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Heavy Quarks + Vector Mesons in Medium

Heavy Quarks + Vector Mesons in Medium. Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA School of Collective Dynamics in High-Energy Collisions “Medium Properties, Chiral Symmetry and Astrophysical Phenomena”

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Heavy Quarks + Vector Mesons in Medium

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  1. Heavy Quarks + Vector Mesons in Medium Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA School of Collective Dynamics in High-Energy Collisions “Medium Properties, Chiral Symmetry and Astrophysical Phenomena” Lawrence Berkeley National Laboratory, 22.05.07

  2. Outline 1.) Introduction: QGP + High-Energy Heavy-Ion Collisions  Achievements and Open Questions 2.) Heavy-Quark Probes (c,b)  Heavy-Quark Diffusion in the sQGP  RHIC Data 3.) Electromagnetic Radiation  Relation to Chiral Symmetry Restoration  In-Medium Vector Mesons  Dileptons: CERES/NA45 and NA60 4.)Conclusions

  3. 1.1 The “Little Bang” in the Laboratory e+ e- c,b r Au + Au QGP ?! (t ≈ 5fm/c) Hadron Gas (t ≈ 10fm/c) “Freeze-Out” Questions:• Thermalization? • QGP Signatures?? • Phase Transition???

  4. pt ≥ 6GeV: pQCD energy-loss (factor ~5 suppression) •  energy densities e0 ≈ 20 GeV fm-3 [Gyulassy, Vitev, Wang, …] • 2GeV ≤ pt ≤ 6GeV: p/p≈1, quark “scaling” in v2 •  quark coalescence [Greco et al, Fries et al, Hwa et al, …] 1.2 Achievements at RHIC:Towards the QGP Hadron Spectra(↔ bulk matter properties) • Momenta pt ≤ 2GeV: Hydrodynamic flow (v0,v2) •  early thermalization, QGP pressure [Shuryak, Heinz,…]  thermal medium, small viscosity, large opacity, partonic, To ≈ 2 Tc(indirect)

  5. Heavy Quarks • ►c- and b-quark energy loss, thermalization, “flow” ? • ►Q-Q bound states (J/y, Y) in sQGP? • Electromagnetic Emission • ►photons: q0=q , thermal radiation? • ►dileptons: (Mee )2= q02 - q2 > 0 : Vector spectral functions in medium? • Chiral Symmetry Restoration? - 1.3 Microscopic Probes: Understanding the QGP • Questions: • - prevalent interactions? • - d.o.f. (resonances in sQGP)? • - phase diagram + transition? •  Advanced studies required:

  6. 2.) Heavy-Quark Probes at RHIC Nuclear Modification Factor Elliptic Flow [Gyulassy etal ’05] RAA = (AA) / (pp) [Armesto et al ’05] pT [GeV] • substantial collectivity • bottom “contamination”? • factor 4-5 suppression • elastic E-loss, pQCD?! • Radiative energy loss smaller for c+b quarks • Elastic interactions? • Collective flow? Heavy-quark diffusion? • experimental tool: electron spectra D,B → eX c,b ?

  7. Microscopic Calculations of Diffusion: 2.1.1 Perturbative QCD [Svetitsky ’88, Mustafa et al ’98, Molnar et al ’04, Zhang et al ’04, Hees+RR ’04, Teaney+Moore‘04] dominated by t-channel gluon-ex.: q c g c • e.g. T =300 MeV, as=0.4: ttherm~15 fm/cslow! (tQGP≤ 5 fm/c) 2.1 Heavy-Quark Diffusion in the QGP • Brownian • Motion: Fokker Planck Eq. [Svetitsky ’88,…] Q scattering rate diffusion constant

  8. _ _ “D” q q c c • no. of D-states (chiral+HQ symm.): • 8 per u and d, 4 for s • resonance cross section isotropic, • pQCD forward 2.1.2 Open-Charm Resonances in QGP “Light”-Quark Resonances [van Hees+ RR ’04] 1.4Tc • effective lagrangian with pseudo/scalar • + axial/vector “D-mesons” [Asakawa+ Hatsuda ’03] • parameters: mD=2GeV , GD, • mc=1.5GeV, mq=0

  9. 2.1.3 Thermal Relaxation of Heavy Quarks in QGP Charm: pQCD vs. Resonances Charm vs. Bottom pQCD “D” • tctherm ≈ tQGP ≈ 3-5 fm/c • bottom does not thermalize • factor ~3 faster with • resonance interactions!

