1. Light and Heavy Hadrons in Medium Ralf Rapp Cyclotron Inst. and Physics Dept. Texas A&M University College Station, USA Frankfurt am Main, 25.06.04

2. 1.Introduction: Towards the Phase Transition note: high-density CFL phase (CSC) characterized by “hadronic” excitations (“  ”, “  ”, …) 0 0.05 0.3 0.75  [GeVfm -3 ] 120 150-160 175 T [MeV] ½   2  0 5  0  hadron  PT many-body degrees of freedom? QGP (2 ↔ 2) (3-body,...) (resonances?) consistent extrapolate pQCD Description of Chiral Symmetry Restoration / Decofinement requires nonperturbative approaches Mean-field models (lin.  -model, NJL) capture many aspects, but incomplete (limited d.o.f., only mass effects,…)

3. 1. Introduction 2. Hadrons below T c 2.1 Light Hadrons: Vacuum 2.2 Hadronic Many-Body Approach: u,d Sector - Mesons: 0 ± (  -  ), 1 ± (  -a 1 ), Baryons:  - Consistency and Constraints (Nuclei, Lattice, …) - Towards a Chiral + Resonance Scheme - URHIC’s 2.3 Charmed Mesons 3. “Hadrons” at and above T c 3.1 Continuity ?! 3.2 Heavy Quarks : Charmonium Regeneration 3.3 Light Quarks: Generalization of Coalescence 4. Conclusions Outline

4. 2.1 Light Hadrons: Vacuum Correlation Function: Timelike (q 2 >0) : Im    q 0,q) → physical excitations  =1 ± (qq) Chiral breaking: Q 2 < (1.5-2 GeV) 2, J ± < 5/2 (?!) (qqq)

5. (ii) Light Sector in Vacuum II: Spacelike Constituent Quark Mass “Data”: lattice [Bowman etal ‘02] Curve: Instanton Model [Diakonov+ Petrov ’85, Shuryak] p and d F 2 Structure Functions Jlab Data  =2x/(1+√1+4M 2 x 2 /Q 2 ) (Nachtmann Variable) average → “Quark-Hadron Duality” [Niculescu etal. ’00]

6. 2.2 Hadronic Many-Body Approach: Light Sector (u,d) 2.2.1 0 ± Mesons: Pion and “Sigma” 2.2.2 1 ± : Rho and a 1 (1260) 2.2.3 Chiral + Resonance Scheme 2.2.4 Baryons:  (1232) 2.2.5 Comparison to Lattice 2.2.6 URHICs: E.M. Probes and Resonances

7. 2.2.1 Pion and Sigma in Medium D  =[k 0 2 -  k 2 -   (k 0,k)] -1  > > = + N,   N -1,  -1 finite  N prevalent “diluted” at T>0 “  ” →  at T c Precursor in nuclei ?!  A→(  ) S-Wave A URHICs: - fluct.   (0,q→0) -  M-spectra - (very) soft photons

8. (i)  (770) + > >    B *,a 1,K 1... N, ,K … Constraints: - branching ratios B,M→  N,  -  N,  A  absorpt.,  N→  N - QCD sum rules Significance of high  B at low M E lab =20-40AGeV optimal?! 2.2.2 1 ± Mesons:

9. (ii) Vector Mesons at RHIC baryon effects important even at  B,tot =0 : sensitive to  Btot =   +  B,  more robust ↔ OZI -

10. (iii) Current Status of a 1 (1260)    > > > > N(1520) … ,N(1900) … a1a1 + +... Exp: - HADES (  A): a 1 →(  +  - )  - URHICs (A-A) : a 1 →  0  =

11. 2.2.3 Towards a Chiral + Resonance Scheme Options for resonance implementation: (i) generate dynamically from pion cloud [Lutz et al. ‘03, …] (ii) genuine resonances on quark level → representations of chiral group [DeTar+Kunihiro ‘89, e.g. Jido etal ‘00, …]  N + N(1535) -  a 1   N(1520) - N(1900) +  (1700) - (?)  (1920) + SS PP SS SS SS SS PP SS SS (a 1 ) S Importance of baryon spectroscopy to identify relevant decay modes!

12. 2.2.4 In-Medium Baryons:  (1232)  long history in nuclear physics ! (  A,  A ) e.g. nuclear photoabsorption: M ,   up by 20MeV  little attention at finite temperature   -Propagator at finite  B and T [van Hees + RR ’04] in-medium vertex corrections incl. g’  -cloud, (“induced interaction”) (1+ f  - f N ) thermal  -gas  →N(1440), N(1520),  (1600) + +...   > > > > > > > > NN -1  N -1

13. (i) Check:  in Vacuum and in Nuclei → ok !

