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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 - PowerPoint PPT Presentation
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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 DynamicsSouth Padre Island (Texas), 09.04.08
1.) Introduction
• Empirical evidence for sQGP at RHIC: - thermalization / low viscosity (low pT)
- energy loss / large opacity (high pT)
- quark coalescence (intermed. pT)
• Heavy Quarks as comprehensive probe:
- connect pT 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
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
2.1 Quarkonia in Lattice QCD
]T/[)]T/([
)T,(d)T,(G2sinh
21cosh
0
• accurate lattice “data” for Euclidean Correlator
• S-wave charmonia little changed to ~2Tc [Iida et al ’06, Jakovac et al ’07, Aarts et al ’07]
c
c
[Datta et al ‘04]
• direct computation of Euclidean Correlation Fct.
spectral function
• Correlator: L=S,P
• Lippmann-Schwinger Equation
In-Medium Q-Q T-Matrix: -
2.2 Potential-Model Approaches for Spectral Fcts.
)'q,k;E(T)k,E(G)k,q(Vdkk)'q,q(V)'q,q;E(T LQQLLL02
[Mannarelli+RR ’05,Cabrera+RR ‘06]
000QQLQQQQL GTGG)E(G
- 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.
Ethr
])(s/[)s(G QQkkQQ20 24
[Karsch et al. ’87, …, Wong et al. ’05, Mocsy+Petreczky ‘06, Alberico et al. ‘06, …]
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
2.3 Charmonium Spectral Functions in QGP withinT-Matrix Approach (lattice U1 Potential)
In-medium mc* (U1 subtraction)
c
• gradual decrease of binding, large rescattering enhancement• c , J/ survive until ~2.5Tc , c up to ~1.2Tc
c
Fixed mc=1.7GeV
2.4 Charmonium Correlators above Tc
• lattice U1-potential, in-medium mc*, zero-mode Gzero ~ T(T)
c
T-Matrix Approach Lattice QCD[Cabrera+RR in prep.] [Aarts et al. ‘07]
• qualitative agreement
c1
QmDT
2
2
p
fD
p)pf(
tf
• Brownian
Motion:
scattering rate diffusion constant
3.) Heavy Quarks in the QGP
Fokker Planck Eq.[Svetitsky ’88,…]Q
k)p,k(wkdp 323 ),(
2
1 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 v1
21 L
parameters: mD , GD
• recent development: lQCD-potential scattering [van Hees, Mannarelli, Greco+RR ’07]
3.2 Potential Scattering in sQGP
Determination of potential• fit lattice Q-Q free energy
• currently significant uncertainty
QQQQQQQQQQ U)r(U)r(V,TSUF
• T-matrix for Q-q scatt. in QGP
• Casimir scaling for color chan. a
• in-medium heavy-quark selfenergy:
[Mannarelli+RR ’05]
aLQq
aL
aL
aL TGVdkVT 0
[Wong ’05][Shuryak+Zahed ’04]
3.2.2 Charm-Light T-Matrix with lQCD-based Potential
• meson and diquark S-wave resonances up to 1.2-1.5Tc
• P-waves and (repulsive) color-6, -8 channels suppressed
[van Hees, Mannarelli, Greco+RR ’07]
Temperature Evolution + Channel Decomposition
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,LQqk
qa,LQ 3 k|)p,k(T|Fkdp 23
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]
3.5 Single-Electron Spectra at RHIC
• heavy-quark hadronization: coalescence at Tc [Greco et al. ’04]
+ fragmentation
• hadronic correlations at Tc ↔ quark coalescence!
• charm bottom crossing at pT
e ~ 5GeV in d-Au (~3.5GeV in Au-Au)
• ~30% uncertainty due to lattice QCD potential
• suppression “early”, v2 “late”
3.6 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
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
5.) Summary and Conclusions
• T-matrix approach with lQCD internal energy (UQQ): S-wave charmonia survive up to ~2.5Tc, 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 Tc ↔ minimum in /s !? - naturally merge into quark coalescence at Tc
• Observables: quarkonia, HQ suppression+flow, dileptons,…
• Consequences for light-quark sector? Radiative processes? Potential approach?
3.5.2 The first 5 fm/c for Charm-Quark v2 + RAA Inclusive v2
• RAA built up earlier than v2
3.2.4 Temperature Dependence of Charm-Quark Mass
• significant deviation only close to Tc
2.3.3 HQ Langevin Simulations: Hydro vs. Fireball
[van Hees,Greco+RR ’05]
Elastic pQCD (charm) + Hydrodynamicss , g
1 , 3.5
0.5 , 2.5
0.25,1.8
[Moore+Teaney ’04]
• Tc=165MeV, ≈ 9fm/c • gQ ~ (s/D)2
s and D~gT independent (D≡1.5T)
• s=0.4, D=2.2T ↔ D(2T) ≈ 20 hydro ≈ fireball expansion
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
• direct ≈ regenerated (cf. )• sensitive to: c
therm , mc* , Ncc
2.5 Observables at RHIC: Centrality + pT Spectra
[X.Zhao+RR in prep]
[Yan et al. ‘06]
• update of ’03 predictions: - 3-momentum dependence - less nucl. absorption + c-quark thermalization
3.2 Model Comparisons to Recent PHENIX Data
Single-e± Spectra [PHENIX ’06]
• coalescence essential for consistent RAA and v2
• 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
3.2.2 Transport Properties of (s)QGP
• small spatial diffusion → strong coupling
Spatial Diffusion Coefficient: ‹x2›-‹x›2 ~ Ds·t , Ds ~ 1/
• E.g. AdS/CFT correspondence: /s=1/4, DHQ≈1/2T
resonances: DHQ≈4-6/2T , DHQ ~ /s ≈ (1-1.5)/
Charm-Quark Diffusion Viscosity-to-Entropy: Lattice QCD[Nakamura +Sakai ’04]
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
• 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
pd
dNE ccqqDD
D fq from , K
Nuclear Modification Factor Elliptic Flow
[Greco et al ’03]
Relativistic Langevin Simulation: • stochastic implementation of HQ motion in expanding QGP-fireball• “hydrodynamic” evolution of bulk-matter T , v2
2.3 Heavy-Quark Spectra at RHIC [van Hees,Greco+RR ’05]
Nuclear Modification Factor
• resonances → large charm suppression+collectivity, not for bottom • v2 “leveling off ” characteristic for transition thermal → kinetic
Elliptic Flow
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
5.3.2 Dileptons II: RHIC
• low mass: thermal! (mostly in-medium )• connection to Chiral Restoration: a1 (1260)→ , 3• int. mass: QGP (resonances?) vs. cc → e+e-X (softening?)-
[RR ’01]
[R. Averbeck, PHENIX]
QGP