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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
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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,…)
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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
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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)
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(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]
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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
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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
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(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:
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(ii) Vector Mesons at RHIC baryon effects important even at B,tot =0 : sensitive to Btot = + B, more robust ↔ OZI -
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(iii) Current Status of a 1 (1260) > > > > N(1520) … ,N(1900) … a1a1 + +... Exp: - HADES ( A): a 1 →( + - ) - URHICs (A-A) : a 1 → 0 =
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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) + SS PP SS SS SS SS PP SS SS (a 1 ) S Importance of baryon spectroscopy to identify relevant decay modes!
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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
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(i) Check: in Vacuum and in Nuclei → ok !
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(ii) (1232) in URHICs broadening: Bose factor, →B repulsion: N -1, NN -1 not yet included: ( N↔
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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]
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Comparison of Hadronic Models to LGT calculate integrate More direct! Proof of principle, not yet meaningful (need unquenched)
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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?
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(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?!
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(iv) Resonance Spectroscopy II : + p Spectra NN Qualitatively in line with data ( eV, MeV) [courtesy P. Fachini] (1232) at RHIC eV ±10)MeV mean-field:
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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]
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3. “Hadrons” at and Above T c 3.1 Continuity ?! 3.2 Charmonium in QGP 3.3 Light Hadrons in QGP
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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
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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 *
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[Grandchamp +RR ’03] Charmonia in URHIC’s SPS RHIC J/ Excitation Function
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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]
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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
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Additional Slides
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[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?!
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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]
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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]
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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:
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