Nonperturbative Heavy-Quark Transport

at RHIC

Ralf Rapp Cyclotron Institute + Physics Department

Texas A&M University College Station, USA

With: H. van Hees (Giessen), D. Cabrera (Madrid), V. Greco (Catania), M. Mannarelli (Barcelona)

417th WE-Heraeus Seminar on “Characterization of the QGP with Heavy Quarks”

Physikzentrum Bad Honnef, 28.06.08

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:

- pT regimes connected via underlying HQ interaction?

- strong coupling: perturbation theory unreliable, resummations required

- simpler(?) problem: heavy quarkonia ↔ potential approach

- similar interactions operative for elastic heavy-quark scattering?

transport in QGP,hadronization

PRELIMINARY

Run-4

Run-7

resonance model[van Hees, Greco+RR ’05]

minimum-bias

1.) Introduction

2.) Heavy Quarkonia in QGP In-Medium T-Matrix with “lattice-QCD” potentials Charmonium Spectral + Correlation Functions In-Medium Mass and Width Effects

3.) Open Heavy Flavor in QGP Heavy-Light Quark T-Matrix HQ Selfenergies + Transport HQ and e± Spectra Implications for sQGP

4.) Conclusions

Outline

• Correlator: L=S,P

• Lippmann-Schwinger Equation

In-Medium Q-Q T-Matrix: -

2.) Quarkonia in QGP: Potential Models

)'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

- quasi-particle propagator:

- bound+scatt. states, 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, …, Shuryak+Zahed ’04, Mocsy+Petreczky‘05, Alberico et al. ‘06, Wong et al. ’07, Laine et al. ‘07 …]

2.2 “Lattice QCD-based” Potentials• free energy: F1(r,T) = U1(r,T) – T S1(r,T) potential?

V1(r,T) ≡ U1(r,T) U1(r=∞,T) or

[Cabrera+RR ’06; Petreczky+Petrov’04]

[Wong ’05; Kaczmarek et al ‘03]

V1=F1 , V1 = F1 +(1-U1

(much) smaller binding:

2.3 Charmonium Spectral Functions in QGP

In-medium mc* (U1 subtraction)

c

• screening reduces binding; large rescattering enhancement• c mass stabilized by decreasing mc*: m= 2mc* B

• c “survives” up to ~2.5Tc (c up to ~1.2Tc)

c

Fixed mc=1.7GeV, c=20MeV

• T-Matrix Approach with V1=U1

2.4 Charmonium Correlators in QGP

• in-medium mc* compensates

reduced binding: m= 2mc* - B

c

T-Matrix with U1

Lattice QCD[Cabrera +RR ‘06]

c[Datta et al ‘04]

[Aarts et al. ‘07]

]T/[)]T/([

)T,(GImd)T,(G2sinh

21cosh

0

])(/s/[)s(G QkkQQ24

2.5 Finite-Width Effects• c-quark width in propagator

• dominant process depends on BJ/ Lifetime

_[Grandchamp+RR ‘01]

• increasing width further stabilizes correlators

• note: = 100 MeV ~60% J/ destroyed in =2fm/c

• effect on correlator (mc=1.7GeV)

c

[Bhanot+Peskin ’79]

[Cabrera+RR ‘06]

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, Gossiaux et al. ’05, …]

• 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: “latt.-QCD 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• augment by magnetic interaction

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

Nf=0[Wong ’05]

Nf=2[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

• large charm-quark width c = -2 Imc ~ 250MeV close to Tc

Selfenergy Friction Coefficient

k|)p,k(T|Fkdp 23

• friction coefficients increase(!) with decreasing T→ Tc!

)kp(T)(fkd)p( a,LQqk

qa,LQ 3

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]

3.4 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)

• ~25% uncertainty due to differences in U1 potential

• suppression “early”, v2 “late”

3.5 Maximal “Interaction Strength” in the sQGP• potential-based description ↔ strongest interactions close to Tc

- minimum in /s at ~Tc

- hadronic correlations at Tc ↔ quark coalescence

• estimate 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

[RR+ van Hees ’08]

4.) Summary and Conclusions

• T-matrix approach with lQCD internal energy (UQQ): - S-wave charmonia survive up to Tdiss ≤ 2.5Tc - finite width can suppress J/ well below Tdiss!

• T-matrix 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 merges into quark coalescence at Tc

• Open problems + challenges: - potential approach/definition, heavy-quark masses - radiative processes, light-quark sector - observables (open charm/bottom, quarkonia, dileptons,…)

3.5.2 The first 5 fm/c for Charm-Quark v2 + RAA Inclusive v2

• RAA built up earlier than v2

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

2.2.3 In-Medium Charm-Quark Mass

• significant deviation only close to Tc

• cf. also [Petreczky QM ‘08]

[Kaczmarek+Zantow ’05]

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