Rene Bellwied (University of Houston) Wroclaw, Poland, May 19-21, 2011

1. Experimental evidence for color-neutral pre-hadronic states above the critical temperature at RHIC and LHC Rene Bellwied (University of Houston) Wroclaw, Poland, May 19-21, 2011 for more detail please see RB and C.Markert (PLB 691, 208 (2010))

2. 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 ? Not addressed by HEP because it is non-perturbative and can not be calculated Phenomenological approach: Fragmentation, Factorization 2/26

3. The formation time of hadrons • Can a hadron form inside the deconfined medium above Tc ? • 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) A parton traverses the medium and fragments outside A parton fragments inside the medium A parton converts into a pre-hadronic state or a quasi-particle which traverses the medium and fragments outside 3/26

4. The treatment of formation time • Formation time is largely ignored in heavy ion collisions. • Based on the simple Lorentz boost argument, which is insufficient for in-medium fragmentation, it was concluded early on that only colored partons will traverse the system and only fragment outside the medium i.e. in vacuum. • All energy loss models (ASW, AMY, GLV) are based on purely partonic energy loss, either collisional or radiative energy loss. • Greiner, Gallmeister, Cassing (Phys. Rev. C67, 044905 (2003)) suggested early hadronization and hadronic energy loss. 4/26

5. The principle: a question of 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). 5/26

6. Schematic Modeling of hadronization e.g. Lund String Model: breaking the color string from the struck parton to the target remnant (constituent length) Energy conservation Lorentz boost Eq = struck quark energy kstr = string tension 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). 6/26

7. Combining inside-out and outside-in in light cone variables Inside-out cascade (boost) to ~ 1 fm/c : proper formation time in hadron rest frame E : energy of hadron m: mass of hadron E/m = g • high energy particles are produced later • heavy mass particles are produced earlier C. Markert, RB, I. Vitev (PLB 669, 92 (2008)) Outside-in Cascade (pre-hadron formation) large z (=ph / pq) = leading particle  shortens formation time 7/26

8. Evolution of a RHIC heavy ion collision(as a function of temperature and time) Model: lQCD SHMBlastwave Effect: hadronization chemical f.o. kinetic f.o. Freeze-out surface: TcritTchTkin(X,W) Tkin(p,k,p,L) Temperature (MeV): 190165 160 80 Expansion velocity (c): b=0.45 b=0.6 Hydro condition ? Tinit 370 MeV References: Lattice QCD: hep-lat/0608013 arXiv:0903.4155 Statistical Hadronization: hep-ph/0511094 nucl-th/0511071 Blastwave: nucl-ex/0307024 arXiv:0808.2041 partons hadrons 0QGP Experiment: time: ~5 fm/c~4 fm/c (STAR, PRL 97:132301,(2006)) 8/26

9. Analytic approach to proper times • What is the proper t0 ? • t0 requires thermalization which is an open issue at RHIC and LHC. Simple collision time tc ~ 2RA/g is definitely too short. • General approach t0 ~ 1/<pT> • Leads to t0(RHIC)=0.44 fm/c and t0(LHC)=0.23 fm/c (with <pT> = 450 and 850 MeV/c respectively) • What is the proper QGP lifetime ? • Upper limit based on longitudinal Bjorken expansion • tQGP = t0 (T0/Tc)3 with T0(t0,RHIC)= 435 MeV and T0(t0, LHC)= 713 MeV and Tc = 180 MeV (see pre-print for more detail) • tQGP (RHIC) = 6.2 fm/c , tQGP (LHC) = 14 fm/c • RHIC result slightly higher than data driven partonic lifetime estimate based on HBT and resonances (tQGP (RHIC) ~ 5 fm/c) 9/26

10. Formation Time of Hadrons in RHIC / LHC QGP(C. Markert, RB, I. Vitev, PLB 669, 92 (2008)) RHIC LHC 10/26

11. What did we really calculate ? • Brodsky & Mueller (PLB 206, 685 (1988)): • First time distinction between tp (production time) and tf (formation time). Production time determines production of co-moving constituent quarks (coherence length). • Since all quark configurations are possible the order parameter becomes the mass difference between all possible states of the same quark configuration. • Kopeliovich (e.g. arXiv:1009.1162): approximate the order parameter by the mass difference between the ground state and the first excited state (resonant state), e.g. for the pion this time is considerably shorter than the time when taking the final hadron mass. • RB & CM: taking the final hadron mass can approximate the formation time of the final hadron wavefunction. 11/26

