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,(G 2sinh

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

pfDp

)pf(tf

• Brownian

Motion:

scattering rate diffusion constant

3.) 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 v12

1 Lparameters: 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,L

Qqkq

a,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 , 3.50.5 , 2.50.25,1.8

[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 DataSingle-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

pddNE 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