14. (ii)  (1232) in URHICs  broadening: Bose factor,  →B  repulsion:  N -1,  NN -1 not yet included: (  N↔ 

15. 2.2.5 Lattice Studies of Medium Effects calculated on lattice  more stable than  below T c ?! (but: quenched) MEM 1-1- 0-0- extracted [Laermann, Karsch ’04]

16. Comparison of Hadronic Models to LGT calculate integrate More direct! Proof of principle, not yet meaningful (need unquenched)

17. 2.2.6 Observables in URHICs (i) Lepton Pairs (ii) Photons Im Π em (M,q) Im Π em (q 0 =q) e+e-e+e- γ baryon density effects! [Turbide,Gale+RR ’03] consistent with dileptons  Brems with soft  at low q?

18. (iii) Resonance Spectroscopy I:  +  - Spectra  Sudden Breakup Emission Rate [Broniowski+Florkowski ’03]    -mass shift ~ -50MeV  small “  ” contribution  underestimates  [Shuryak+ Brown ’03] Broadening+“  ”+BE not enough?!

19. (iv) Resonance Spectroscopy II :  + p Spectra NN Qualitatively in line with data (    eV,    MeV) [courtesy P. Fachini]  (1232) at RHIC    eV    ±10)MeV  mean-field:

20. 2.3 Charm(onium) below T c Dissociation rate  J  → DD,D*D  QCD-SR Mes-Ex CQM pQCD Reduced DD threshold:  m D (T c )≈-140MeV (NJL)   J/  robust   ’ fragile: direct  ’→ DD decays [Grandchamp+RR ’03]

21. 3. “Hadrons” at and Above T c 3.1 Continuity ?! 3.2 Charmonium in QGP 3.3 Light Hadrons in QGP

22. 3.1 Continuity?! Light Hadron “Masses” [Shuryak, Zahed, Brown ’04] However: peak in susceptibilities at T c ↔ m  → 0 Observables ? e + e - + , fluct, , J/  E.M. Emission Rates

23. 3.2 Charmonium in QGP D  =[M 2 -m  2 -   ] -1, m  ≈const (QCD-SR, LGT) gluo-dissociation, inefficient for m  ≈ 2 m c * “quasifree” diss. [Grandchamp+RR ’01] if c-quarks thermalize include back-channel : “jumps” across T c sensitive to m c *

24. [Grandchamp +RR ’03] Charmonia in URHIC’s SPS RHIC J/  Excitation Function

25. 3.3 Light Hadrons in QGP “Resonance” matter at 1-2T c ?! - EoS can be ok [ Shuryak+Zahed’04 ] assess formation rates from inelastic reactions (as in charmonium case): q+q ↔ “  ”+X, etc. solve (coupled) rate equations accounts for energy conservation, no “sudden” approximation   -formation more reliable To be resolved: quark masses are not “constituent”: role of gluons? (not really heavier than quarks…), … generalizes coalescence [Greco,Ko+RR, in progress] 

26. 4. Conclusions Hadronic Many-Body Theory can provide: - valuable insights into hadron properties in medium - understanding of observables in nuclear reactions The physics is often in the width (exception: e.g. “  ”) Interpretations? - many spectral properties appear to vary smoothly - connections to phase transition to be established - need nonperturbative symmetry-conserving approach, e.g. selfconsistent  -derivable thermodyn. potential

27. Additional Slides

28. [PHENIX] preliminary [PHENIX] preliminary 4.3 Charm I: Open Charm (Central A-A) (i) Yields RHIC: -30% for  =0  2: CGC [Tuchin], Color-Dipole [Raufeisen] LHC: CGC: N part ; nonlin. DGLAP: enhanced! [Kolhinen] (ii) p T -Spectra dE/dx : Null Effect?! [Djordjevic] v 2 (e ± ) : Thermalization?!

29. 3.4 Hydro vs. Coalescence: The 2-6GeV Regime v 2 : mass-dependent But: p/  (4GeV)≈0.3 [PHENIX]: 1±0.15 [Hirano,Nara] Challenges: p/  =1 + jet correlation,   elliptic flow [Fries,Hwa,Molnar]  universal partonic v 2 (p T /n) / n soft-soft ≈ thermal ( p T » m ) soft-hard: explicit thermal+jet (correlations!) [Greco et al.] [PHENIX] [STAR]

30. Direct Photons at SPS and RHIC large “pre-equilibrium” yield from parton cascade (no LPM) thermal yields ~ consistent QGP undersaturation small effect pQCD Cronin ~ π 0  T 0 ≈205MeV sufficient new WA98 points:  -Bremsstr. via soft  ? [Turbide etal]

31. RHIC central: N cc ≈10-20, QCD lattice: J/  ’s to  ~2T c 4.3 Charm II: Charmonium Regeneration in QGP / at T c J/  + g c + c + X → ← [PBM etal, Thews etal] N part [Grandchamp] sensitivity to m c * - If c-quarks thermalize: