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

2.  Relevance for :  the Heavy-Quark Sector   /s of sQGP  A role in the Mach Cones ?  Observation at RHIC  hadronization modified  R AA -R CP -V 2 for baryon and mesons Outline Intro to Basic Idea & Relevance for sQGP  Basic Theory of coalescence (phase –space)  coal. vs fragm. - application to RHIC  R AA – v 2 and B/M in the coalescence mechanism  Extensions from early realizations  Robustness and open issues  Formulation from Boltzmann collision integral

3. Surprises… In vacuum pp collisions: p/  ~ 0.3 Hadronization has been modified 1 10 T max ) PHENIX, PRL89(2003) Baryon/Mesons Protons appear not suppressed! Quenching Au+Au p+p  Jet quenching should affect both   suppression: evidence of jet quenching before fragmentation

4. Hadronization in Heavy-Ion Collisions 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 Parton spectrum H Baryon Meson Coal. Fragmentation V. Greco et al. / R.J. Fries et al., PRL 90(2003) Fragmentation:  energy needed to create quarks from vacuum  hadrons from higher p T  partons are already there $ to be close in phase space $  p h = n p T,, n = 2, 3 baryons from lower momenta (denser) Coalescence: ReCo pushes out soft physics by factors x2 and x3 !

5. Basic Theory Discard details of dynamics -> adiabatic approximation: instantaneous projection of initial state onto final cluster - Go in the  momentum frame - Neglect the transverse momentum - Neglect r,p correlations -> only p-space - direct production (no resonances)  M (r,q) Meson wave function All fairly good approximations At p T > 2 GeV/c x i light-cone momentum fraction Approximation in FMNB (Hwa-Yang) C M spin-isospin color factor fragmenting: P h = z p q, z<1 Recombining : X 1 P h +x 2 P h =P h Fries, QM’04 Fries-Nonaka-Muller-Bass, PRC68(03)

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

7. Phase-Space Coalescence ( GKL ) f H hadron Wigner function 3D-geometry with radial flow space-momentum correlation E T ~ 740 GeV T ~ 170 MeV  (r)  ~ 0.5 r/R  GeV  fm -3 dS/dy ~ 4800 Experiments lQCD T c like Hydro L/  T=170 MeV P. Levai et al., NPA698(02) quenched softhard Bulk matter consistent with hydro, experiments, lQCD Bulk matter consistent with hydro, experiments, lQCD  x =  p

8. Meson & Baryon Spectra 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 Au+Au @200AGeV (central)  Proton suppression hidden by coalescence! sh GKL FMNB ReCo dominates up to 4 (meson)  6(baryon) GeV/c; Fragmentation + energy loss takes over above.

9. Baryon/Meson ratio   TAMU FMNB Hwa-Yang Strange particles from a common quark flow

10. A Coalescence process carries with it another feature thanks to non-equilibrium x y z pxpx pypy c 2 s =dP/d   

11.  Mass-dependence of v 2 (p T ) suggests common transverse velocity field large  At higher p T v 2 for Baryon=Mesons in both - hydrodynamics - jet fragmentation  Again surprise Baryon ≠ Mesons : v 2 larger for Baryons Elliptic flow at intermediate p T

12. Coalescence carries another features … Enhancement of v 2 Coalescence scaling baryons mesons Molnar and Voloshin, PRL91 (2003)  Considering only momentum space  x - p correlation neglected  narrow wave function  collinear approximation  v 2 for baryon is larger and saturates at higher p T v 2q fitted from v 2  GKL  Quark number scaling! Again agreement with unexpected observation No free parameter !

