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Heavy-Quark Diffusion, Flow and Recombination at RHIC

Heavy-Quark Diffusion, Flow and Recombination at RHIC. Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA With: H. van Hees, V. Greco ( …) Strangeness in Quark Matter Conference 2006 Los Angeles, 30.03.06.

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Heavy-Quark Diffusion, Flow and Recombination at RHIC

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  1. Heavy-Quark Diffusion, Flow and Recombination at RHIC Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA With: H. van Hees, V. Greco (…) Strangeness in Quark Matter Conference 2006 Los Angeles, 30.03.06

  2. 1.) Introduction-I: The Virtue of HQ’s in URHICs • , production follows • N-N collision-scaling •  Valuable Probe of Medium: [PHENIX ’04] • distinguishable from gluons • mass + charge-dependence of jet quenching (induced radiation?) • elastic rescattering, (approach to) thermalization, collective flow: • pQCD?! sQGP?! • coalescence at low(er) pT: • cq→ D (even in pp), cc → Y

  3. 1.2 Intro-II: pQCD Jet Quenching [Armesto et al ’05] [Gyulassy et al ’05] Challenges: • enough quenching? (upscaled transport coefficient) • Gluon Plasma (maximal color charge) • pions over-quenched (pT ≤ 4GeV) • “drag” on heavy quarks → flow • consistency v2 ↔ RAA

  4. 1.3 Intro-III: Single-e± Elliptic Flow ? [Armesto et al ’05] jet-quench [Djordjevic et al ’04] coalescence assuming v2c=v2q vs. jet quenching Challenges: • dynamical origin of re-interactions: • radiative vs. elastic scattering, 3↔3 • bottom contribution • transition soft – intermediate - hard • … [Liu+Ko’06]

  5. Outline 2.) Baseline Spectra in p-p, d-Au • Charm vs. Bottom 3.) Heavy-Quark Elastic Scattering in QGP • Brownian Motion and Thermal Relaxation • pQCD vs. Resonances 4.) Heavy-Quark and Electron Spectra at RHIC • Langevin Simulation, Hadronization • RAA and v2 5.) Heavy Quarkonia • Charmonium pT-Spectra 6.)Summary

  6. 2.) Heavy-Flavor Baseline Spectra at RHIC Semileptonic Electrons D-Mesons • bottom crossing at 5GeV!? (~pQCD[Cacciari et al ’05]) • strategy: fix charm with D-mesons, adjust bottom in e±-spectra

  7. Microscopic Calculation of Diffusion: 3.1 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 =400 MeV, as=0.4: ttherm~10 fm/cslow! (tQGP≤ 5 fm/c) 3.) Heavy-Quark Elastic Scattering 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 3.2 Open-Charm Resonances in QGP “Light”-Quark Resonances [van Hees+ RR ’04] 1.4Tc • effective model with pseudo/scalar • + axial/vector “D-mesons” [Asakawa+ Hatsuda ’03] • parameters: mD=2GeV , GD, • mc=1.5GeV, mq=0

  9. Charm vs. Bottom • tcrelax ≥ Dt(T>0.25GeV) ≈ 1fm/c • tbottom ≈ 3 tcharm 3.3 Heavy-Quark Thermalization Times in QGP Charm: pQCD vs. Resonances pQCD “D” • decreased by factor ~3 • with resonances

  10. Nuclear Modification Factor Elliptic Flow • characteristic “leveling-off” • factor 3-4 from resonances • resonance effects large • bottom much less affected 4.) Heavy-Quark and Electron Spectra at RHIC 4.1 Relativistic Langevin Simulations for HQs • initialize heavy quarks (Glauber) in elliptic QGP fireball • realistic time evolution of bulkv0,v2 • simulate HQ paths with drag and diffusion in QGP [van Hees, Greco+RR ’05]

  11. Fragmentation only • large suppression from resonances, elliptic flow underpredicted (?) • bottom sets in at pT~2.5GeV 4.2.1 Single-e± at RHIC: Effect of Resonances • hadronize output from Langevin HQs (d-fct. fragmentation, coalescence) • semileptonic decays: D, B → e+n+X

  12. 4.2.2 Single-e± at RHIC: Resonances + Q-q Coalescence fqfrom p, K [Greco et al ’03] Elliptic Flow Nuclear Modification Factor • less suppression and morev2forpT ~ 1-5 GeV • anti-correlation RAA ↔ v2 from coalescence (both up) • radiative E-loss at pT ≥ 5GeV ?!

