1. Heavy-Flavor Transport at FAIR
6/4/2018
Ralf Rapp
Cyclotron Institute +
Dept of Phys & Astro
Texas A&M University
College Station, USA
HICforFAIR Workshop
“Heavy-Flavor Physics with CBM”
FIAS (Frankfurt, Germany),

2. 1.) Introduction: Why Heavy Quarks in URHICs?
“Large” scale mQ >> LQCD, T (Q = c, b):
pair production in primordial NN collisions
→ well defined initial condition, flavor conserved
thermal relaxation time tQ~ mQ/T ~ 5-20 ≥ tfireball
→ incomplete thermalization, “gauge” of interaction strength
simplifications in theoretical treatment
→ diffusion: Brownian markers of QGP
→ access to soft interactions in QGP / hadronization
→ potential theory
→ quantitative connections to lattice QCD
→ direct window on QGP transport coefficient

3. 1.2 Heavy-Quark Evolution in URHICs
| | | |
t [fm/c] D c
initial cond.
(shadowing,
Cronin),
pre-equil. fields
c-quark diffusion
in QGP liquid
c-quark
hadronization
D-meson
diffusion in
hadron liquid
Consistency
- weak coupling: pQCD + fragmentation
- strong coupling: non-pert. diffusion + recombination

4. 1.3 Matter Evolution at CBM
mqch[MeV] 5 80
130
150
significant time around (even above) Tc
need to control:
- Q interactions with quarks
- D, D and Lc interactions in hadronic matter -

5. Outline 1.) Introduction 2.) Heavy-Quark Transport in QGP
6/4/2018
Outline
1.) Introduction
2.) Heavy-Quark Transport in QGP
3.) D-Meson Transport in Hadronic Matter
4.) Hadronization
5.) Heavy-Ion Phenomenology
6.) Conclusions

6. 2.) Heavy-Quark Transport Coefficient
p2 ~ mQ T >> k2 ~ T2  Brownian Motion: Q
Fokker Planck Eq.
thermalization rate diffusion coefficient
thermal relaxation time tQ = 1/g
Einstein relation: → check FP approximation
spatial diffusion constant: Ds = T / g mQ
relation to bulk medium: Ds (2pT) ~ h / s

7. 2.1 Leading-Order Perturbative QCD
gluon exchange regularized by Debye mass:
[Svetitsky ’88, Mustafa et al ’98,
Molnar et al ’04, Zhang et al ’04,
Hees+RR ’04, Teaney+Moore‘04] 2
dominated by forward scattering off gluons
thermalization time g -1 = tc ≥ 20 fm/c long (T≤ 300MeV, as=0.4)

8. 2.2 Perturbative QCD with Running Coupling
run as to mD ~ gT, rather than 2pT
reduced Debye mass
[Peshier ‘07]
[Gossiaux+
Aichelin ‘08]
factor ~10 faster thermalization: tc ≈ 2-3 fm/c
perturbative regime? Need to resum large diagrams…

9. 2.3 T-Matrix Approach In-medium scattering amplitude
thermal 2-particle propagator:
Field-theoretic potential approach:
- effective propagator: Coulomb + string
- fit to lattice-QCD free energy
[Megias
et al ‘07]

10. 2.3.2 T-Matrix + Lattice-Potential Approach
heavy-light T-matrix → HQ transport
[Riek+RR ’10]
In-Medium Amplitude
Thermalization Rate -
c-q
gc [1/fm]
vacuum spectroscopy + pQCD limit
“Feshbach” resonances in medium
factor 3-4 faster than pQCD:
tc ≈ 4-6 fm/c
3-momentum dependence:
transition strong → weak

11. 3.) D-Meson Transport in Hadronic Matter
6/4/2018
gD [fm-1]
effective D-h scattering amplitudes
[He,Fries+RR ’11,
Tolos+Torres-Ricon ‘13]
D-meson in pion gas:
- consistent with unitarized HQET
- factor ~10 larger in
heavy-meson cPT
[Cabrera
et al ‘11]
[Laine ‘11]
gD [fm-1]
hadron gas at ~Tc: tD ≈ 10fm/c

12. Summary of Charm Diffusion in Matter
6/4/2018
Hadronic Matter vs. QGP vs. Lattice QCD
[He et al ’11,
Riek+RR ’10,
Ding et al ‘11,
Gavai et al ‘11]
AdS/QCD [Gubser ‘07]
Shallow minimun around Tc ?
Quark-Hadron Continuity?

13. 4.) Heavy-Flavor Hadronization
Hadronization is an interaction!
High pT: pQCD with fragmentation
Low + Intermediate pT
- heavy flavor conserved through transition
- hadron formation with thermal quarks:
resonant Qq recombination
- same interaction as in non-pert. diffusion
- contributes to equilibration! - qq c D - q D T c
[Ravagli+RR ‘07]

14. 5.) Charm Transport at RHIC + LHC
5.1 QGP – Hadronization – Hadronic Matter
increased QGP-v2 from recombination + hadronic diffusion
increased Ds-RAA from strangeness enhancement
[He et al ’12]

15. 5.2 Modeling of D-mesons at LHC
No single consistent description yet
Perturbative approaches too weakly coupled

16. 5.3 Heavy-Flavor Electrons at √s=62GeV
10%
[He et al in prep]
Importance of flow and Cronin at lower energies

17. 6.) Conclusions
Non-perturbative interactions govern heavy flavor at CBM:
- Dt ~ 5fm/c around Tc and in hadronic phase
Large mq / T ≥ 1 → importance of Qq interactions
→ Effective “potential” theory, controlled by
- spectroscopy + pQCD (vacuum)
- lattice QCD (finite T)
In-medium hadronization: resonance correlations manifest
Quantitative effective hadronic theory
Implications for charmonia

18. 2.3 AdS/CFT-QCD Correspondence
3-momentum independent
[Herzog et al, Gubser ‘06]
match energy density
(d.o.f = 120 vs. ~40)
and coupling constant
(heavy-quark potential)
to QCD
Lat-QCD
TQCD ~ 250 MeV 
≈ (4-2 fm/c)-1 at T= MeV
[Gubser ‘07]

19. 3.3 Quarkonium Spectral Functions + Correlators
[Aarts et
al ‘07]
limiting cases:
assume V=U or F
[Satz et al ’01+’08, Mocsy+Petreczky ’05+’08, Wong ’06,
Cabrera,Riek+RR ’06+’10, Beraudo et al ’06, Lee et al ’09, …]

20. → ← - 3.4 Quarkonium Transport J/y + q,g c + c + X - D J/y c
Rate Equation for
J/y + q,g c + c + X
J/y D - c
reaction rate equilibrium limit
(y -width)
in-med properties: spectral function, encodes screening/dissociation
formation sensitive to HQ distributions
[cf. also
Andronic et al,
Zhuang et al,
Ferreiro et al, …]

21. 4.1 Quantitative Bulk-Medium Evolution
initial conditions (compact, initial flow?)
EoS: lattice (QGP, Tc~170MeV) + chemically frozen hadronic phase
spectra + elliptic flow: multistrange at Tch ~ 160MeV
p, K, p, L, … at Tfo ~ 110MeV
v2 saturates at Tch, good light-/strange-hadron phenomenology
[He et al ’11]