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V. Greco Università di Catania, Italy INFN-LNS

Coalescence models for hadronization in uRHIC. ?. V. Greco Università di Catania, Italy INFN-LNS. International Workshop XXXVIII on Gross Properties of Nuclei and Nuclear Excitations Hirschegg, Austria, January 17 - 23, 2010. Intro to Basic Idea & Relevance for sQGP.

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V. Greco Università di Catania, Italy INFN-LNS

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  1. Coalescence models for hadronizationin uRHIC ? V. Greco Università di Catania, Italy INFN-LNS International Workshop XXXVIII on Gross Properties of Nuclei and Nuclear ExcitationsHirschegg, Austria, January 17 - 23, 2010

  2. Intro to Basic Idea & Relevance for sQGP • Observation at RHIC -> hadronization modified • RAA-RCP-V2 for baryon and mesons • Basic Theory of coalescence(phase –space) • coal. vs fragm. - application to RHIC • RAA – v2 and B/M in the coalescence mechanism Outline • Extensions from early realizations • Robustness and open issues • Formulation from Boltzmann collision integral • Relevance for : • the Heavy-Quark Sector • h/s of sQGP • A role in the Mach Cones ?

  3. Surprises… Baryon/Mesons Quenching Au+Au p+p p0 suppression: evidence of jet quenching before fragmentation PHENIX, PRL89(2003) In vacuum pp collisions: p/p ~ 0.3 Protons appear not suppressed! • Jet quenching should affect both Hadronization has been modified 1< pT < 5-6GeV !? (> 10 Tmax)

  4. Hadronization in Heavy-Ion Collisions H Partonspectrum • Initial state: no partons in the vacuum but a thermal ensemble of partons • The bulk hadronization dynamics much less violent (t ~ 4 fm/c) • dense parton systems no need for creation and splitting of partons Fragmentation: • energy needed to create quarks from vacuum • hadrons from higher pT Baryon Coal. Coalescence: Meson • partons are already there $ to be close in phase space $ • ph= n pT ,, n = 2,3 baryons from lower momenta (denser) Fragmentation ReCo pushes out soft physics by factors x2 and x3 ! V. Greco et al./ R.J. Fries et al., PRL 90(2003)

  5. Basic Theory Discard details of dynamics -> adiabatic approximation: instantaneous projection of initial state onto final cluster FM(r,q) Meson wave function Recombining : X1Ph+x2Ph=Ph Approximation in FMNB (Hwa-Yang) • - Go in the  momentum frame • - Neglect the transverse momentum • Neglect r,p correlations -> only p-space • direct production (no resonances) fragmenting: Ph = z pq, z<1 Fries, QM’04 All fairly good approximations At pT > 2 GeV/c xi light-cone momentum fraction CM spin-isospin color factor Fries-Nonaka-Muller-Bass, PRC68(03)

  6. Specific features of Reco in HIC P-> ∞or m=0 • ReCo is very effective for thermal spectra: Meson Baryon Both mesons and baryons have the same distribution at variance with fragmentation • ReCo for power law jet spectra • Fragmentation for power law spectra: d shift small power enhancement Suppressed by a power n=# of quarks for power law spectra Even if eventually Fragmentation takes over … Need of Coalescence + Fragmentation model

  7. T=170 MeV ET ~ 740 GeV T ~ 170 MeV b(r)~ 0.5 r/R quenched soft hard L/l=3.5 P. Levai et al., NPA698(02) e ~ 0.8 GeVfm-3 dS/dy ~ 4800 Phase-Space Coalescence (GKL) 3D-geometry with radial flow space-momentum correlation Experiments lQCD Tc like Hydro Bulk matter consistent with hydro, experiments, lQCD fHhadron Wigner function Dx = 1/Dp

  8. FMNB Meson & Baryon Spectra Au+Au @200AGeV (central) sh GKL 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 (meson)-6(baryon) GeV/c; Fragmentation + energy loss takes over above.

  9. Baryon/Meson ratio TAMU r-> pp Strange particles from a common quark flow Hwa-Yang FMNB

  10. z y x py px A Coalescence process carries with it another feature thanks to non-equilibrium l=(sr)-1 c2s=dP/de

  11. Elliptic flow at intermediate pT • Mass-dependence of v2(pT) suggests common transverse velocity field large • At higher pT v2 for Baryon=Mesons in both - hydrodynamics - jet fragmentation • Again surprise Baryon ≠Mesons : v2 larger for Baryons

  12. Coalescence carries another features … Coalescence scaling Enhancement of v2 v2q fitted from v2p GKL • Considering only momentum space • -> x - p correlation neglected • narrow wave function • collinear approximation Molnar and Voloshin, PRL91 (2003) • v2 for baryon is larger and saturates at higher pT • Quark number scaling! baryons Again agreement with unexpected observation mesons No free parameter !

