Color-neutral bound states above the QCD transition from equilibrium and non-equilibrium processes Rene Bellwied (University of Houston) Rene Bellwied (University of Houston) in collaboration with Equilibrium: M. Cristoforetti (Trento), C. Ratti (U Torino) Non-equilibrium: C. Markert (UT Austin), I. Vitev (LANL)

Are there bound states above T c ? Survival or formation – a question of perspective The deconfinement order parameter in lQCD: Polyakov loop 2/28 Bazavov et al., arXiv: Low energy collisions (AGS, SPS, RHIC scan, FAIR): survival of resonant states High energy collisions (RHIC, LHC): formation of pre-hadronic states survival formation

Are there bound states above T c ? A long standing question in the literature Survival: Rapp et al. (arXiv: ) – chiral symmetry restoration signatures in the transition region (mass shifts, width broadening, Brown-Rho scaling, etc. of surviving resonant states in particular of heavy quarks) 3/28 Formation: Shuryak (PRD 70 (2004)054507) – colored bound states. Leads to phase diagram with differing quark condensates

The fundamental questions How do hadrons form ? ◦ Parton fragmentation or string fragmentation or recombination ◦ An early color neutral object (pre-hadron) or a long-lived colored object (quasi-particle or constituent quark) When do hadrons form ? ◦ Inside the deconfined medium or in the vacuum ? Why investigate it now ? 1.) more precise lattice QCD calculations for the case of formation out of equilibrium 2.) a better understanding of fragmentation (non-equilibrium formation) 3.) better data from RHIC and LHC to follow formation as a function of time, temperature and particle momentum 4/28

Why distinguish between equilibrium and non-equilibrium ? There is plenty of evidence for two components in the particle spectra at RHIC and LHC. Breakdown of hydrodynamics at high pT, power law at high pT Two component model: soft (bulk, equil.) / hard (fragmentation, non-equil,) Kharzeev / Nardi scaling for yield: Levi-Tsallis fit for spectra (exponential + power-law): 5/28

Is equilibrium and non-equilibrium production equally relevant ? Fragmentation will populate full spectrum Thus non-equilibrium production surprisingly sizeable: 30% at RHIC, based on untriggered correlation measurements (e.g. T.A. Trainor ( Phys.Rev.C80:044901,2009) Up to 50% at the LHC e.g. Eskola et al. (hep-ph/ ) 6/28

How to approach the problem ? Equilibrium Statistical Hadronization Model (SHM) Hadronic resonance gas (HRG) Lattice QCD (lQCD) 7/28 Recombination PNJL model Non - Equilibrium Fragmentation Formation time Recent Work: Equilibrium: RB, M. Cristoforetti, C. Ratti – in preparation Non-equilibrium: RB, C. Markert, Phys. Lett. B691, 208 (2010) C. Markert, RB, I. Vitev, Phys. Lett. B669, 92 (2008)

The non-equilibrium case a short re-cap of my talk from the Hadronization Workshop in Sardinia (2010) 8/28

The formation time of hadrons (for parton fragmentation in medium) Can a hadron form inside the deconfined medium above T c ? Three Scenarios: Is the energy loss in medium affected by the formation of the hadronic state ? Are the properties of the hadronic state affected by the formation in medium ? Signatures: any early probe which is sensitive to the medium (e.g. energy loss or v2) 9/28 A parton traverses the medium and fragments outside A parton converts into a pre-hadronic state or a quasi-particle which traverses the medium and fragments outside A parton fragments inside the medium

The treatment of formation time There is per-se no reason to believe that, in heavy ion collisions, a process such as fragmentation, which does not thermalize with the surrounding medium, would take more or less time than in vacuum. One could use in-vacuum formation time. BUT there are two aspects to consider in-medium: ◦ Lorentz boost : the higher the energy the longer the formation time (based on Heisenberg’s uncertainty principle, true for string fragmentation) ◦ Energy conservation : the higher the fractional momentum the shorter the formation time, since partons lose energy through bremsstrahlung in medium (true for parton fragmentation in medium). 10/28

Schematic Modeling of Hadronzation Inside-out cascade (boost)  o ~ 1 fm/c : proper formation time in hadron rest frame E : energy of hadron m: mass of hadron E/m =   high energy particles are produced later   heavy mass particles are produced earlier Outside-in Cascade (pre-hadron formation) large z (=ph / pq) = leading particle  shortens formation time C. Markert, RB, I. Vitev (PLB 669, 92 (2008)) 11/28 Bjorken (1976): The higher the energy and the lighter the final state, the later the hadron will form (inside-outside cascade) Kopeliovich (1979): A high z particle has to form early otherwise the initial parton loses too much energy (outside-inside cascade).