  10. Nuclear Modification Factor Elliptic Flow • resonances → large charm suppression+collectivity, not for bottom • v2 “leveling off”’ characteristic for transition thermal → kinetic 2.2 Heavy-Quark Spectra at RHIC Relativistic Langevin Simulation: stochastic implementation of heavy-quark motion in expanding QGP- fireball with “hydrodynamic” evolution of bulk-matterbT , v2 [van Hees,Greco+RR ’05]

  11. 2.2.2 HQ Langevin Simulations: Hydro vs. Fireball Elastic pQCD (charm) + Hydrodynamics [Moore and Teaney ’04] as , g 1 , 3.5 0.5 , 2.5 0.25,1.8 • Tc=165MeV, • t ≈ 9fm/c • as and mD~gT • independent • (mD≡1.5T) • sgQ ~ (as/mD)2 • as=0.4 ↔ • D(2pT) ≈ 20 •  hydro ≈ • fireball • expansion [van Hees,Greco+RR ’05]

  12. Fragmentation only • large suppression from resonances, elliptic flow underpredicted (?) • bottom sets in at pT~2.5GeV 2.3 Single-e± at RHIC: Effect of Resonances • hadronize output from Langevin HQs (d-fct. fragmentation, coalescence) • semileptonic decays: D, B → e+n+X

  13. 2.3.2 Single-e± at RHIC: Resonances + Q-q Coalescence fqfrom p, K [Greco et al ’03] Elliptic Flow Nuclear Modification Factor • less suppression and morev2 • anti-correlation RAA ↔ v2 from coalescence (both up) • radiative E-loss at high pT?!

  14. coalescence essential for • consistent RAA and v2 • other mechanisms: • 3-body collisions, … [Liu+Ko’06, Adil+Vitev ‘06] 2.4 Model Comparisons to Recent PHENIX Data Single-e±Spectra[PHENIX ’06] • pQCD radiative E-loss with • 10-fold upscaled transport coeff. • Langevin with elastic pQCD + • resonances + coalescence • Langevin with 2-6 upscaled • pQCD elastic

  15. 2.5. Transport Properties of (s)QGP ‹x2›-‹x›2=Dx·t, Dx=2d·(T/mQ)/g, Ds=Dx/2d Spatial Diffusion Coefficient Charm-Quark Diffusion Viscosity-to-Entropy: Lattice QCD [Nakamura +Sakai ’04] • small spatial diffusion → strong coupling E.g. strongly coupled gauge theory (AdS/CFT):h/s=1/4p, DHQ≈1/2pT  resonances: DHQ≈4-6/2pT , DHQ ~ h/s ≈ (1-1.5)/p

  16. Applications • → Schröd.-Eq. • → bound states (sQGP)! • scattering states? imaginary parts? • → Lippmann-Schwinger Equation [Shuryak,Zahed, Brown ’04] - q-qT-Matrix  solve numerically [Mannarelli+RR ’05] 2.6 Potential Scattering in sQGP Lattice Q-Q Free Energy [Bielefeld Group ’04]

  17. 2.6.2 Charm-light Cross Sections with Lat-QCD Potential Temperature Evolution Channel Decomposition • interaction strength concentrated • close to threshold • meson and diquark channels • dominant

  18. 2.6.3 Friction Coefficients (Relaxation Rate): Lat-QCD vs. Resonance Model T ≈ 200 MeV T ≈ 250 MeV • uncertainty in potential extraction from lattice QCD • potential scattering comparable to resonance model close toTc

  19. 2.6.4 Charm-Quark Spectra at RHIC Elliptic Flow Nuclear Suppression Factor • nonperturbative effects stronger than elastic pQCD • radiative (2↔3) scattering?

  20. e- e+ q q _ e+ e- e+e- → hadrons r+w+f _ qq γ • Radiation Sources:Relevance: • Quark-Gluon Plasma: high mass + temp. • qq → e+e-, …M > 1.5GeV, T >Tc • Hot + Dense Hadron Gas: M ≤ 1 GeV • p +p - → e+e-, … T ≤ Tc - e+ e- p- p+ r 3.) Electromagnetic Radiation E.M. Correlation Function: Im Πem(M,q;mB,T) Im Πem(q0=q; mB,T)

  21. at Tc: Chiral Restoration • Low-Mass Dilepton Rate: r -meson dominated! ImPem ~ [ImDr+ImDw /10+ImDf /5] • Axialvector Channel:p±ginvariant mass-spectra~ Im Da1(M) ?! 3.2 EM Radiation and Chiral Symmetry ~ “r - a1(1260)” (chiral partners) Axial-/Vector in Vacuum pQCD continuum

  22. 3.3 Medium Effects: Hadronic Many-Body Theory > > [Chanfray et al, Herrmann et al, RR et al, Weise et al, Koch et al, Post et al, Eletsky et al, Oset et al, …] Dr (M,q;mB ,T) = [M 2- mr2 –Srpp –SrB -SrM ] -1 r-Propagator: r B*,a1,K1... r Sp SrB,M = Srpp = r-Selfenergies: N,p,K… Sp Constraints: - vacuum decays: B,M→ rN, rp, ... - scattering data:gN ,gA , pN→rN - QCD sum rules Nuclei rN=0.8r0 [Ko et al ’92, Klingl et al ’97, Leupold et al ’98] gN gA p-ex [Urban et al ’98]