  13. Better scaling vs KET/nq <–> energy conservation R. Lacey, PoS CFRNC2006:021,2006. e-Print: nucl-ex/0610029 Scaling widely confirmed for all species and centralities But it also means that v2q~ v2h/2 Is the v2 (pT) needed by coalescence compatible with a fluid h/s ~ 0.1-0.2 ?

  14. Motivation for a Transport approach Solved discretizing the space in (h, x, y)a cells • It is a 3+1D (viscous hydro 2+1D till now) • No gradient expansion, full calculation • valid also at intermediate pT out of equilibrium -> QNS • valid at high h/s ->study the effect of the hadronic phase • include hadronization by coalescence+fragmentation • Extension to Bulk viscosity z (related also to chiral mass generation) Simulate a fluid at constant shear viscosity Cascade code Relativistic Kinetic theory =cell index in the r-space G. Ferini, PLB670(2009)325 V. Greco, Prog. Part. Nucl. Phys. 62 (2009) 562 Extensions to NJL dynamics - Plumari et al., 1001.2736 [hep-ph] - yesterday Time-Space dependent cross section evaluated locally (see also D. Molnar arXiV:0806.0026)

  15. 20-30% centrality Role of Reco for h/s estimate Parton Cascade at fixed shear viscosity Hadronic h/s included -> shape for v2(pT) consistent with that needed by coalescence A quantitative estimate needs an EOS with phase transition: vs2(T) < 1/3 -> v2 suppression ~30% -> h/s ~ 0.1 may be in agreement with coalesccence Agreement with Hydro at low pT • 4/s >3  too low v2(pT) at pT1.5 GeV/c even with coalescence • 4/s =1 not small enough to get the large v2(pT) at pT2 GeV/c without coalescence

  16. RCP and v2 Correlation:putting together observations! Coalescence reverts the correlation between RAA & v2: both are enhanced This rules out other explanations: Baryon junctions, hydro+jets Rcp~1 with large v2 P.Sorensen This effect is essential also for the study of charm quark interaction !

  17. Ok, but this is really too naive… !? Less important at high pT Stability of Reco results respect uncertainties in their treatment high pT the problem suppressed by m/pT but even at low pT is not so drammatic • Resonances(included in GKL) • Finite width Wave function • Gluons • ALCOR, GKL : mass suppressed, quark dressing, splitting • Higher Fock States, Fries-Muller-Bass, PLB618 (05) 4) Energy Conservation • not large 17% in GKL, resonances decay & v2 • Boltzmann Collision Integral approach: Ravagli-Rapp PLB655(2007) • 5) Entropy Conservation • 15% like energy – mass, resonances, expansion • 6) Relation to jet-like correlations • Consistent with ReCo-Fries et al., PRL94, but need of a transport description • 7) Space-momentum correlations affect v2 scaling Pratt-Pal PRC71, Molnar nucl-th/0408044, Greco-Ko nucl-th/0505061, Rapp-Ravagli PRC79

  18. w.f. + resonance decay p from K & p * Resonances & v2 scaling Does mesons & baryons from resonance decay preserve the QNS? K, L, p …v2 not affected by resonances! p coal. moved towards data Greco-Ko, PRC 70 (03) 2 ->1->2 can exihibt the scaling!

  19. Dependence on wave function of v2 scaling Baryon-to-Meson breaking of the scaling Dp momentum width of w.f. Breaking : • increasing with Dp • decreasing with pT Wavefunction+ Resonance decays

  20. Higher Fock State Costituent quark picture is a good description of hadron PDF as Q2 < 1 GeV2 (higher Fock state are suppressed) Spectra are not affected (at least pT >> m ) Standard higher twist w.f For narrow w.f. limit v2 scaling is preserved • Fock state, nn= # partons s = # of sea partons B. Muller et al., PLB618(05)

  21. Entropy Conservation? Assuming hadronization linear with t during a mixed phase with the spectra of the static GKL model (r,w,D,K* ...) • Entropy- Energy Conservation Energy is also not conserved ! Entropy violation is also related to energy conservation and not to ReCo Greco, EPJ ST155(2008) • 15% violation, No factor 2 : • resonances • mass of the particle • degeneracies

