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