12. Pre-hadron formation time (p) A. Accardi, arXiv:0808.0656: A quark q created in a hard collision turns into a colored pre-hadron, which subsequently neutralizes its color and collapses on the wave function of the observed hadron h B) RB & CM: Using the final hadron mass will increase the formation time since the final mass is smaller than the difference between the ground and excited states. 12/26

13. Quasi-particle or pre-hadron ? Is their a difference ? • 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) • 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 ?) 13/26

14. A hybrid model (Cassing & Bratkovskaya, PRC 78, 034919 (2008)) • Partons dress up throughout the partonic phase = quasi-particles (PHSD = parton-hadron string dynamics) • At hadronization very massive pre-hadronic resonances form through recombination of dressed (constituent) quarks = color neutral states (DQPM = dynamic quasi-particle model) • Resonances subsequently decay into ground state mesons and octet baryons • Color neutrality is achieved LATE ! 14/26

15. Lattice QCD inspired quasi-particle mass calculations Levai & Heinz, PRC 57, 1879 (1998) Ratti, Greco et al., arXiv:1103.5611 Slight difference in temperature dependence of the quasi-particle masses for two lattice QCD actions Important is the general trend just above Tc. Quasi-particle masses increase and exceed the constituent quark masses. 15/26

16. Does this make sense near the QCD phase transition ?A re-interpretation of the Polyakov Loop calculation in lattice QCD 16/26

17. A key concept for experimental signatures: Color transparency (P. Jain et al., Phys. Rep. 271, 67 (1996)) • Color transparency reduces (or eliminates) the interaction probability between color-neutral and colored objects. • In the strictest sense only applicable to point-like configurations, i.e. directly produced color-neutral states from higher twist diagrams (Brodsky, Sickles). • Kopeliovich showed that early produced color-neutral states (i.e. pre-hadrons) also have reduced interaction cross section. 17/26

18. Experimental Signatures • Reduction in pT 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, see next talk…) • Reduction of v2 at high pT due to early formation and color transparency (masked by loss of collectivity at high pT) • Reduction in energy loss due to color transparency of color-neutral pre-hadrons in medium (evidence at RHIC and LHC) 18/26

19. Recombination in medium Fragmentation in vacuum B/M ratio in AA can be attributed to recombination or to color transparency (Sickles & Brodsky, PLB 668 (2008)) A directly (or early) produced proton (color-neutral) will undergo almost no rescattering, thus its high pT yield is enhanced relative to later formed mesons. 19/26

20. Nuclear suppression patterns in HI collisions become more complex Surprising particle dependence in RAA (hadro-chemistry or flavor change) ? This is not simple partonic energy loss. Early hadronization or enhanced species dependent gluon-splitting factors (Sapeta & Wiedemann) S&W use a parameter in their splitting probability that depends on the final hadron mass (ad-hoc parametrization) 20/26

21. Predictions for energy loss RB & C. Markert (PLB 691, 208, 2010)) 21/26

22. Comparison to preliminary STAR data STAR preliminary pT (GeV/c) 22/26

23. The latest evidence: RAA at the LHC ALICE, PLB 696, 30 (2011) Shadowing & quenching (P.Levai, arXiv:1104.4162) RAA is not constant at high pT. Extreme shadowing and eloss pathlength dependence ? 23/26

24. An explanation based on color-neutral states and color transparencyKopeliovich et al., PRC83,021901(2011) • 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. 24/26

25. Summary • Hadronization in QCD is highly relevant to understand the evolution of the initial deconfined, chirally symmetric QCD phase. • Studies of pT, width, mass broadening, nuclear suppression, yields and ratios of identified particles and resonances in the fragmentation/recombination region of their spectrum gives us a unique tool to answer these many decade old questions: • Is there local parton-hadron duality ? • Is hadronization due to recombination or fragmentation ? • Do color neutral objects form early and are they less likely to interact with the colored medium ? • When does the hadronic wave function (or mass) form ? • There is evidence at high pT that energy loss in medium is not featureless even for light quark particles. 25/26

26. Measure signatures inside & outside of jet cones at sufficiently high fractional momentum (pT = 3-10 GeV/c): • baryon / meson ratios • rare particle species (s,c,b) • resonances • pT broadening • energy loss 26/26