  22. Transport approach to Coalescence->Energy Conservation Miao et al., PRC75(2007) Rapp-Ravagli, PLB655(2007) Equilibrium solution th>>teq gives Production Absorption • Essential property: • Product f(p1)* f(p2) of 2 distr. funct. • suppressed when p1-p2 is too large • Solve energy conservation (except p) • Clarify relation to statistical model • Keeps features of coalescence: - show a KET scaling of v2/nq - baryon/meson enhancement f meson

  23. V2 quark # Scaling with Energy Conservation Scattering for q,Q in QGP • Good quark number scaling except for too large Q value (<300 MeV) • (similar to not too large width • and or non zero quark mass) • KET scaling down to low pT r-p from Fokker Planck still preserve Quark Number Scaling Including space-momentum correlation Ravagli et al.PRC79 (2008)

  24. What happens to heavy quarks?

  25. Problematic relation of RAA and V2 for heavy quarks Up-Scaling elastic scattering from pQCD G.D. Moore and D. Teaney, PRC70 (2005) nucl-th/0412346 data data Too low RAA or too low v2 Coalescence modify v2D- RAA correlation The same problem (even worse!) for radiative energy loss: S. Wicks et al., nucl-th/07010631(QM06), N. Armesto et al., PLB637(2006)362

  26. Spectral function in lQCD & Resonances Opposite T-dependence of g lQCD Friction coefficient pQCD A(w)=w2r (w) Asakawa J/Y V(r) - lQCD q-c “Im T” dominated by meson and diquark channel

  27. Impact of Hadronization for heavy quarks sQGP HQ scattering in QGP Langevin simulation in Hydro bulk g, D from resonant scattering according to lQCD V(r) Hadronization Coalescence + Fragmentation D,B c,b Impact of hadronization • Improved RAA - V2correlation • toward a better agreement with data thanks to • a T dependence of the scattering opposite to pQCD • coalescence can be viewed as • a manifestation of T-matrix interaction • in the hadronization process Van Hees-Mannarelli-Greco-Rapp, PRL100 (2008)

  28. No feed-down No direct contr. J/Y coal. Implication for Quarkonium • Till now we have mainly looked at only J/Y yield, but thanks to coalescence there is a common c-quark collective dynamics with D meson … • Regeneration is revealed in : • - pt spectra • elliptic flow v2Y from v2D : measure of Ncoal/NINI Greco, Ko, Rapp PLB595(2004) Coalecence only pT- Quarkonia from regeneration are consistent with Open heavy flavor!? Suppression only

  29. The open issue with the Mach-Cone with G. Torrieri, J. Noronha, M. Gyulassy A first look at the problem in the coalescence model

  30. High pT Parton  Lower pT “Mach Cone”? near Medium away Cone Jet (medium excitation) Afaniasev, PRL101 (2008) Q = 1 rad • Properties of the cone: • angle does not depend on pt • ratio of B/M similar to the bulk one at the same pt • Peaks at the same angle for Baryon and Mesons Range of pT is that where coalescence has manifested its features …

  31. The double peak is not so easily produced in Hydro Linearized hydro + AdS CFT Hydro simulation Pure E depos. At such pT coalescence is expected to play a role … Can it affect the peak structure?! B.Betz,JPG35 Quark distribution function before space integration Pure p depos. UL=UT=0.3 is the collective velocity in the wave generated by the jet We used the Montecarlo simulations

  32. f dN / d p Results for mesons pT Meson Mesons at 2 GeV show a dN/df with 2 peaks even if they come from quarks at 1 GeV that have only 1 peak The position of the peaks is independent on pT like in experiments Quark V.G., Torrieri, Noronha,Gyulassy, NPA830(2009)

  33. Meson vs Baryon One may expect a difference between baryon and meson! In the experiment is not observed a difference But indeed coalescence generates a similar shape for both angle and width Angle and depth of the signal look very similar. Why one should expect the same angle? and especially The same depths of the peaks

  34. Why two peaks? Why similar shape for Baryon and Meson? meson Meson Considering only one side quark Why the peak shows up? The peak is created by the locality od coalescence. The two branches of the wave does not talk. Coalescence enhances the peak at each side and then summing up a dip appears. Why baryons=mesons? Correlation should increase, but at pT/3 angular correlations is weaker -> exact compensation and meson/baryon Mach shape are similar.

