1. Heavy-Quark Diffusion, Flow and Recombination at RHIC
4/17/2017
Ralf Rapp
Cyclotron Institute
+ Physics Department
Texas A&M University
College Station, USA
With: H. van Hees, V. Greco (…)
Strangeness in Quark Matter Conference 2006
Los Angeles,

2. 1.) Introduction-I: The Virtue of HQ’s in URHICs
, production follows
N-N collision-scaling
 Valuable Probe of Medium:
[PHENIX ’04]
distinguishable from gluons
mass + charge-dependence of jet quenching (induced radiation?)
elastic rescattering, (approach to) thermalization, collective flow:
pQCD?! sQGP?!
coalescence at low(er) pT:
cq→ D (even in pp), cc → Y

3. 1.2 Intro-II: pQCD Jet Quenching
[Armesto et al ’05]
[Gyulassy et al ’05]
Challenges:
enough quenching? (upscaled transport coefficient)
Gluon Plasma (maximal color charge)
pions over-quenched (pT ≤ 4GeV)
“drag” on heavy quarks → flow
consistency v2 ↔ RAA

4. 1.3 Intro-III: Single-e± Elliptic Flow?
[Armesto
et al ’05]
jet-quench
[Djordjevic
et al ’04]
coalescence assuming v2c=v2q vs jet quenching
Challenges:
dynamical origin of re-interactions:
radiative vs. elastic scattering, 3↔3
bottom contribution
transition soft – intermediate - hard …
[Liu+Ko’06]

5. Outline 2.) Baseline Spectra in p-p, d-Au
4/17/2017
2.) Baseline Spectra in p-p, d-Au
• Charm vs. Bottom
3.) Heavy-Quark Elastic Scattering in QGP
• Brownian Motion and Thermal Relaxation
• pQCD vs. Resonances
4.) Heavy-Quark and Electron Spectra at RHIC
• Langevin Simulation, Hadronization
• RAA and v2
5.) Heavy Quarkonia
• Charmonium pT-Spectra
6.) Summary

6. 2.) Heavy-Flavor Baseline Spectra at RHIC
Semileptonic Electrons
D-Mesons
bottom crossing at 5GeV !? (~pQCD [Cacciari et al ’05])
strategy: fix charm with D-mesons, adjust bottom in e±-spectra

7. 3.) Heavy-Quark Elastic Scattering in the QGP
Brownian
Motion:
Fokker Planck Eq. Q
[Svetitsky ’88,…]
scattering rate diffusion constant
e.g. T =400 MeV, as=0.4: ttherm~10 fm/c slow! (tQGP ≤ 5 fm/c)
3.1 Perturbative QCD g c
dominated by
t-channel gluon-ex.:
Microscopic Calculation of Diffusion: q
[Svetitsky ’88, Mustafa et al ’98, Molnar et al ’04
Zhang et al ’04, Hees+RR ’04, Teaney+Moore‘04]

8. 3.2 Open-Charm Resonances in QGP
“D” _ q
“Light”-Quark Resonances
[van Hees+
RR ’04]
1.4Tc
effective model with pseudo/scalar
+ axial/vector “D-mesons”
[Asakawa+
Hatsuda ’03]
no. of D-states (chiral+HQ symm.):
8 per u and d, 4 for s
resonance cross section isotropic,
pQCD forward
parameters: mD=2GeV , GD ,
mc=1.5GeV, mq=0

9. 3.3 Heavy-Quark Thermalization Times in QGP
Charm: pQCD vs. Resonances
tcrelax ≥ Dt(T>0.25GeV) ≈ 1fm/c
tbottom ≈ 3 tcharm
Charm vs. Bottom
pQCD
“D”
decreased by factor ~3
with resonances

10. 4. ) Heavy-Quark and Electron Spectra at RHIC 4
4.) Heavy-Quark and Electron Spectra at RHIC 4.1 Relativistic Langevin Simulations for HQs
initialize heavy quarks (Glauber) in elliptic QGP fireball
realistic time evolution of bulk v0 , v2
simulate HQ paths with drag and diffusion in QGP
[van Hees,
Greco+RR ’05]
Nuclear Modification Factor
resonance effects large
bottom much less affected
characteristic “leveling-off”
factor 3-4 from resonances
Elliptic Flow

11. 4.2.1 Single-e± at RHIC: Effect of Resonances
hadronize output from Langevin HQs (d-fct. fragmentation, coalescence)
semileptonic decays: D, B → e+n+X
large suppression from resonances, elliptic flow underpredicted (?)
bottom sets in at pT~2.5GeV
Fragmentation only

12. 4.2.2 Single-e± at RHIC: Resonances + Q-q Coalescence
fq from p, K
[Greco et al ’03]
Nuclear Modification Factor
Elliptic Flow
less suppression and more v2 for pT ~ 1-5 GeV
anti-correlation RAA ↔ v2 from coalescence (both up)
radiative E-loss at pT ≥ 5GeV ?!

