Download presentation
Presentation is loading. Please wait.
Published bySarah Flowers Modified over 8 years ago
1
Heavy Flavor in the sQGP Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA With: H. van Hees, D. Cabrera (Madrid), X. Zhao, V. Greco (Catania), M. Mannarelli (Barcelona) 24. Winter Workshop on Nuclear Dynamics South Padre Island (Texas), 09.04.08
2
1.) Introduction Empirical evidence for sQGP at RHIC: - thermalization / low viscosity (low p T ) - energy loss / large opacity (high p T ) - quark coalescence (intermed. p T ) Heavy Quarks as comprehensive probe: - connect p T regimes via underlying HQ interaction? - strong coupling: perturbation theory becomes unreliable, resummations required - simpler(?) problem: heavy quarkonia ↔ potential approach - similar interactions operative for elastic heavy-quark scattering? transport in QGP, hadronization
3
1.) Introduction 2.) Heavy Quarkonia in QGP Charmonium Spectral + Correlation Functions In-Medium T-Matrix with “lattice-QCD” potential 3.) Open Heavy Flavor in QGP Heavy-Light Quark T-Matrix HQ Selfenergies + Transport HQ and e ± Spectra Implications for sQGP 4.) Constituent-Quark Number Scaling 5.) Conclusions Outline
4
2.1 Quarkonia in Lattice QCD accurate lattice “data” for Euclidean Correlator S-wave charmonia little changed to ~2T c [Iida et al ’06, Jakovac et al ’07, Aarts et al ’07] cc cc [Datta et al ‘04] direct computation of Euclidean Correlation Fct. spectral function
5
Correlator: L=S,P Lippmann-Schwinger Equation In-Medium Q-Q T-Matrix: - 2.2 Potential-Model Approaches for Spectral Fcts. [Mannarelli+RR ’05,Cabrera+RR ‘06] - 2-quasi-particle propagator: - bound+scatt. states, nonperturbative threshold effects (large) bound state + free continuum model too schematic for broad / dissolving states 2 J/ ’’ cont. E thr [Karsch et al. ’87, …, Wong et al. ’05, Mocsy+Petreczky ‘06, Alberico et al. ‘06, …]
6
2.2.2 “Lattice QCD-based” Potentials accurate lattice “data” for free energy: F 1 (r,T) = U 1 (r,T) – T S 1 (r,T) V 1 (r,T) ≡ U 1 (r,T) U 1 (r=∞,T) [Cabrera+RR ’06; Petreczky+Petrov’04] [Wong ’05; Kaczmarek et al ‘03] (much) smaller binding for V 1 =F 1, V 1 = (1- U 1 + F 1
7
2.3 Charmonium Spectral Functions in QGP within T-Matrix Approach (lattice U 1 Potential ) In-medium m c * (U 1 subtraction) cc gradual decrease of binding, large rescattering enhancement c, J/ survive until ~2.5T c, c up to ~1.2T c cc Fixed m c =1.7GeV
8
2.4 Charmonium Correlators above T c lattice U 1 -potential, in-medium m c *, zero-mode G zero ~ T (T) cc T-Matrix Approach Lattice QCD [Cabrera+RR in prep.] [Aarts et al. ‘07] qualitative agreement c1
9
Brownian Motion: scattering rate diffusion constant 3.) Heavy Quarks in the QGP Fokker Planck Eq. [Svetitsky ’88,…] Q pQCD elastic scattering: -1 = therm ≥20 fm/c slow q,g c Microscopic Calculations of Diffusion: [Svetitsky ’88, Mustafa et al ’98, Molnar et al ’04, Zhang et al ’04, Hees+RR ’04, Teaney+Moore‘04] D-/B-resonance model: -1 = therm ~ 5 fm/c c “D” c _ q _ q parameters: m D, G D recent development: lQCD-potential scattering [van Hees, Mannarelli, Greco+RR ’07]
10
3.2 Potential Scattering in sQGP Determination of potential fit lattice Q-Q free energy currently significant uncertainty T-matrix for Q-q scatt. in QGP Casimir scaling for color chan. a in-medium heavy-quark selfenergy: [Mannarelli+RR ’05] [Wong ’05] [Shuryak+ Zahed ’04]
11
3.2.2 Charm-Light T-Matrix with lQCD-based Potential meson and diquark S-wave resonances up to 1.2-1.5T c P-waves and (repulsive) color-6, -8 channels suppressed [van Hees, Mannarelli, Greco+RR ’07] Temperature Evolution + Channel Decomposition
12
3.2.3 Charm-Quark Selfenergy + Transport charm quark widths c = -2 Im c ~ 250MeV close to T c friction coefficients increase(!) with decreasing T→ T c ! Selfenergy Friction Coefficient
13
3.3 Heavy-Quark Spectra at RHIC T-matrix approach ≈ effective resonance model other mechanisms: radiative (2↔3), … relativistic Langevin simulation in thermal fireball background p T [GeV] Nuclear Modification Factor Elliptic Flow p T [GeV] [Wiedemann et al.’05,Wicks et al.’06, Vitev et al.’06, Ko et al.’06]
14
3.5 Single-Electron Spectra at RHIC heavy-quark hadronization: coalescence at T c [Greco et al. ’04] + fragmentation hadronic correlations at T c ↔ quark coalescence! charm bottom crossing at p T e ~ 5GeV in d-Au (~3.5GeV in Au-Au) ~30% uncertainty due to lattice QCD potential suppression “early”, v 2 “late”
15
3.6 Maximal “Interaction Strength” in the sQGP potential-based description ↔ strongest interactions close to T c - consistent with minimum in /s at ~T c - strong hadronic correlations at T c ↔ quark coalescence semi-quantitative estimate for diffusion constant: [Lacey et al. ’06] weak coupl. s ≈ n tr =1/5 T D s strong coupl. s ≈ D s = 1/2 T D s s ≈ close to T c
16
4.) Constitutent-Quark Number Scaling of v 2 CQNS difficult to recover with local v 2,q (p,r) “Resonance Recombination Model”: resonance scatt. q+q → M close to T c using Boltzmann eq. quark phase-space distrib. from relativistic Langevin, hadronization at T c : [Ravagli+RR ’07] [Molnar ’04, Greco+Ko ’05, Pratt+Pal ‘05] energy conservation thermal equil. limit interaction strength adjusted to v 2 max ≈ 7% no fragmentation K T scaling at both quark and meson level
17
5.) Summary and Conclusions T-matrix approach with lQCD internal energy (U QQ ): S-wave charmonia survive up to ~2.5T c, consistent with lQCD correlators + spectral functions T-matrix approach for (elastic) heavy-light scattering: large c-quark width + small diffusion “Hadronic” correlations dominant (meson + diquark) - maximum strength close to T c ↔ minimum in /s !? - naturally merge into quark coalescence at T c Observables: quarkonia, HQ suppression+flow, dileptons,… Consequences for light-quark sector? Radiative processes? Potential approach?
