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

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?

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

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]

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

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

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

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?

2.5 Comparison of Drag Coefficients

• pert. QCD with running coupling ~ AdS/CFT• increase with temperature except T-matrix (melting resonances)

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]

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

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

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

• RAA built up earlier than v2

Time Evolution

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]

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

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

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, …

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]

3.2.3 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

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

2.2.2 “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

3.2.4 Temperature Dependence of Charm-Quark Mass

• significant deviation only close to Tc

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

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]

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