V. Greco Universita’ di Catania, Italy INFN-LNS Zimanyi 75 Memorial, July 2007 – Budapest (Hungary) Light and heavy quark coalescence In Heavy-ion collisions ? Work done in collaboration with Van Hees, Ko, Levai, Rapp

First proceedings on QGP I looked at… “In the ALCOR model we assume that just before the hadronization the dense matter can be described as a mixture of dressed up, massive quarks and antiquarks. The effetive mass of the gluons at this point is much larger than that of the quarks [9], consequently the gluon fission into quark- antiquark pairs is enhanced and massive gluons disappear from the mixture.” [9] Heinz & Levai, PRC57 Before instead I was working on RMFT

 From RHIC to LHC (new QGP phase)?!  Similar R AA & v 2 proof of Qq resonances in the RHIC-QGP  presence of heavy-light Qq resonances (lQCD)  Heavy quark thermalization  R AA –v 2 correlation of single e  link J/Y – D : one underlying HQ distribution Outline Hadronization mechanism & QGP structure  Modification of hadronization mechanism  coalescence + fragmentation ( R AA &v 2 Bar. – Mes. )  Robustness – development s - open issues Relevance of Coalescence in the Heavy-Quark sector Light Hadrons and intermediate p T

Nuclear Modification Factor In-medium Non-abelian energy-loss Strong (Flat) suppression explained by jet quenching Proton not suppressed ?! Strong (Flat) suppression explained by jet quenching Proton not suppressed ?!

Surprises… In the vacuum p/  due to Jet fragmentation Hadronization has been modified p T < 4-6GeV !? p T < 4-6GeV !? PHENIX, PRL89(2003) Baryon/Mesons Parton spectrum H Use medium and not vacuum More easy to produce baryons Greco, Ko, Levai, PRL 90 –PRC68 Coalescence Baryon Meson Coal. Fragmentation Au+Au p+p

Phase-Space Coalescence f q invariant parton distribution function  thermal with radial flow (  =0.5r/R)  quenched minijets (GLV- L/ = 3.5) f H hadron Wigner function  x =  p E T ~ 730 GeV T ~ 170 MeV  (r)  ~ 0.5 r/R  GeV  fm -3 dS/dy ~ D geometry with radial flow space-momentum correlation Bulk matter consistent with hydro, experiments,  c Bulk matter consistent with hydro, experiments,  c  just overlap of f q with wave function L/  T=170 MeV P. Levai et al., NPA698(02) quenched softhard

Baryons vs Meson   OREGON TAMUDUKE TAMU v 2q fitted from v 2 

Meson & Baryon Spectra Greco-Ko-Levai, PRL90 (03) PRC68(03) R. Fries et al., PRL90(03) PRC68(03)44902 Hwa and Yang, PRC66(02) (central)  Proton suppression hidden by coalescence! sh ReCo dominates up to 4  6 GeV/c; fragmentation and energy loss takes over above. Fries et al., PRC68 

x y z A message from the early stage Enhancement of v 2 Coalescence scaling baryons mesons Molnar and Voloshin, PRL91 (2003)  n q - not a mass effect  Most of flow is partonic PHENIX, PRL (07) x - p correlation neglected narrow wave function v 2 develops t<5fm Hydro & cascade x-p correlation in Greco-Ko-Levai still small scaling violation

Ok, but this is really too naive… (!?) 1)Resonances 2)Wave function finite width 3)Gluons  ALCOR, TAMU-coalescence : mass suppressed, splitting, quark dressing  Higher-Fock state, Fries-Muller-Bass, PLB618 (05) 4) Energy Conservation  not large 17% in PRC68, resonances decay & v 2  Ravagli-Rapp arXiv: for v 2 (KE T ) 5)Entropy Conservation  15% like energy – Dynamical coalescence V(r,T) 6) Relation to jet-like correlations Fries et al.,PRL94 but need of transport description 7) Space-momentum correlations affect v 2 scaling (Pratt-Pal PRC71, Molnar nucl-th/ , Greco-Ko nucl-th/ ) (At LHC they will still be so nice ?!) already included Greco-Ko-Levai, PRC68 & 70 (less important at high p T ) high p T no problem … but at lower p T is not so drammatic