13. 4.2.3 Formfactor Effect on Resonance Formation
“D” _ q
replace (renormalized) point
vertex by formfactor (L=1GeV)
Charm-Quark RAA
Charm-Quark v2
formfactor affects higher pT
rather far from equilibrium

14. 5.) J/y pT-Spectra in Au-Au at RHIC
Recombination via Quark Coalescence at Tc
Zero vs. Maximal Reinteraction “Realistic” Input from Langevin
J/y Elliptic Flow
largest sensitivity!
[Greco,Ko+RR ’04]
pQCD scatt.
resonance scatt.
[Greco,van Hees+RR in prep]
total yields different by up to factor 3
rather sensitive to radial flow (bt,max= )
Cronin effect for quantitative RAA

15. 6.) Summary “D”-/”B”- resonances in sQGP (elastic scattering)
- accelerate c-/b-quark thermalization (factor ~3 over pQCD)
- coalescence increases both v2 and RAA (consistency!)
existence of resonances (q-Q, q-q) to be scrutinized
complete treatment incl. elastic + radiative processes
- discriminate with angular correlations (tagged Q-jets)?
pQCD energy loss ↔ Gluon-Plasma, color charge
resonances ↔ Quark-Gluon Plasma, nonpert. dynamics
consistency with / impact on: - light-parton spectra
- quarkonia (v2!)
- IM dileptons (vs. QGP radiation)

16. 2.4.1 Langevin-Simul. at RHIC: Heavy-Quark RAA
Charm-pQCD (as, mD=1.5T)
Resonances vs. pQCD
as , g
1 , 3.5
0.5 , 2.5
0.25,1.8
hydro with Tc=165MeV, t ≈ 9fm/c
as and Debye mass independent
expanding fireball ≈ hydro
pQCD elastic scatt. moderate
resonance effects substantial
[Moore and Teaney ’04]
[van Hees,Greco+RR ’05]

17. 4.1.2 HQ Langevin-Simulations with Hydro + pQCD
Charm-pQCD cross sections with variable as , mD=1.5T fix
Hydrodynamic bulk evolution with Tc=165MeV, t ≈ 9fm/c
Nuclear Modification
Elliptic Flow
as , g
1 , 3.5
0.5 , 2.5
0.25,1.8
correlation: small RAA ↔ large v2
realistic coupling / decoupling ?
[Moore+Teaney ’04]

18. 4.2.3 Semi-Central e± RAA at RHIC
Elliptic QGP fireball with D-/B-resonances, coal./frag. and decay
Fragmentation only
Coal. + Frag.
coalescence favored
[van Hees,Greco
+RR ’05]

19. 4.2.3 Light-Parton Jet-Quenching RHIC
pion quenching in pQCD
[Armesto et al.]
problems below ~4-5GeV

20. 3.4.3 Scrutinizing Charmonium Regeneration II:
J/y Elliptic Flow
Suppression only
Thermal Coalescence at Tc
[Greco etal ’04]
[Wang+Yuan ’02]
MB Au-Au
factor ~5 different!
transition in pt!?

21. 5.) Resonances in QGP from Lattice QCD_
Lattice Q-Q Free Energy
Applications
→ Schröd.-Eq.
→ bound states (sQGP)!
scattering states + imaginary parts:
Lippmann-Schwinger Equation
[Shuryak,Zahed,
Brown ’04]
[Bielefeld
Group ’04]
 Selfconsistency Problem
[Mannarelli+RR ’05]
q-q T-Matrix -
Quark-
Selfenergy

22. 5.2 Lattice Spectral Functions vs. T-Matrix in QGP_
LQCD Spectral Function:
Charmonium
Q-Q T-Matrix (ladder approx.)
based on Lattice Potential
[Datta etal ’03]
[Mannarelli+RR ’05]
reasonable qualitative agreement
 Evidence for Resonances in sQGP!? more studies required …

23. 4.3 Single-e± at RHIC: Transport Calculations
[MPC,
AMPT]
Parton Cascade with fixed s(q,g-c), forward/isotropic, coalescence
Elliptic Flow
pT-Spectra
similar to Langevin; Xsection effect on pT-spectra moderate
no bottom
[Zhang,Chen+Ko ‘05]

24. c-Quark Drag and Diffusion Coefficients in QGP
[van Hees+RR ’04]
Thermalization Times
Coordinate Space Diffusion
‹x2› - ‹x›2 = Dx t ≈ (5 fm)2
~ fireball size at Tc
pQCD
“D”
substantially smaller for
resonances

25. 4.4 Charmonium in A-A J/y Excitation Function
4/17/2017
SPS RHIC
[Grandchamp
+RR ’03]
J/y Excitation Function
same net suppression at SPS + RHIC!
Pb(158AGeV)-Pb
QGP-regeneration dominant
sensitive to:
mc* , (Ncc )2 ↔ rapidity, √s, A
QGP-suppression prevalent
no “jump” in theory
[Grandchamp etal. ’03]