  23. rB /r0 0 0.1 0.7 2.6 Model Comparison [Eletsky etal ’01] [RR+Wambach ’99] 3.3.2r-Meson Spectral Functions at SPS Hot+Dense Matter Hot Meson Gas [RR+Wambach ’99] [RR+Gale ’99] • r-meson “melts” in hot and dense matter (→ pQCD continuum) • baryon densitymore important than temperature • reasonable agreement between models

  24. 3.4 Pb-Au Collisions at SPS: CERES/NA45 → Evolve dilepton rates over thermal fireball QGP+Mix+HG: • T0≈205MeV, Tfo≈110MeV • QGP contribution small • medium effects onr-meson!

  25. quantitative theory? 3.5 In-In at SPS: Dimuons from NA60 [PRL ’06] • excellent mass resolution and statistics • for the first time, dilepton excess spectra could be extracted!

  26. [van Hees +RR ‘06] 3.5.2 Dimuon Excess Spectra at SPS • Central In-In fireball: T0-fo=195→120MeV, Tc=175MeV, tFB=7fm Full Spectral Functions Switch off Medium Effects • predicted ”melting”-r confirmed, average (Gr)med ≈ 350MeV ≈ mr/2 • relative strength of thermal sources fix, absolute yield ↔ fireball lifetime • baryon effects essential; probing matter close to Tc!?

  27. 3.6 Chiral Virial Approachvs. NA60 • chiral reduction of scatt. ME’s + low-density expansion • also: compare fireball vs. hydrodynamics [Dusling,Teaney+Zahed ’06] [van Hees+RR ‘06] • good agreement fireball - hydro (pT-spectra!) • lack of broadening

  28. 3.7 NA60pT-Spectra Fireball + Many-Body Hydro + Chiral Virial • theory slopes • too soft • ok with data • hadronic emission • prevalent [Dusling+Zahed ’06] [van Hees+RR ’06] • freezeout-r: g-factor! good model agreement • other fireball model: harder slopes, QGP dominant at M≥1GeV [Renk+ Ruppert ’06]

  29. 4.) Summary and Conclusions • Heavy quarks probe the (s)QGP: strong suppression, collectivity • Importance of elastic collisions; need explicit charm • pQCD not enough, resonances in sQGP?! • Microscopic description (lattice QCD potentials, correlators) • Electromagnetic probes are becoming a precision tool • Equilibrium radiation from QCD matter!? • Average r-meson width G≈mr/2 (G→mr toward Tc) • T- and mB-dependence of bare parameters in the Lagrangian? • hard exp. pT-spectra

  30. 3.3 Dilepton Emission Rate: Hadron Gas vs. QGP • “matching” of HG and QGP • emission close to Tc • In-Medium Reduction of • “Quark-Hadron Duality” • Threshold ?!

  31. 4.3 NA60pT-Spectra vs. Hadronic Many-Body • improved freezeout-r (g-factor!) + Drell-Yan (pT>1.5GeV) • approx. agreement (local slopes?!) See parallel talks by H.van Hees, J.Ruppert

  32. - q-qT-Matrices 3.2 Selfconsistent T-Matrix and Selfenergy [Mannarelli+RR ’05] T=1.2Tc T=1.5Tc T=1.75Tc • assume mq(gluon)=0.1GeV • transition from bound (1.2Tc) • to resonance states! • quark-width≈0.3GeV≈(2/3fm)-1 • (≈ mass ↔ liquid!?) • colored states, equat. of state? Quark Self- Energy T=1.5Tc

  33. WA98 “Low-qt Anomaly” • addt’l meson-Bremsstrahlung • pp→ ppgpK→pKg • substantial at low qt [Liu+ RR’05] 5.) Electromagnetic Probes 5.1.1 Thermal Photons I : SPS Expanding Fireball + pQCD • pQCD+Cronin at qt >1.6GeV •  T0=205MeV suff., HG dom. [Turbide,RR+Gale’04]

  34. 5.1.2 Thermal Photons II: RHIC • thermal radiation qt<3GeV ?! • QGP window 1.5<qt<3GeV ?! • also: g-radiation off jets • shrinks QGP window qt<2GeV ?! [Gale,Fries,Turbide,Srivastava ’04]

  35. 5.3.2 Dileptons II: RHIC [R. Averbeck, PHENIX] [RR ’01] QGP • low mass: thermal! (mostly in-medium r) • connection to Chiral Restoration: a1 (1260)→ pg ,3p • int. mass:QGP (resonances?)vs.cc → e+e-X (softening?) -

  36. 4.2.4 NA60 Data: Chiral Virial Approach • also compare fireball vs. hydrodynamics [ van Hees+RR ‘06] [Dusling,Teaney+Zahed ‘06] • lack of broadening • good agreement hydro - fireball

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