Effect of Resonances & wave function K, , p … v 2 not affected by resonances!  coal. moved towards  data Greco-Ko, PRC 70 (03) w.f. + resonance decay K & p *  from

 On v 2 it is mainly a shift in p t ->KE T  v 2 pions from rho decay (Greco-Ko-Levai, PRC68&70)  Q value effect in a Boltzmann approach (Ravagli-Rapp, arXiv: [hep-ph] ) Greco-Ko-Levai, PRC68 But, the energy is not conserved ! 15% violation, No factor 2 : - resonances - mass of the particle - degeneracies About Energy & Entropy … Dynamical coalescence with interaction effects can conserve the entropy …  Entropy- Energy Conservation

1) Dynamical coalescence ( no sudden f.o. - Molnar-QM05 ) 2)Where is confinement ? V(r,T) (beyond sudden approx.) especially for heavy quarks - lQCD 3) How to go from thermal to chiral masses? Although thermal quark mass does not breal chiral Symmetry and similar magnitude of both quantities near T c may facilitate the formation of hadrons from 2- and 3-quark clusters ( Heinz and Levai, PRC57). 4) Quasiparticle with spectral function quark mass distribution (Zimanyi-Birò-Levai, JPG31 (05) 771)  good p,  specra and ratio Deeper questions… and difficult answers

Take home messages from the light sector  Hadronization from 2-3 body phase SPACE (p T < 5-6 GeV):  dense medium decrease vacuum role  massive quarks close in phase space  hadrons at p t comes from quarks p t /n (change of soft scale)  Universal elliptic flow (dynamical quarks “visible”):  carried by quarks  enhanced by coalescence What happens to heavy quarks? Fries, Greco, Lacey, Sorensen - Ann. Rev. Part. Sci. (2008)

Some years ago… V 2q from , p,  v 2D 5% no c interaction but V 2 of electrons Greco-Ko-Rapp, PLB595 (04) 202 S. Kelly,QM04 Flow mass effect

N. Armesto et al., PLB637(2006)362S. Wicks et al.,nucl-th/ (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 -pQCD  Radiative energy loss not sufficient  sQGP: non perturbative effect q q

A(  )   2  (  ) Asakawa J/  J/  ( p  0 ) disappears between 1.62T c and 1.70T c “Light”-Quark Resonances 1.4T c [ Asakawa+ Hatsuda ’03 ] Spectral function in lQCD Similar from Potential model for J/  Mannarelli, Rapp - PRC72 (Bruckner-like) Alberico, Beraudo, De Pace - PRD 72 & 75 Petrecsky,Mocsy,Wong….

 t eq down to 5 fm/c at RHIC ! Open-Charm Resonances in QGP effective model with pseudo/scalar + axial/vector “D-like” mesons [chiral + HQ symmetry] ISOTROPIC cross section ISOTROPIC more microscopic from lQCD potential+many-body [Mannarelli et al.,in preparation] Ok, but can it describe R AA and v 2 ? with dimensional regularization or form factors

The model Hard production PYTHIA (PDF’s + pQCD ) HQ scattering in QGP Langevin simulation in Hydro bulk Hadronization Coalescence + Fragmentation Semileptonic decay R AA & v 2 of “non-photonic” e sQGP c,b quarks K e e c,b D,B

Charm reaching thermalization?! Therm+Flow Pythia

Reson. pQCD Single-Electron v 2 and R AA at RHIC f q from , K Greco,Ko,Levai - PRL90 coalescence + fragment. resonant scattering more effective for R AA – v 2 correlation coalescence increases both R AA and v 2 (anti-correlation) resonant scattering more effective for R AA – v 2 correlation coalescence increases both R AA and v 2 (anti-correlation) Hees, Greco, Rapp - PRC73 Uncertainty: -better estimate of B/C contribution Improvements: - include radiative E-loss - resonances from lQCD – potential model - no-sudden coalescence (full transport) Uncertainty: -better estimate of B/C contribution Improvements: - include radiative E-loss - resonances from lQCD – potential model - no-sudden coalescence (full transport)

