Heavy Quark Diffusion

in Heavy Ion Collisions

Ralf Rapp Cyclotron Institute + Physics Department

Texas A&M University College Station, USA

With: H. van Hees, V. Greco, M. Mannarelli

Conference on “Early Time Dynamics in Heavy Ion Collisions”McGill University (Montreal, Canada), 16.07.07

1.) Introduction: Heavy Quarks at RHIC• c, b quarks (more!?) sensitive to: - thermalization (low pT)

- energy loss (high pT)

- coalescence (int. pT?)

[PHENIX ’07]

Direct relation to other observables

• quarkonia: - interaction with c, b within bound state - regeneration →

• intermediate-mass dileptons: → e+e X competes with thermal (QGP) radiation

cc

cc

Diffusion/interactionsin sQGP at all pT

Hadronization (low pT?)

1.) Introduction Single-Electron Puzzle at RHIC

2.) Heavy-Quark Diffusion in (s)QGP Fokker-Planck Approach Resonance Model HQ and e± Spectra at RHIC

3.) Lattice-QCD Based Potential Approach In-Medium Heavy-Light Quark T-Matrix Transport Coefficients HQ RAA and v2

4.) Conclusions

Outline

pT [GeV]

RA

A =

(A

A)

/ (p

p)

[Gyulassy etal ’05]

[Armesto et al ’05]

• substantial collectivity• bottom “contamination”?

Elliptic FlowNuclear Modification Factor

• factor 4-5 suppression• elastic E-loss, pQCD?!

1.2 Expectations at RHIC• Radiative energy loss smaller for c+b quarks• Elastic interactions? • Collective flow? Heavy-quark diffusion? • experimental tool: electron spectra D,B → eX

c,b

?

QmDT

2

2

p

fD

p)pf(

tf

• Brownian

Motion:

scattering rate diffusion constant

2.) Heavy-Quark Diffusion in the QGP

Fokker Planck Eq.[Svetitsky ’88,…]Q

• e.g. T =300 MeV, s=0.4:therm~15 fm/c slow! (QGP ≤ 5 fm/c)

2.1.1 Perturbative QCD

g

c

dominated by t-channel gluon-ex.:

Microscopic Calculations of Diffusion:

q

c gT~,~ DD

scg

2

2elast

[Svetitsky ’88, Mustafa et al ’98, Molnar et al ’04,Zhang et al ’04, Hees+RR ’04, Teaney+Moore‘04]

k)p,k(wkdp 323 ),(

2

1 kpkwkdD

2.1.2 Open-Charm Resonances in QGP

h.c.2

v1 c)(

qG DDDcq L

• effective lagrangian with pseudo/scalar + axial/vector “D-mesons”

551 ,,,

“Light”-Quark Resonances

1.4Tc

[Asakawa+ Hatsuda ’03]

• parameters: mD=2GeV , GD , mc=1.5GeV, mq=0 • chiral (u,d) + HQ (c,b) symmetry

• resonance cross section isotropic, pQCD forward

[van Hees+ RR ’04]

c

“D”

c

_q

_q

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

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

2.3.2 The first 5 fm/c for Quark-v2 and -RAA Inclusive v2

• RAA built up earlier than v2

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

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]

2.5 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

2.5.2 Transport Properties of (s)QGP

• small spatial diffusion → strong coupling

Spatial Diffusion Coefficient ‹x2›-‹x›2=Dx·t, Dx=2d·(T/mQ)/Ds=Dx/2d

E.g. strongly coupled gauge theory (AdS/CFT): /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]

3.) Potential Scattering in sQGPLattice Q-Q Free Energy

TSUF QQQQ

QQQ mU 2

[BielefeldGroup ’04]

solve numerically

Q-q T-Matrix -

Applications

• → Schrödinger-Eq. → bound states (sQGP)

• scattering states + imaginary parts → Lippmann-Schwinger Eq.

QQU [Shuryak+ Zahed ’04, …]

[Mannarelli+RR ’05]

3.2 Charm-Light Cross Sections with lQCD-based Potential

Temperature Evolution Channel Decomposition

• interaction strength close to threshold • meson and diquark channels dominant

2

3.3 Friction Coefficients (Relaxation Rate): Lat-QCD vs. Resonance Model

• uncertainty in potential extraction from lattice QCD• potential scattering comparable to resonance model close to Tc

T ≈ 200 MeV T ≈ 250 MeV

3.4 Charm-Quark Spectra at RHIC

Nuclear Suppression Factor Elliptic Flow

• supports importance of nonperturbative effects• radiative (2↔3) scattering?

4.) Summary and Conclusions

• Heavy quarks probe the (s)QGP: strong suppression, collectivity

• Importance of elastic collisions

• Indications for nonperturbative interactions

• Supported by microscopic description: lQCD-based T-matrix,

scrutinize: lQCD correlators, U1 vs. F1, finite-T quark masses

• “Hadronic” correlations dominant (meson + diquark)

↔ natural connection to quark-coalescence at Tc [Ravagli+RR ’07]

• Impact on other observables: light sector, quarkonia, dileptons,…

3.2 Selfconsistent T-Matrix and Selfenergy [Mannarelli+RR ’05]

• assume mq(gluon)=0.1GeV

• transition from bound (1.2Tc) to resonance states! • quark-width ≈0.3GeV≈(2/3fm)-1 (≈ mass ↔ liquid!?) • colored states, equat. of state?

q-q T-Matrices -

Quark Self-

Energy

T=1.2Tc

T=1.5Tc

T=1.75Tc

T=1.5Tc

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