Formation Time of Hadrons in RHIC / LHC QGP (C. Mar kert, RB, I. Vitev, PLB 669, 92 (2008)) RHIC LHC 12/28

A quasi-particle is a colored object, i.e. a dressed up quark which has attained a thermal mass that can potentially exceed the final state hadron mass and then decay into the hadronic state. (e.g. Cassing et al. (DQPM model) or Ratti et al. (lattice QCD)) A pre-hadron is a color neutral object that approaches the final hadronic wave function during its evolution, i.e. quark content fixed but not all hadron properties fixed (e.g. Kopeliovich or Accardi or RB/CM) A colored object will continue to interact and not develop a hadronic wave function early on (constituent quark or quasi-particle) A color-neutral object will have a reduced size and interaction cross section (color transparency) and develop wave function properties early Only a color neutral state can exhibit hadronic features (e.g. can pre- resonance decay prior to pion hadronization ?) Quasi-particle or pre-hadron ? Is their a difference ? 13/28

The equilibrium case Recent work with M. Cristoforetti (Trento) & C. Ratti (Torino) 14/28

Evolution of the phase transition as a function of finer lattice spacing smaller quark masses (the cross-over becomes smoother = a longer mixed phase ?) 15/28 new old

Lattice QCD inspired quasi-particle mass calculations (Evidence for massive states above T c ) Levai & Heinz, PRC 57, 1879 (1998) Ratti, Greco et al., arXiv: Slight difference in temperature dependence of the quasi-particle masses for two lattice QCD actions Important is the general trend just above T c. Quasi-particle masses increase and exceed the constituent quark masses. 16/28

But could there be color-neutral bound states ? A re-interpretation of the Polyakov Loop in lattice QCD (measure of deconfinement) 17/28

An interpretation pushed early on in a slightly different variation (Shuryak & Zahed, hep-ph/ ) 18/28 Bound states above T c Due to exclusion of color-neutral states above T c by early lattice calculations, the authors focused on colored, mostly gluonic, bound states

New lattice results: diagonal and non-diagonal correlators in limited T-range above T c (Ratti et al., QM 2011) 19/28 diagonal correlators non-diagonal correlators

Recent work: how much of this is due to fluctuations in the deconfined medium rather than bound states Comparison of lattice to PNJL (RB, M.Cristoforetti, C.Ratti) 20/28 PNJL variations PNJL-MF: pure mean field calculation PNJL-PL: mean field plus Polyakov loop fluctuations PNJL-MC: mean field plus all fluctuations (incl. chiral and Kaon condensate fluctuations) Conclusion: even the inclusion of all possible flucutations is not sufficient to describe lattice data above Tc. There has to be a contribution from bound states

Can we estimate the contribution of bound states above the critical temperature ? 21/28 The ratio between PNJL and lattice results tells us the percentage of bound state in the QGP mixed phase It agrees with the lattice continuum estimate for the Polyakov loop. ~50% bound states at 1.5 Tc ! L ren

Properties of bound states above T c : Flavor dependence even in the light sector 22/28 The heavier the quark the longer the mixed phase More strange bound states than light bound states above T c ?

Properties of bound states above T c : Baryon-meson dependence in correlator 23/28 Upswing in lattice correlator shows that baryon contribution rises with T, but the correlator never turns positive -> the contribution of bound states above T c must be predominantly of mesonic nature until final deconfinement C. Ratti, Hadronic resonance gas (HRG) calculation: Baryonic bound states dominate at T>190 MeV.

Experimental Signatures Reduction in p T broadening of final state due to color transparency in medium (verified in HERMES results) Medium modification of early produced resonances due to chiral restoration in medium (project at LHC) Reduction of v2 at high p T due to early formation and color transparency (masked by loss of collectivity at high p T ) Reduction in energy loss due to color transparency of color-neutral pre- hadrons in medium (evidence at RHIC and LHC) 24/28

Predictions for energy loss RB & C. Markert (PLB 691, 208, 2010)) 25/28

Flavor dependence at the LHC 26/28 QM 2011: Simone Schuchmann, Harry Appelshaeuser (ALICE) Data can be described with differing formation time for baryons and mesons, if one assumes rather short existence of pre-hadron in mixed phase (late formation). (CM & RB, 2011) Alternative: recombination

The latest evidence: R AA at the LHC 27/28 Data: ALICE, PLB 696, 30 (2011) An explanation based on color-neutral states and color transpareny The color-neutral state (in this case labeled color dipole) will form the earlier the higher the fractional momentum. No distinction between pre-hadrons of different flavor. All charged hadrons are based on the same color dipoles which traverse the medium and exhibit color transparency. Alternative: strong shadowing Theory: Kopeliovich et al., PRC83, (2011)

Summary 28/28 There is evidence for flavor and mass dependent color-neutral bound state formation in the medium above the QCD phase transition based on lattice QCD and fragmentation studies. A comparison of lattice QCD to HRG and PNJL calculations allows us to quantify the relative abundance of the confined and deconfined states in the equilibrated mixed phase around the critical temperature as a function of T. Experimental studies of p T, width, mass broadening, nuclear suppression, yields and ratios of identified particles and resonances give us a unique tool to answer fundamental questions of hadron formation.