  13. _ _ “D” q q c c 4.2.3 Formfactor Effect on Resonance Formation • replace (renormalized) point • vertex by formfactor (L=1GeV) Charm-Quark RAA Charm-Quark v2 • formfactor affects higher pT • rather far from equilibrium

  14. J/yElliptic Flow [Greco,Ko+RR ’04] largest sensitivity! 5.) J/y pT-Spectra in Au-Au at RHIC • Recombination via Quark Coalescence atTc Zero vs. Maximal Reinteraction “Realistic” Input from Langevin pQCD scatt. resonance scatt. [Greco,van Hees+RR in prep] • total yields different by up to factor 3 • rather sensitive to radial flow (bt,max=0.5-0.65) • Cronin effect for quantitative RAA

  15. 6.) Summary • “D”-/”B”- resonances in sQGP (elastic scattering) • - accelerate c-/b-quark thermalization (factor ~3 over pQCD) • - coalescence increases both v2 and RAA (consistency!) • existence of resonances (q-Q, q-q) to be scrutinized • complete treatment incl. elastic + radiative processes • - discriminate with angular correlations (tagged Q-jets)? • pQCD energy loss ↔ Gluon-Plasma, color charge • resonances ↔ Quark-Gluon Plasma, nonpert. dynamics • consistency with / impact on: - light-parton spectra • - quarkonia (v2!) • - IM dileptons (vs. QGP radiation)

  16. 2.4.1 Langevin-Simul. at RHIC: Heavy-Quark RAA Resonances vs. pQCD Charm-pQCD (as,mD=1.5T) as , g 1 , 3.5 0.5 , 2.5 0.25,1.8 • hydro with Tc=165MeV, t ≈ 9fm/c • as and Debye mass independent • expanding fireball ≈ hydro • pQCD elastic scatt. moderate • resonance effects substantial [Moore and Teaney ’04] [van Hees,Greco+RR ’05]

  17. 4.1.2 HQ Langevin-Simulations with Hydro + pQCD • Charm-pQCD cross sections with variableas,mD=1.5Tfix • Hydrodynamic bulk evolution with Tc=165MeV, t ≈ 9fm/c Elliptic Flow Nuclear Modification as , g 1 , 3.5 0.5 , 2.5 0.25,1.8 • correlation: small RAA ↔ large v2 • realistic coupling / decoupling ? [Moore+Teaney ’04]

  18. 4.2.3 Semi-Central e±RAA at RHIC • Elliptic QGP fireball with D-/B-resonances, coal./frag. and decay Fragmentation only Coal. + Frag. • coalescence favored [van Hees,Greco +RR ’05]

  19. 4.2.3 Light-Parton Jet-Quenching RHIC • pion quenching in pQCD [Armesto et al.] • problems below ~4-5GeV

  20. 3.4.3 Scrutinizing Charmonium Regeneration II: J/y Elliptic Flow Suppression only Thermal Coalescence at Tc [Greco etal ’04] [Wang+Yuan ’02] MB Au-Au • factor ~5 different! • transition inpt!?

  21. Applications • → Schröd.-Eq. • → bound states (sQGP)! • scattering states + imaginary parts: • Lippmann-Schwinger Equation [Shuryak,Zahed, Brown ’04] - q-qT-Matrix Quark- Selfenergy  Selfconsistency Problem [Mannarelli+RR ’05] _ 5.) Resonances in QGP from Lattice QCD Lattice Q-Q Free Energy [Bielefeld Group ’04]

  22. 5.2 Lattice Spectral Functions vs. T-Matrix in QGP _ LQCD Spectral Function: Charmonium Q-QT-Matrix (ladder approx.) based on Lattice Potential [Datta etal ’03] [Mannarelli+RR ’05] • reasonable qualitative agreement  Evidence for Resonances in sQGP!? more studies required …

  23. [MPC, AMPT] 4.3 Single-e±at RHIC: Transport Calculations • Parton Cascade with fixed s(q,g-c), forward/isotropic, coalescence Elliptic Flow pT-Spectra • similar to Langevin; Xsection effect on pT-spectra moderate • no bottom [Zhang,Chen+Ko ‘05]

  24. Coordinate Space Diffusion • ‹x2› - ‹x›2 = Dx t ≈ (5 fm)2 • ~ fireball size at Tc c-Quark Drag and Diffusion Coefficients in QGP [van Hees+RR ’04] Thermalization Times pQCD “D” • substantially smaller for • resonances

  25. J/yExcitation Function [Grandchamp +RR ’03] • QGP-regeneration dominant • sensitive to: • mc* , (Ncc )2 ↔ rapidity, √s, A same net suppression at SPS + RHIC! 4.4 Charmonium in A-A SPSRHIC Pb(158AGeV)-Pb • QGP-suppression prevalent • no “jump” in theory [Grandchamp etal. ’03]

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