Heavy-Quark Diffusion, Flow and Recombination at RHIC

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Heavy-Quark Diffusion, Flow and Recombination at RHIC 4/17/2017 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

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

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

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]

Outline 2.) Baseline Spectra in p-p, d-Au 4/17/2017 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

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

3.) Heavy-Quark Elastic Scattering in the QGP Brownian Motion: Fokker Planck Eq. Q [Svetitsky ’88,…] scattering rate diffusion constant e.g. T =400 MeV, as=0.4: ttherm~10 fm/c slow! (tQGP ≤ 5 fm/c) 3.1 Perturbative QCD g c dominated by t-channel gluon-ex.: Microscopic Calculation of Diffusion: q [Svetitsky ’88, Mustafa et al ’98, Molnar et al ’04 Zhang et al ’04, Hees+RR ’04, Teaney+Moore‘04]

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

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

4. ) Heavy-Quark and Electron Spectra at RHIC 4 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 bulk v0 , v2 simulate HQ paths with drag and diffusion in QGP [van Hees, Greco+RR ’05] Nuclear Modification Factor resonance effects large bottom much less affected characteristic “leveling-off” factor 3-4 from resonances Elliptic Flow

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 large suppression from resonances, elliptic flow underpredicted (?) bottom sets in at pT~2.5GeV Fragmentation only

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

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

5.) J/y pT-Spectra in Au-Au at RHIC Recombination via Quark Coalescence at Tc Zero vs. Maximal Reinteraction “Realistic” Input from Langevin J/y Elliptic Flow largest sensitivity! [Greco,Ko+RR ’04] 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

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)

2.4.1 Langevin-Simul. at RHIC: Heavy-Quark RAA Charm-pQCD (as, mD=1.5T) Resonances vs. pQCD 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]

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

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]

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

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 in pt!?

5.) Resonances in QGP from Lattice QCD _ Lattice Q-Q Free Energy Applications → Schröd.-Eq. → bound states (sQGP)! scattering states + imaginary parts: Lippmann-Schwinger Equation [Shuryak,Zahed, Brown ’04] [Bielefeld Group ’04]  Selfconsistency Problem [Mannarelli+RR ’05] q-q T-Matrix - Quark- Selfenergy

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

4.3 Single-e± at RHIC: Transport Calculations [MPC, AMPT] 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]

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

4.4 Charmonium in A-A J/y Excitation Function 4/17/2017 SPS RHIC [Grandchamp +RR ’03] J/y Excitation Function same net suppression at SPS + RHIC! Pb(158AGeV)-Pb QGP-regeneration dominant sensitive to: mc* , (Ncc )2 ↔ rapidity, √s, A QGP-suppression prevalent no “jump” in theory [Grandchamp etal. ’03]