  35. Take home messages(please!) • Hadronization from 2-3 body phase SPACE (pT< 5-6 GeV): • dense medium decrease the role of the vacuum • massive quarks close in phase space • hadrons at pt comes from quarks pt/n (shift of soft scale) • Universal elliptic flow (dynamical quarks “visible”): • carried by quarks • enhanced by coalescence • consistent with h/s =0.1 ?! Result are robust against, uncertainty in resonance production, wave function, higher Fock states, energy conservation It’s not a question of twiggling parameters to get a better fit to the data, but there is a physical mechanism that generates relations between RAA (RCp) - v2 for light and heavy quarks + baryon/meson branches hard to get without a coalescence model R.J. Fries, V. Greco, P. Sorensen - Ann. Rev. Part. Sci. 58, 177 (2008)

  36. More Recent Perspectives • Heavy Quark interaction in QGP: • RAA and v2(pT) explained only if coalescence is present • Consistency between D and J/Y spectra: one underlying c • Role in h/s determination: • Transport Theory can entail a consistency between QNS and h/s =0.1-0.2 • Mach-Cone like peaks: • Hard to get but again coalescence can only help … and this is another consistency

  37. Open Issues • Role of Confinement - Vij(r,T) from lQCD (for heavy quarks) - String Fragm.+ Coalescence+ Indipendent Fragmentation • Statistical Model (RR,Miao-Gao…) - Probability of resonance formation (entropy-energy) • Implementation coupled to Transport equations: - role in of correlation in v2 scaling - 2-3 particle jet correlation

  38. Role of finite mass - 3D 2 schematic cases • Importance of 3D phase-space lowering pT • At low pT scaling can be largely broken • but dumped by the shape of v2(pT) • Lower mass lead to larger breaking • of the scaling due to coalescence • between quark with large q=p1-p2 realistic shape The observed scaling tells that the coalescing quarks have small relative momentum!

  39. Exercise: Entropy of a gas with g d.o.f Non-Relativistic No quantistic • g -> p (suppose mg =mH) - 70% decrease Pion gas out-of-equilibrium Gluon gas at equilibrium Volume expansion needed to compensate the decrease is much larger than in coalecence model 2) Only qq ->m - 28% decrease 3) Coalescence with r, w, K*, D(PRC68, 034904) - 16 % decrease

  40. RAA , v2 of single e – Jet Quenching q q S. Wicks et al., nucl-th/07010631(QM06) N. Armesto et al., PLB637(2006)362 • Radiative energy loss not sufficient • sQGP:non perturbative effect Main Challenge is the in-medium quark interaction lQCD resonant (bound) states persist for QQ and qq -> Qq (D-like) resonant scattering

  41. Effect of h/s on the hadronic phase

  42. Does the NJL chiral phase transition affect the elliptic flow of a fluid at fixed h/s? e-Print: arXiv:1001.2736 [hep-ph] - yesterday

  43. 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 Correlations cik Neglecting: Hadronic diffusion Gluons Close to the value used in GKL, PRC68 : Nq ~ 1200 ALCOR, PLB**: Nq ~ 1300 Recombination with all the quark converted into baryon and meson ( ) nonet mesons +octet & decuplet baryons

  44. Same Side Correlation at intermediate pt trigger Assoc. quenched Same away Trigger is a particle at 4 GeV < pTrig < 6 GeV Associated is a particle at 2 GeV < pT < pTrig Yield of correlated Hadrons respect to pp Away Side: quenching has di-jet structure Same Side: hadrons correlated like in jet framentation at the same pT where Reco manifest itself . Is this compatible?

  45. Correlations Any residual interaction in f(p) 2-parton correlation from jet-bulk interaction lead correlation in the coalescing hadrons Similar to effect on v2 c0 and f0 fixed to fit data Baryon trigger Meson trigger Coalescence+Fragmentation reproduce the relative strength with baryon and meson trigger Fries et al., PRL94 (2005) to be seen the assumed Cab is dynamical reproduceble at RHIC -> coupling to transport approach

  46. Baryon and Mesons spectra Miao et al., PRC76(07) - using the Bolzmann Collision approach protons pions Particles included -> agreement also On yields

  47. Leading Particle Effect Reservoir of partons modifies hadronization Quark-Antiquark Recombination in the Fragmentation Region • K.P. Das & R.C. Hwa: Phys. Lett. B68, 459 (1977): • Braaten, Jia, Mehen: Phys. Rev. Lett. 89, 122002 (2002) Sea quarks Recombination at XF = 0 • Rapp and Shuryak, Phys. Rev. D67, 074036 (2003) E791 - beam: - hard cc production; - c recombine with d valence from - -> D- enhancement beam =0 from LO fragmentation Similarly for p+/p-, K+/K- at ISR/Fermilab (late ‘70) In HIC the resorvoir is the thermal bulk!

  48. A drawback: for themal distrbution there is exact compensation between the shift in pT of coalescence and the enhancement of correlation with pT

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