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Ralf Rapp Cyclotron Institute + Physics Department
Texas A&M University College Station, USA
International Conference on Strangeness in Quark Matter 2008
Tsinghua University Beijing (China), 07.10.08
Theory and Phenomenology of Heavy Flavor at RHIC
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1.) Introduction• The virtue of Heavy Quarks (Q=b,c): - “large” scale mQ >> QCD
- “factorization” even at low pT
- T/mQ << 1 → Brownian motion (elastic scattering)
- flavor conserved in hadronization → coalescence!?• Heavy Quarks as comprehensive probe: - connect pT regimes via underlying HQ interaction? - strong coupling: perturbation theory unreliable, resummations required - simpler(?) problem: heavy quarkonia ↔ potential approach - constraints for elastic heavy-quark scattering?
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1.) Introduction
2.) Heavy-Quark Diffusion in QGP Fokker-Planck Equation Diffusion coefficients: - peturbative QCD - lattice-QCD based T-matrix - AdS/CFT
3.) Heavy-Flavor Spectra at RHIC Bulk Evolution Langevin Simulations + Quark Spectra e± Spectra and Flow
4.) Viscosity and “sQGP”
5.) Conclusions
Outline
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QmDT
2
2
pfDp
)pf(tf
• Brownian
Motion:
scattering rate diffusion coefficient
2.) Heavy Quarks in the QGPFokker Planck Eq.
[Svetitsky ’88,…]Q
k)p,k(wkdp 323 ),(
21 kpkwkdD
• pQCD elastic scattering: -1= therm ≥20 fm/c slow
q,g
c
Microscopic Calculations of Diffusion
2
2elast
D
scg ~
[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
c)(qG DDDcq 2v1 L
parameters: mD , GD[van Hees+RR ’04]
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2.2 Potential Scattering using Lattice QCD
Determination of Potential• fit lattice Q-Q free energy• check on : no over-binding of charmonia at ~Tc
(+ lat-QCD correlators)
QQQQQQQQQQ U)r(U)r(V,TSUF
• T-matrix for Q-q scatt. in QGP
• Casimir scaling for color chan. a• GqQ: Q-q propagator [Mannarelli+RR ’05]
aLQq
aL
aL
aL TGVdkkVT 2
[quench. lat-QCD, Wong ’05]
[2-flavor lat-QCD, Shuryak+Zahed ’04]
QQV
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2.2.2 Charm-Light QuarkT-Matrix + Drag Coefficient
• supports effective resonance model: S-wave mesons and diquarks up to 1.2-1.5 Tc , -1 ≈ 7 fm/c• P-waves and color a=6, 8 suppressed• “collisional dissociation” [Adil+Vitev ‘06] ↔ vacuum potential
[van Hees,Mannarelli,Greco+RR ’07]• based on lattice-QCD internal energy
T-Matrix Thermalization Rate
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2.3 AdS/CFT-QCD Correspondence
[Gubser ‘07]
pdtdp 2
2 SYMc
CFT/ADS Tm
cCFT/ADS m
T)..(2
5012
• match energy density (d.o.f = 120 vs. ~40) and coupling constant (heavy-quark potential) to QCD
3-momentum independent
[Herzog et al, Gubser ‘06]
≈ (4-2 fm/c)-1 at T=180-250 MeV
Lat-QCD
TQCD ~ 250 MeV
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2.4 Perturbative QCD with Running Coupling
[Peshier ‘07]
• run QCD coupling to mD ~ gT rather than 2T
[Gossiaux+ Aichelin ‘08]
• factor ~10 increase in heavy-quark drag coefficient• perturbative regime?
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2.5 Comparison of Drag Coefficients
• pert. QCD with running coupling ~ AdS/CFT• increase with temperature except T-matrix (melting resonances)
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3.) Phenomenology at RHIC• Medium evolution - hydrodynamics or parameterizations thereof - realistic bulk-v2 (~5-6%)
- stop evolution after QGP; hadronic phase?
• Hadronization - fragmentation: c → D + X - coalescence: c + q → D, adds momentum and v2
- chemistry (e.g. c enhancement)
• Semileptonic electron decays - approx. conserve v2 and RAA of parent meson - charm/bottom composition in p-p
[Hirano et al ’06]
[Martinez et al, Sorensen et al ‘07]
[Greco et al, Dong et al ‘04]
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3.1 HQ Langevin Simulations: Hydro vs. Fireball Elastic pQCD + Hydrodynamics [Moore+Teaney ’05]
• b=6.5 fm Tc=165 MeV ≈ 9 fm/c
•Tc=180 MeV bulk-v2 ~5.5%QGP ≈ 5 fm/c
Resonance Model + Expanding Fireball
[van Hees,Greco +RR ’05]
Ds (2T) ≈ 6
v2max ~ 5-6%RAA~ 0.3
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3.2 Model Predictions vs. PHENIX DataSingle-e± Spectra [PHENIX ’06]
• coalescence increases both RAA and v2
• pQCD radiative E-loss with upscaled transport coeff.