13. Better scaling vs KE T /n q energy conservation Scaling widely confirmed for all species and centralities R. Lacey, PoS CFRNC2006:021,2006. e-Print: nucl-ex/0610029 Is the v 2 (p T ) needed by coalescence compatible with a fluid  /s ~ 0.1-0.2 ? But it also means that v 2q ~ v 2h /2

14. Motivation for a Transport approach Solved discretizing the space in  x, y   cells It is a 3+1D (viscous hydro 2+1D till now)  No gradient expansion, full calculation valid also at intermediate p T out of equilibrium  QNS  valid also at intermediate p T out of equilibrium  QNS  valid at high  /s  study the effect of the hadronic phase  include hadronization by coalescence+fragmentation  Extension to Bulk viscosity  (related also to chiral mass generation) Simulate a fluid at constant shear viscosity  =cell index in the r-space Time-Space dependent cross section evaluated locally (see also D. Molnar arXiV:0806.0026) Relativistic Kinetic theory Cascade code 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

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

16. R cp ~1 with large v 2 reverts Coalescence reverts the correlation between R AA & v 2 : both are enhanced This rules out other explanations: Baryon junctions, hydro+jets This effect is essential also for the study of charm quark interaction ! P.Sorensen R CP and v 2 Correlation:putting together observations!

17. Ok, but this is really too naive… !? 1)Resonances (included in GKL) 2)Finite width Wave function 3)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 & v 2  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 v 2 scaling Pratt-Pal PRC71, Molnar nucl-th/0408044, Greco-Ko nucl-th/0505061, Rapp-Ravagli PRC79 Less important at high p T Stability of Reco results respect uncertainties in their treatment high p T the problem suppressed by m/p T but even at low p T is not so drammatic

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

19. Dependence on wave function of v 2 scaling  p momentum width of w.f. Baryon-to-Meson breaking of the scaling Wavefunction+ Resonance decays Breaking :  increasing with  p  decreasing with p T

20. Higher Fock State Costituent quark picture is a good description of hadron PDF as Q 2 < 1 GeV 2 (higher Fock state are suppressed) B. Muller et al., PLB618(05) v 2 scaling is preserved Spectra are not affected (at least p T >> m ) Fock state, n = # partons s = # of sea partons For narrow w.f. limit Standard higher twist w.f

21. Entropy Conservation? Assuming hadronization linear with t during a mixed phase with the spectra of the static GKL model (    Energy is also not conserved ! 15% violation, No factor 2 : - resonances - mass of the particle - degeneracies  Entropy- Energy Conservation Entropy violation is also related to energy conservation and not to ReCo Greco, EPJ ST155(2008)

22. Transport approach to Coalescence->Energy Conservation Miao et al., PRC75(2007) Rapp-Ravagli, PLB655(2007)  Solve energy conservation (except  )  Clarify relation to statistical model  Keeps features of coalescence: - show a KET scaling of v 2 /n q - show a KET scaling of v 2 /n q - baryon/meson enhancement - baryon/meson enhancement Equilibrium solution  h >>  eq gives Production Absorption  meson Essential property: - Product f(p 1 )* f(p 2 ) of 2 distr. funct. - suppressed when p 1  p 2 is too large

23. r-p from Fokker Planck still preserve Quark Number Scaling Ravagli et al. PRC79 (2008)  Good quark number scaling except for too large Q value (<300 MeV) (similar to not too large width and or non zero quark mass)  KE T scaling down to low p T V 2 quark # Scaling with Energy Conservation Scattering for q,Q in QGP Including space-momentum correlation

24. What happens to heavy quarks?

25. G.D. Moore and D. Teaney, PRC70 (2005) nucl-th/0412346 Problematic relation of R AA and V 2 for heavy quarks Up-Scaling elastic scattering from pQCD Too low RAA or too low v 2 Coalescence modify v 2D  R AA correlation data 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. A(  )   2  (  ) Asakawa J/  Spectral function in lQCD & Resonances q-c “Im T” q-c “Im T” dominated by meson and diquark channel lQCD pQCD Opposite T-dependence of  Friction coefficient V(r) - lQCD

27. Impact of Hadronization for heavy quarks HQ scattering in QGP Langevin simulation in Hydro bulk Hadronization Coalescence + Fragmentation sQGP c,b D,B , D from resonant scattering according to lQCD V(r) Van Hees-Mannarelli-Greco-Rapp, PRL100 (2008) Improved R AA - V 2 correlation 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 Impact of hadronization

28. Regeneration is revealed in : - p t spectra - elliptic flow 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 … Greco, Ko, Rapp PLB595(2004) J  coal. No feed-down No direct contr. Suppression only v 2  from v 2D : measure of N coal /N INI Coalecence only p T - Quarkonia from regeneration are consistent with Open heavy flavor!?

