1. Light and Heavy Hadronic Modes in Medium Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA Universität Bielefeld, 11.01.05

2. 1. Motivation: Relativistic Heavy-Ion Collisions Au + Au → X e + e - Signatures of the QGP? Suppression of J/  -Mesons Decays of  -Mesons Photons …  J/  

3. 1.2 Current Status: Towards QGP Discovery So far: RHIC observables ↔ bulk properties of the produced matter: - energy density  ≈20GeVfm -3 ↔ jet quenching (high-p t ) - thermalization + EoS ↔ hydrodynamics (v 0,v 2 ) - partonic degrees of freedom ↔ coalescence (p/ , v 2 -scal) Future: need to understand microscopic properties (phase transition, “QGP” !?): - Deconfinement ↔ quarkonia (J/ , , …) - Chiral Symmetry Restoration ↔ dileptons ( - temperature ↔ photons )

4. 1. Introduction 2. Vacuum: Chiral Symmetry (Breaking) 3. (Light) Hadrons below T c 3.1 Mesons: 0 ± (  -  ), 1 ± (  -a 1 ), Baryons: N,  3.2 Towards Chiral + Resonance Scheme 3.3 URHICs: Dileptons + Photons 4. Heavy-Quark Modes 4.1 Charmed Hadrons below T c 4.2 Heavy-Quark Equilibration 4.3 Quarkonia in the QGP 4.4 URHICs: Suppression vs. Regeneration 5. Conclusions Outline

5. 2.) Chiral Symmetry in QCD: Vacuum SU(2) L × SU(2) R invariant (m u,d ≈0) Spontaneous Breaking: strong qq attraction  Bose Condensate fills QCD vacuum! > > > > qLqL qRqR qLqL - qRqR - [cf. Superconductor: ‹ee›≠0 Magnet ‹ M ›≠0, … ] - Profound Consequences: energy gap: ↔ mass generation! massless Goldstone bosons  0,± “chiral partners” split,  M≈0.5GeV: J P =0 ± 1 ± 1/2 ±

6. 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)

7. 2.2 “Melting” the Chiral Condensate How? Excite vacuum (hot+dense matter) quarks “percolate” / liberated  Deconfinement ‹qq› condensate “melts”,  iral Symm. chiral partners degenerate Restoration (  - ,  - a 1, … medium effects → precursor!) 0 0.05 0.3 0.75  [GeVfm -3 ] 120, 0.5  0 150-160, 2  0 175, 5  0 T[MeV],  had   PT many-body degrees of freedom? QGP (2 ↔ 2) (3-body,...) (resonances?) consistent extrapolate pQCD - 1.0 T/T c mm ‹qq› - lattice QCD

8. 3. Hadrons in Medium: Light Sector (u,d) 3.1.1 0 ± Mesons:  and “  ” 3.1.2 1 ± :  (770) and a 1 (1260) 3.2 Chiral + Resonance Scheme 3.3 Baryons:  (1232), N 3.4 Comparison to Lattice 3.5 URHICs: E.M. Probes (and Resonances)

9. 3.1.1 Pion and Sigma in Medium D  =[k 0 2 -  k 2 -   (k 0,k)] -1  > > = + N,   N -1,  -1  N prevalent, smeared at T>0 D  → D  at T c Precursor in nuclei ?!  A→(  ) S-Wave A URHICs: - fluct.   (0,q→0) -  M-spectra - (very) soft photons

10. > >    B *,a 1,K 1... N, ,K … Constraints: - B,M→  N,  -  N,  A,  N→  N - QCDSRs, lattice 3.1.2 (Axial-) Vector Mesons in Medium D  (M,q:  B,T)=[M 2 -m  2 -   -   B -   M ] -1 (a) Hadronic Many-Body Theory Propagator: [Chanfray etal, Herrmann etal, RR etal, Koch etal, Weise etal, Post etal, Eletsky etal, Oset etal, …] (b) Effective Field Theory O HLS with  L ≡  (“VM”); vacuum: loop exp. O (p/  , m  /  , g) In-Med.: T-dep. of bare m  (0), g  via matching to OPE,  match <   + RG-running to on-shell  dropping  -mass [Harada, Yamawaki, Sasaki etal]

11. [RR+Gale ’99] (i)  -Mesons at SPS  -meson “melts” in hot and dense matter baryon density  B more important than temperature  B /  0 0 0.1 0.7 2.6 Hot+Dense Matter Hot Meson Gas [RR+Wambach ’99] [Eletsky etal ’01] Model Comparison [RR+Wambach ’99]

12. (ii) Vector Mesons at RHIC baryon effects important even at  B,net =0 : sensitive to  B,tot =   +  B,  more robust ↔ OZI - e + e - Emission Rates: dR ee /dM ~ f B Im  em Quark-Hadron Duality ?! in-med HG ≈ in-med QGP ! [qq→ee] [qq+O(  s )] ----

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

14. 3.2 Towards a Chiral + Resonance Scheme Options for resonance implementation: (i) generate dynamically from pion cloud [Kolomeitsev etal ‘03, …] (ii) genuine resonances on quark level → representations of chiral group [DeTar+Kunihiro ‘89, Jido etal ’00, …] e.g.  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!