• Langevin with elastic pQCD + resonances + coalescence
• Langevin with upscaled pQCD elastic
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3.2.2 The first 5 fm/c for Charm-Quark v2 + RAA Inclusive v2
• RAA built up earlier than v2
Time Evolution
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3.3 T-Matrix Approach vs. e± Spectra at RHIC
• RAA early, v2 “late” ↔ max. int. strength at ~Tc
• hadronic correlations at Tc ↔ quark coalescence
[van Hees,Mannarelli,Greco+RR ’07]
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3.4 Hydrodynamic Evolution + “AdS/CFT” Drag• 10-20% central, ~5fm/c (middle of mixed phase) [Akamatsu,Hatsuda
+Hirano ’08]
Further discussion: • running s, validity of FP → [P. Gossiaux, Wednesday] • charm correlations → [X. Zhu, Wednesday]
Charm-Quark RAA Charm-Quark v2
• ~30-50% larger v2, RAA at b=7fm, f0=0 → v2max =4-5% Ds(2T) ≈ 6
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4.) Maximal “Interaction Strength” in the sQGP• potential-based description ↔ strongest interactions close to Tc
- consistent with minimum in /s at ~Tc
- strong hadronic correlations at Tc ↔ quark coalescence • semi-quantitative estimate for diffusion constant:
[Lacey et al. ’06]
weak coupl. s ≈n <p> tr=1/5 T Ds
strong coupl.s≈ Ds= 1/2 T Ds
s≈ close toTc
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5.) Summary and Conclusions
• “Different” approaches to Heavy-Quark diffusion related pert-QCD running s T-matrix + lQCD pot AdS/CFT
• Constraints essential (e.g. HQ potential, lattice correlators)
• Q-q T-matrix with lQCD motivated potential: - “hadronic” correlations close to Tc ↔ quark coalescence - max. int. strength at ~Tc ↔ min. /s !? gluons? U, F or …?
• Radiative diffusion? light-quark sector? …
• RHIC non-photonic e± Ds (2T) ≈ 4-6 - v2 - RAA correlation revealing (coalescence? kt-broad.? ) - scrutinize medium evolution, Fokker-Planck, … - D/B separation, correlations, quarkonia, …
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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
pT [GeV]
Nuclear Modification Factor Elliptic Flow
pT [GeV]
[Wiedemann et al.’05,Wicks et al.’06, Vitev et al.’06, Ko et al.’06]
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3.2.3 Charm-Quark Selfenergy + Transport
• charm quark widths c = -2 Imc ~ 250MeV close to Tc
• friction coefficients increase(!) with decreasing T→ Tc!
Selfenergy Friction Coefficient)kp(T)(fkd)p( a,L
Qqkq
a,LQ 3 k|)p,k(T|Fkdp 23
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4.) Constitutent-Quark Number Scaling of v2
• CQNS difficult to recover with local v2,q(p,r)
• “Resonance Recombination Model”: resonance scatt. q+q → M close to Tc using Boltzmann eq.
• quark phase-space distrib. from relativistic Langevin, hadronization at Tc:
[Ravagli+RR ’07]
[Molnar ’04, Greco+Ko ’05, Pratt+Pal ‘05]
• energy conservation• thermal equil. limit • interaction strength adjusted to v2
max ≈7%• no fragmentation• KT scaling at both quark and meson level
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2.2.2 “Lattice QCD-based” Potentials• accurate lattice “data” for free energy: F1(r,T) = U1(r,T) – T S1(r,T)• V1(r,T) ≡ U1(r,T) U1(r=∞,T)
[Cabrera+RR ’06; Petreczky+Petrov’04]
[Wong ’05; Kaczmarek et al ‘03]
• (much) smaller binding for V1=F1 , V1 = (1-U1 + F1
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3.2.4 Temperature Dependence of Charm-Quark Mass
• significant deviation only close to Tc
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3.6 Heavy-Quark + Single-e± Spectra at LHC
• harder input spectra, slightly more suppression RAA similar to RHIC
• relativistic Langevin simulation in thermal fireball background• resonances inoperative at T>2Tc , coalescence at Tc
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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 pT~2.5GeV
Fragmentation only
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• less suppression and more v2 • anti-correlation RAA ↔ v2 from coalescence (both up) • radiative E-loss at high pT?!
2.4.2 Single-e± at RHIC: Resonances + Q-q Coalescence
frag2
2333
)p(f)p(f|)q(|qd)(
pdg
pddNE ccqqDD
D fq from , K
Nuclear Modification Factor Elliptic Flow
[Greco et al ’03]
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2.1.3 Thermal Relaxation of Heavy Quarks in QGP
• factor ~3 faster with resonance interactions!
Charm: pQCD vs. Resonances
pQCD
“D”
• ctherm ≈ QGP ≈ 3-5 fm/c
• bottom does not thermalize
Charm vs. Bottom