18
3.5.2 The first 5 fm/c for Charm-Quark v 2 + R AA Inclusive v 2 R AA built up earlier than v 2
19
3.2.4 Temperature Dependence of Charm-Quark Mass significant deviation only close to T c
20
2.3.3 HQ Langevin Simulations: Hydro vs. Fireball [van Hees,Greco+RR ’05] Elastic pQCD (charm) + Hydrodynamics s, g 1, 3.5 0.5, 2.5 0.25,1.8 [Moore+Teaney ’04] T c =165MeV, ≈ 9fm/c gQ ~ ( s / D ) 2 s and D ~gT independent ( D ≡1.5T) s =0.4, D =2.2T ↔ D(2 T) ≈ 20 hydro ≈ fireball expansion
21
3.6 Heavy-Quark + Single-e ± Spectra at LHC harder input spectra, slightly more suppression R AA similar to RHIC relativistic Langevin simulation in thermal fireball background resonances inoperative at T>2T c, coalescence at T c
22
direct ≈ regenerated (cf. ) sensitive to: c therm, m c *, N cc 2.5 Observables at RHIC: Centrality + p T Spectra [X.Zhao+RR in prep] [Yan et al. ‘06] update of ’03 predictions: - 3-momentum dependence - less nucl. absorption + c-quark thermalization
23
3.2 Model Comparisons to Recent PHENIX Data Single-e ± Spectra [PHENIX ’06] coalescence essential for consistent R AA and v 2 other mechanisms: 3-body collisions, … [Liu+Ko’06, Adil+Vitev ‘06] pQCD radiative E-loss with 10-fold upscaled transport coeff. Langevin with elastic pQCD + resonances + coalescence Langevin with 2-6 upscaled pQCD elastic
24
3.2.2 Transport Properties of (s)QGP small spatial diffusion → strong coupling Spatial Diffusion Coefficient: ‹x 2 ›-‹x› 2 ~ D s ·t, D s ~ 1/ E.g. AdS/CFT correspondence: /s=1/4 , D HQ ≈1/2 T resonances: D HQ ≈4-6/2 T, D HQ ~ /s ≈ (1-1.5)/ Charm-Quark Diffusion Viscosity-to-Entropy: Lattice QCD [Nakamura +Sakai ’04]
25
2.4 Single-e ± at RHIC: Effect of Resonances hadronize output from Langevin HQs ( -fct. fragmentation, coalescence) semileptonic decays: D, B → e+ +X large suppression from resonances, elliptic flow underpredicted (?) bottom sets in at p T ~2.5GeV Fragmentation only
26
less suppression and more v 2 anti-correlation R AA ↔ v 2 from coalescence (both up) radiative E-loss at high p T ?! 2.4.2 Single-e ± at RHIC: Resonances + Q-q Coalescence f q from , K Nuclear Modification Factor Elliptic Flow [Greco et al ’03]
27
Relativistic Langevin Simulation: stochastic implementation of HQ motion in expanding QGP-fireball “hydrodynamic” evolution of bulk-matter T, v 2 2.3 Heavy-Quark Spectra at RHIC [van Hees,Greco+RR ’05] Nuclear Modification Factor resonances → large charm suppression+collectivity, not for bottom v 2 “leveling off ” characteristic for transition thermal → kinetic Elliptic Flow
28
2.1.3 Thermal Relaxation of Heavy Quarks in QGP factor ~3 faster with resonance interactions! Charm: pQCD vs. Resonances pQCD “D” c therm ≈ QGP ≈ 3-5 fm/c bottom does not thermalize Charm vs. Bottom
29
5.3.2 Dileptons II: RHIC low mass: thermal! (mostly in-medium ) connection to Chiral Restoration: a 1 (1260)→ , 3 int. mass: QGP (resonances?) vs. cc → e + e - X (softening?) - [RR ’01] [R. Averbeck, PHENIX] QGP
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.