The formation of hadrons inside the deconfined matter at RHIC & LHC

1. The formation of hadrons inside the deconfined matter at RHIC & LHC Rene Bellwied Wayne State University Christina Markert University of Texas at Austin Phys. Lett. B669, 92 (2008) = arXiv:0807.1509 (w. Ivan Vitev) Phys. Lett. B691, 208 (2010) = arXiv:1005.5416

2. The fundamental questions How do hadrons form ? Fragmentation or recombination An early color neutral object (pre-hadron) or a long-lived colored object (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 Fragmentation, Factorization

3. The ‘purposefully ignorant’ 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. This makes the energy loss calculation much easier. 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. The principle: a question of time There is per-se no reason to believe that a process such as fragmentation, which does not thermalize with the system (i.e. the surrounding medium), would take more or less time in-medium than in vacuum. (Almost true, see below). One could use in-vacuum formation time. Two aspects in-medium: Lorentz boost: the higher the energy the longer the formation time Energy conservation: the higher the fractional momentum the shorter the formation time (since partons lose energy through bremsstrahlung in medium). But the early formed hadron can not have a fully developed wave function because of the uncertainty principle = pre-hadron (quark content fixed but not all properties fixed)

5. The concept of formation time • In string fragmentation as well as general QM considerations (e.g. Heisenberg’s uncertainty principle) the formation time of a hadron is given by: • This leads to the principle known as ‘inside-outside cascade’ (Bjorken (1976))

6. Modeling of hadronization Breaking the color string from the struck parton to the target remnant (constituent length) Lund String Model: Energy conservation Lorentz boost Eq = struck quark energy kstr = string tension Kopeliovich: the Lorentz boost in formation is offset by energy conservation in fragmentation. A high z particle has to form early otherwise the initial parton loses too much energy (outside-inside cascade).

7. Combining inside-out and outside-in in light cone variables Inside-outside 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-inside Cascade (pre-hadron formation) large z (=ph / pq) = resonance is leading particle in jet  shortens formation time 7

8. Statistical evolution of relativistic heavy ion collisions 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: b=0.45 b=0.6 Hydro condition ? partons References: Lattice QCD: hep-lat/0608013 arXiv:0903.4155 Statistical Hadronization: hep-ph/0511094 nucl-th/0511071 Blastwave: nucl-ex/0307024 arXiv:0808.2041 hadrons time: ~4 fm/c~4 fm/c (nucl-ex/0604019) Fast equilibration measurements: strangeness enhancement & v2

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)

10. Formation Time of Hadrons in RHIC / LHC QGP(C. Markert, RB, I. Vitev, 0807.1509) RHIC LHC 10

11. Two questions of increasing complexity – (1) What sets the scale in our light cone variable approach ? The mass. Which mass ? Final hadron mass

12. Brodsky and Mueller (1988) First time distinction between tp (production time) and tf (formation time). Production time determines production of co-moving constituent quarks. Since all quark configurations are possible the order parameter becomes the mass difference between all possible states of the same quark configuration. Kopeliovich: approximate by the mass difference between the ground state and the 1st 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.

13. Pre-hadron formation: A. Accardi, 0808.0656 parton pre-hadron hadron • dressed parton has inelastic cross section comparable to hadronic one = pre-hadron (h*). • undressed quark lifetime (tP), color neutralization time (tcn) • sometimes to simplify tP = tcn, hadron formation time (th)

14. The difference in our approach 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.

15. Is the in-medium state colored or color neutral ? Kopeliovich, Accardi: color neutral DOF Cassing et al.: colored DOF A colored object will continue to interact and not develop a hadronic wave function early on (constituent quark) 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 ?) Two questions of increasing complexity – (II)

16. Alternate: Cassing et al., 0808.0022 Partons dress up throughout the partonic phase (PHSD = parton-hadron string dynamics) At hadronization very massive pre-hadronic resonances form through recombination of dressed (constituent) quarks = quasi-particles (DQPM = dynamic quasi-particle model) Resonances subsequently decay into ground state mesons and octet baryons.

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

18. Color transparency (P. Jain et al., Phys. Rep. 271, 67 (1996)) • An important concept in our paper, since it 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 objects (i.e. coalescing constituent quarks) also have reduced interaction cross section.

19. Experimental Signatures Reduction in pT broadening due to color transparency in medium Reduction in energy loss due to color transparency in medium of color-neutral pre-hadrons Medium modification of early produced resonances due to chiral restoration

20. pT broadening as signature in DIS Difference in <pt> between nuclear and elementary collisions pT broadening occurs when partons interact, pre-hadron would have little interaction cross section, thus no pT broadening If pre-hadron is formed in nucleus: (exponent = 0.5 from HERMES analysis but also close to LUND model prediction) similar to Cronin effect If quark fragments outside then there is no dependence on z or n

21. HERMES results on <pT> broadening

22. Two distinctly different hadronization processes (both postulated in 1977) More likely in vacuum ? More likely in medium ? • 22

23. 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.

24. 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)

25. Our predictions for energy loss

26. STAR preliminary pT (GeV/c)

27. Additional measurement in nDIS Multiplicity ratio: Nh = hadron multiplicity in (n,Q2) bin Ne = inclusively scattered lepton in same bin with z = hadron fractional energy n = virtual photon energy pt2 = hadron transverse momentum Q2 = lepton four-momentum squared In dense partonic medium either • Short production time • and in-medium • hadronization (l > 0) or • Long lived quarks with • lose energy and fragment • outside the medium (l < 0)

28. side 1 near away side 2 Resonances: measure vacuum and medium hadronization in same event • See arXiv: 0807.1509: in medium-modification inside/outside jets (either jet cone or quadrant analysis)

29. Example: Hadron – f(1020) correlation in Cu+Cu Hadron trigger pT > 3 GeV (2.5M) f(1020) asso pT =1-2 GeV STAR preliminary Width: 6.0±0.7 MeV First bin in delta phi M(K+ K-) GeV/c2 Not corrected for v2 Width: 7.2±0.9 MeV STAR preliminary M(K+ K-) GeV/c2 No evidence for mass shifts and width broadenings on the away-side  Need higher pT resonances

30. For the LHC In quadrants or inside/outside jets at sufficiently high fractional momentum (pT = 3-10 GeV/c): • baryon / meson ratios • rare particle species (s,c,b) • resonances • pT broadening • Can all already be done in pp (underlying event analysis). Need statistics at high pT in pp and AA.

31. Summary • The question of hadronization in QCD is highly relevant for the evolution of the initial deconfined and 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 ? • In the ALICE year-1, studies of high multiplicity proton proton collisions will give additional important clues. 31