15. 3.3 In-Medium Baryons:  (1232) and N(939)  long history in nuclear physics ! (  A,  A ) e.g. nuclear photoabsorption: M ,   up by 20-40MeV  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

16.  in Nuclear  Absorption  in Nuclei and Heavy-Ion Collisions  broadening: Bose factor,  →B  repulsion:  N -1,  NN -1  (1232) Spectral Fct. at RHIC Nucleon Spectral Fct. at RHIC  substantial broadening due to resonant  N → B scattering

17. 3.4 Lattice Studies of Medium Effects calculated on lattice MEM 1-1- 0-0- extracted [Laermann, Karsch ’04]

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

19. 3.5 Observables in URHICs (i) Dileptons (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?

20. 4. Heavy-Quark Modes 4.1 Charmed Mesons below T c 4.2 Heavy-Quark Equilibration 4.3 Charmonium in QGP 4.4 URHICs: Suppression vs. Regeneration

21. 4.1 Charmed Mesons in Hadronic Matter  reduced threshold for  → DD  J/  robust   ’ fragile:  ’→ DD decays [ Grandchamp+RR ’03] m D (T,  B ) expected to decrease (Chiral Symmetry Restoration) [Weise etal ’01]

22. 1-D Fokker Planck Eq. scatt. rate diff. const. 4.2 Heavy-Quark Thermalization in QGP ? Naively: 1 scatt. Q 2 ≈ T 2, (p t,therm ) 2 ≈ m c T  N scatt ≈(p t,therm /Q) 2 ≈5 more quantitative: Boltzmann Eq. [Svetitsky ’88]  e.g.: pQCD Xsections, T=500MeV,  s =0.6(0.3)   =0.25 (0.06) fm -1 ↔ 4-15fm/c (very) slow! Resonance cross section c + q → “D” → c + q ?!

23. 4.2.1 Resonant Open-Charm Rescattering effective model with pseudo/scalar + axial/vector “D-mesons” c + q → “D” → c + q “Light”-Quark Resonances 1.4T c [Asakawa+ Hatsuda ’03] _ _ chirally symmetric for light quarks heavy-quark symmetry  j  conserved to LO(1/m c ) parameters: m D (0), G D [van Hees+RR ’04]

24. 4.2.2 Heavy-Quark Thermalization Times in QGP resonance scatt. isotropic secondary open-charm ?! [50% for ] [van Hees+RR ’04] pQCD “D” Charm Quarks Bottom vs. Charm bottom quarks “barely” thermalize at RHIC

25. 4.2.3 Single-e ± Spectra at RHIC: D → e + X dynamical origin of resonances? cc production? onset of pQCD regime: p t >5-6GeV ? open bottom? _ [Müller etal ’95, Molnar’04] practically indistinguishable PHENIX 130AGeV e±e± B D [Batsouli etal. ’02] p t -Spectra: p-p vs Hydro Ellitpic Flow + Coalescence jet- quench [Djordjevic etal ’04] does charm equilibrate?

26. 4.2 Charmonium in QGP Lattice:  c, J/  survive up to ~2T c mass m  ≈ const ~ 2m c * width: [Datta etal ’03] gluo-dissociation “quasifree” diss. [Bhanot+Peskin ‘84] [Grandchamp+RR ‘01] Cross Sections Dissociation Times

27. “jumps” at T c sensitive to rather direct link to lattice QCD! 4.3.1 Charmonium Regeneration vs. Suppression statistical coalescence at T c : chem.+therm. equil. charmonia above T c  formation in QGP: detailed balance! for thermalized c-quarks: Equilibration close to T c ?! [PBM etal ’01, Gorenstein etal ’02, …] [Thews etal ’01, Ko etal ’02 … Grandchamp+RR ’02] J/  + g c + c + X ← → -

28. QGP regeneration dominant sensitive to: m c *, open-charm degeneracy, (N cc ) 2 ↔ rapidity, √s, A [Grandchamp +RR ’03] 4.3.2 Charmonium in A-A SPS RHIC J/  Excitation Function

29. [Lumpkins, Grandchamp, van Hees, Sun +RR ’05] 4.3.3 Upsilon in A-A RHIC LHC bottomonium suppression as unique QGP signature ?! caveat:  equil. number (very) sensitive to (m b )*,  therm

30. 5. 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

31. Additional Slides

32. (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?!

33. (iv) Resonance Spectroscopy II :  + p Spectra NN Qualitatively in line with data (    eV,    MeV) [courtesy P. Fachini]  (1232) at RHIC    eV    ±15)MeV  mean-field:  (1232) Spectral Fct. at RHIC

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

35. 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]

36. J/  Width from Lattice QCD

37. E.M. Emission Rates [RR+Wambach ’99] 3.1 Continuity?! Light Hadron “Masses” However: peak in susceptibilities at T c ↔ m  → 0 Observables ? e + e - + , fluct, , J/  [Shuryak, Zahed, Brown ’04] [Turbide,Gale+RR ’03]

38. 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] 

39. 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:

40. 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]