Regeneration is revealed in : - p t spectra - elliptic flow Quarkonium  Heavy-Quark  Till now we have looked only at J/  yield, but thanks to such a strong collective dynamics … Greco, Ko, Rapp PLB595(2004) J  coal. No feed-down No direct contr. p T - Quarkonia from regeneration consistent with Open!? Suppression only v 2Y from v 2D : measure of N coal /N INI Coalecence only T diss (p T ) decrease – AdS Liu et al. hep-ph/

From RHIC to LHC? For min. bias. Hydro bulk dN/dy=1100 T init = 3 T c Radial flow  max =0.68 V 2q light quark =7.5 % (hydro or numerology) v 2q (p T ) from a cascade [VG, Colonna, Ferini, Di Toro] Resonances off T>2T c

From RHIC to LHC - R AA RHICLHC  Suppression: R AA similar at RHIC and LHC!  Harder initial spectra at LHC  Resonance ineffective (“melted” T>2T c ) at early stage! bottom charm bottom

From RHIC to LHC – v 2 electrons  v 2 similar at RHIC and LHC!  Resonance effective when anisotropy is reduced  Strong drag with the bulk flow at later stage!  v 2 slightly higher at low p t RHICLHC from D only ALICE Warning! Radiative energy loss to be included!

Summary  Coalescence from a bulk consistent with exp. and hydro  Yields, ratios, D-fluctuations  R AA, R cp,V 2 /n q vs p T  Beyond naïve coalescence -> better data description  3D, resonances, wave function, Fock states, energy conservation  R AA - v 2e anti-correlation for HQ entails: - presence of Q-q resonances (lQCD)  Similar R AA & v 2 at RHIC- LHC: - if from RHIC to LHC a new QGP phase is created !  Consistency of D and J/  with one underlying distribution ?!  better insight into coalescence at low p T – V(r,T) 2-3 body phase-space behind hadronization Relevance of Coalescence in the Heavy-Quark sector

Back up slides

Baryon contamination due to coalescence … Contamination of Lc in single e : enhance v 2e : v 2  c > v 2D enahencement modest + BRe 4.5% but if one can verify those prediction … Heavy-Flavor and jet quenching- Workshop, Padova P. Soresen, nucl-ex/ G. Martinez-Garcia et al., hep-ph/ Apparent reduction if  c /D ~1 consistent with RHIC data (pt~2-4 GeV) coal. coal.+ fragm.  = 0.75 GeV

Thermalization w “D”-Mesons pQCD “D” QGP- RHIC Isotropic angular distribution s res essential for thermalization Transport approximated Fokker-Plank equation Background not affected by heavy quarks What is the R AA and v 2 ? Cross sectionEquilibration time

Heavy-Flavor Baseline Spectra at RHIC Single-Electron Decays D-Mesons bottom crossing at 5GeV !? strategy: fix charm with D-mesons, adjust bottom in e ± -spectra

Improve treatment of fluctuations (not Gaussian) Include hadronization: coal+ fragmentation I. Vitev, A. Adil, H. van Hees, hep-ph/ Inclusion of radiative E-loss w/o gluon radiation

R AA & v 2 for D/B mesons at LHC R AA & v 2 for D/B mesons at LHC  D and B via coalescence+ fragmentation!  coalescence leads to increase both R AA and v 2  resonant scattering factor 3 in v 2

What happens at lower energy p + /  increase by 20% p  /  decrease slight decrease Greco,Ko, Vitev - PRC71 Without changing any coalescence parameter! Balance between fragmentation (w quenching) and coalescence Uncertainties: amount of quenching, bulk properties (E T,  b,..), p fragmentation function

What happens at higher energy - LHC? Fries, Muller, EPJ C34:S279 (2004). Similar trend for MICOR + pQCD(quenched) P. Levai - ALICE Week- February 2007 Uncertainties: - radial flow (  = ) - jet quenching What about the v 2 ? we will see the scaling? r-p correlation will be so nice at LHC?

Charm reaching thermalization? Shadowing not included yet! Spectra same parameter of PPR-ALICE Therm+Flow Pythia  LHC spectra considerably harder !  At Tc charm nearly thermalized  Resonances switched-off above 2 T c