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

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

32. Results for mesons Mesons at 2 GeV show a dN/d  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 p T like in experiments Meson p ddN  / Quark pTpT 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 Why one should expect the same angle? and especially The same depths of the peaks Angle and depth of the signal look very similar.

34. 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. Meson Why baryons=mesons? Correlation should increase, but at p T /3 angular correlations is weaker -> exact compensation and meson/baryon Mach shape are similar. Why two peaks? Why similar shape for Baryon and Meson? quark meson Considering only one side

35. Take home messages Take home messages (please!)  Hadronization from 2-3 body phase SPACE (p T < 5-6 GeV):  dense medium decrease the role of the vacuum  massive quarks close in phase space  hadrons at p t comes from quarks p t /n (shift of soft scale)  Universal elliptic flow (dynamical quarks “visible”):  carried by quarks  enhanced by coalescence  consistent with  /s =0.1 ?! R.J. Fries, V. Greco, P. Sorensen - Ann. Rev. Part. Sci. 58, 177 (2008) 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 R AA (R Cp ) - v 2 for light and heavy quarks + baryon/meson branches hard to get without a coalescence model

36. More Recent Perspectives More Recent Perspectives Mach-Cone like peaks  Mach-Cone like peaks:  Hard to get but again coalescence can only help … and this is another consistency Role in  /s determination:  Role in  /s determination:  Transport Theory can entail a consistency between QNS and  /s =0.1-0.2 Heavy Quark interaction in QGP:  Heavy Quark interaction in QGP:  R AA and v 2 (p T ) explained only if coalescence is present  Consistency between D and J/Y spectra: one underlying c

37. Open Issues  Role of Confinement - V ij (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 v 2 scaling - 2-3 particle jet correlation

38. Role of finite mass - 3D  Importance of 3D phase-space lowering p T  At low p T scaling can be largely broken but dumped by the shape of v 2 (p T )  Lower mass lead to larger breaking of the scaling due to coalescence between quark with large q=p 1 -p 2 2 schematic cases The observed scaling tells that the coalescing quarks have small relative momentum! realistic shape

39. Exercise: Entropy of a gas with g d.o.f Non-Relativistic No quantistic 1)g    suppose m g  m    70% decrease 3) Coalescence with    (PRC68, 034904) - 16 % decrease Gluon gas at equilibrium Pion gas out-of-equilibrium Volume expansion needed to compensate the decrease is much larger than in coalecence model 2) Only qq  m  28% decrease

40. N. Armesto et al., PLB637(2006)362S. Wicks et al., nucl-th/07010631(QM06) lQCD resonant (bound) states persist for QQ and qq -> Qq (D-like) resonant scattering lQCD resonant (bound) states persist for QQ and qq -> Qq (D-like) resonant scattering R AA, v 2 of single e – Jet Quenching  Radiative energy loss not sufficient  sQGP: non perturbative effect q q Main Challenge is the in-medium quark interaction

41. Effect of  /s on the hadronic phase

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

43. Bulk : Charge Fluctuations Recombination with all the quark converted into baryon and meson Correlations c ik Neglecting: Hadronic diffusion Gluons Close to the value used in GKL, PRC68 : N q ~ 1200 ALCOR, PLB**: N q ~ 1300 Statistical model N had at T c & from recombination N quark C. Nonaka et al., nucl-th/0501028 N had = 507 (635) N quark = 1125 (1377) ( ) nonet mesons +octet & decuplet baryons STAR, PRC68 (2003) 44905

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

45. Correlations Coalescence+Fragmentation reproduce the relative strength with baryon and meson trigger Any residual interaction in f(p) lead correlation in the coalescing hadrons Similar to effect on v2 to be seen the assumed C ab is dynamical reproduceble at RHIC -> coupling to transport approach Fries et al., PRL94 (2005) Meson trigger Baryon trigger 2-parton correlation from jet-bulk interaction c 0 and  0 fixed to fit data

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

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

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