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Heavy Quark Diffusion in Heavy Ion Collisions

Heavy Quark Diffusion in Heavy Ion Collisions. Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA With: H. van Hees, V. Greco, M. Mannarelli Conference on “Early Time Dynamics in Heavy Ion Collisions”

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Heavy Quark Diffusion in Heavy Ion Collisions

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  1. Heavy Quark Diffusion in Heavy Ion Collisions Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA With: H. van Hees, V. Greco, M. Mannarelli Conference on “Early Time Dynamics in Heavy Ion Collisions” McGill University (Montreal, Canada), 16.07.07

  2. Diffusion/interactions in sQGP at all pT Hadronization (low pT?) • Direct relation to other observables • quarkonia: - interaction with c, b within bound state • - regeneration → Y • intermediate-mass dileptons: • → e+e- X competes with • thermal (QGP) radiation [PHENIX ’07] 1.) Introduction: Heavy Quarks at RHIC • c, b quarks (more!?) sensitive to: • - thermalization (low pT) • - energy loss (high pT) • - coalescence (int. pT?)

  3. Outline 1.) Introduction  Single-Electron Puzzle at RHIC 2.) Heavy-Quark Diffusion in (s)QGP  Fokker-Planck Approach  Resonance Model  HQ and e± Spectra at RHIC 3.) Lattice-QCD Based Potential Approach  In-Medium Heavy-Light Quark T-Matrix  Transport Coefficients  HQ RAA and v2 4.)Conclusions

  4. 1.2 Expectations 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 ?

  5. 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.) Heavy-Quark Diffusion in the QGP • Brownian • Motion: Fokker Planck Eq. [Svetitsky ’88,…] Q scattering rate diffusion constant

  6. _ _ “D” q q c c • chiral (u,d) + HQ (c,b) symmetry • 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

  7. 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!

  8. Nuclear Modification Factor Elliptic Flow • resonances → large charm suppression+collectivity, not for bottom • v2 “leveling off ” characteristic for transition thermal → kinetic 2.3 Heavy-Quark Spectra at RHIC • Relativistic Langevin Simulation: • stochastic implementation of HQ motion in expanding QGP-fireball • “hydrodynamic” evolution of bulk-matterbT , v2 [van Hees,Greco+RR ’05]

  9. 2.3.2 The first 5 fm/c for Quark-v2 and -RAA Inclusive v2 • RAA built up earlier than v2

  10. 2.3.3 HQ Langevin Simulations: Hydro vs. Fireball Elastic pQCD (charm) + Hydrodynamics [Moore+Teaney ’04] as , g 1 , 3.5 0.5 , 2.5 0.25,1.8 • Tc=165MeV, • t ≈ 9fm/c • sgQ ~ (as/mD)2 • as and mD~gT • independent • (mD≡1.5T) • as=0.4, mD=2.2T • ↔ D(2pT) ≈ 20 •  hydro ≈ • fireball • expansion [van Hees,Greco+RR ’05]

  11. Fragmentation only • large suppression from resonances, elliptic flow underpredicted (?) • bottom sets in at pT~2.5GeV 2.4 Single-e± at RHIC: Effect of Resonances • hadronize output from Langevin HQs (d-fct. fragmentation, coalescence) • semileptonic decays: D, B → e+n+X

  12. 2.4.2 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?!

  13. coalescence essential for • consistent RAA and v2 • other mechanisms: • 3-body collisions, … [Liu+Ko’06, Adil+Vitev ‘06] 2.5 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

  14. 2.5.2 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

  15. Applications • → Schrödinger-Eq. • → bound states (sQGP) • scattering states + imaginary parts • → Lippmann-Schwinger Eq. [Shuryak+ Zahed ’04, …] - [Mannarelli+RR ’05] Q-qT-Matrix  solve numerically _ 3.) Potential Scattering in sQGP Lattice Q-Q Free Energy [Bielefeld Group ’04]

  16. 2 3.2 Charm-Light Cross Sections with lQCD-based Potential Temperature Evolution Channel Decomposition • meson and diquark channels • dominant • interaction strength close to threshold

  17. 3.3 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

  18. 3.4 Charm-Quark Spectra at RHIC Elliptic Flow Nuclear Suppression Factor • supports importance of nonperturbative effects • radiative (2↔3) scattering?

  19. 4.) Summary and Conclusions • Heavy quarks probe the (s)QGP: strong suppression, collectivity • Importance of elastic collisions • Indications for nonperturbative interactions • Supported by microscopic description: lQCD-based T-matrix, • scrutinize: lQCD correlators, U1 vs. F1, finite-T quark masses • “Hadronic” correlations dominant (meson + diquark) • ↔ natural connection to quark-coalescence at Tc[Ravagli+RR ’07] • Impact on other observables: light sector, quarkonia, dileptons,…

  20. - 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

  21. 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?) -

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