Correlations cik Hadronic diffusion Gluons Close to the value used in V.G., PRC68 : Nq ~ 1100 Can we understand the results of fluctuations measurements? Are they compatible with a deconfined medium? Recombination with all the quark converted into baryon and meson ( ) nonet mesons +octet & decuplet baryons

22. Entropy Conservation • g -> p (suppose mg =mp) 70% decrease But, the energy is not conserved ! Non-Relativistic/ no quantum effect 2) Our Coalescence (PRC68, 034904) 16 % decrease Volume expansion (t ~ 4 fm/c) • No factor 2 or more due to: • mass of the particle • off- equilibrium effect Moreover entropy in the quark phase May be reduced by interaction C. Nonaka et al., nucl-th/0501028

23. What is the role of the mass? Massive quarks mu ~ 0.3 GeV ms ~ 0.5 GeV What mass is it? 0.02 GeV It’s a thermal mass (zero component of vector self energy) 0.3 GeV

24. Thermal masses and energy conservation Although thermal quark mass does not breal chiral Symmetry and similar magnitude of both quantities (Mq = 300-350 MeV) near Tc may facilitate the formation of hadrons from 2- and 3- quark clusters. (U . Heinz and P. Levai, PRC57, (2003) 1879) Thermal masses are related to EOS in a quasi-particle picture, but interaction is still important ! Self-consistent Dirac-Brueckner (DB) with a LQCD potential : -> hadronic resonances with chiral restored phase M.Mannarelli and R.Rapp, work in progr. Spectral function represents an effective way of treating off-shell effect due to the presence of the medium Check Consistency with LQCD resonance spectral function

25. Recombination with thermal masses (from LQCD) • Link to LQCD • Energy Conservation • (-> Entropy , Resonances) EOS LQCD DB V(r) Spectral function To be checked: properties of standard coalescence are preserved Input of Coalescence • Confinement, or use of all Nquark is still pending

26. Dynamical Coalescence Quasi particle massive quarks interacting through LQCD potential Investigation of Coalescence-Clusterization like in molecular dynamics • Use of all quarks • Energy - Entropy conservation? • Need for string mechanism at low pT ? • Effect of q-q potential (entropy, pT, link to EOS) • Natural account for Correlation effect in the Fluctuation • Jet-like Correlations Better enviroment for: Does Coalescence work at low pT ?

27. Summary • Bulk used in coalescence consistent with present knoweledge (ET, S, D..) • Elliptic flow of resonances deep insight on ReCo and medium effect • Polarization (further check inside into the scaling) • Charge Fluctuation • ReCo can be connected to QCD inside the validity of a massive interacting quasi-quark approach • This will allow to base ReCo on microscopic many-body calculation based on LQCD - Link to EOS - Investigation of Energy, entropy .. Heavy quark should be a better starting point for a decription In term of q-q potential, more sophisticated model for J/Y, Y … Of Course our hope is to invalidate recombination! Right!