1. From Heavy-Flavor Transport to Bulk and Spectral Properties of the QGP
11/28/2018
Ralf Rapp
Cyclotron Institute +
Dept of Phys & Astro
Texas A&M University
College Station, TX, USA +
EMMI (GSI, Darmstadt, GER)
HIC for FAIR Nuclear Physics Colloquium
Frankfurt University (Germany)
June 14, 2018

2. 1.) Heavy Quarks: A “Calibrated” QCD Force
[GeV]
V [½ GeV]
r [½ fm]
[Bazavov et al ‘13]
Vacuum quarkonium spectroscopy well described
Confinement ↔ linear part of potential
Objective: Determine medium-modifications of QCD force
 deduce transport properties + spectral functions of
heavy flavor, probing QGP at varying resolution
Exploit mQ >> LQCD , Tc , TRHIC,LHC

3. 1.2 Quarkonia in Medium In-medium spectral functions:
- Mass / binding energy EB(p,T)
- Inelastic reaction rate Gin(p,T,EB)
(dissociation and regeneration)
(1S): color-Coulomb force
J/y, (2S), …: confining force
How do heavy quarks within quarkonia
interact with the medium?
Not a good thermometer…

4. 1.3 Heavy Quarks in Medium Q Diffusion: “Brownian motion”
Thermalization delayed by mQ/T
→ memory in URHICs
Direct access to transport coefficient
Ds (2πT) (~ η/s ~ sEM/T !?)
Scattering rates
→ widths (quantum effects); quasiparticles? (mQT)
→ simple estimate: Ds(2pT)=3  GQ ~1GeV
- Implications for QGP structure?
Non-perturbative effects
Probe of hadronization (Ds, Lc) Q
QGP Q

5. Outline 1.) Introduction 2.) Quarkonia ● Transport Coefficients
11/28/2018
Outline
1.) Introduction
2.) Quarkonia
● Transport Coefficients
● Phenomenology
3.) Open Heavy Flavor
● Brownian Motion of Heavy Quarks
4.) Many-Body Theory of Heavy Quarks + QGP
● T-Matrix Approach
● QGP Properties
5.) Conclusions

6. 2.1 Quarkonium Transport in Heavy-Ion Collisions
[PBM+Stachel ’00, Thews et al ’01, Grandchamp+RR ‘01,
Gorenstein et al ’02, Ko et al ’02, Andronic et al ‘03,
Zhuang et al ’05, Ferreiro et al ‘11, …]
Inelastic reactions:
detailed balance: → -
J/y D - c
J/y + g c + c + X ←
Rate
equation:
Transport coefficients
- Equilibrium limit Nyeq(my,T; Ncc)
q q
gluo-dissosciation (“singlet-to-octet”)
• “quasi-free”/ Landau damping
“Strong” binding EB ≥ T
“Weak” binding EB < mD
- Reaction Rate Gy (EB(T))

7. 2.2 Excitation Functions: SPS - RHIC - LHC
Charmonium Bottomonium
Gradual increase of total J/y RAA
Regeneration and suppression increase
Regeneration concentrated at low pT!
[data: NA50, PHENIX, STAR, ALICE, CMS]
Gradual suppression
Regeneration (Nϒeq) small
Qualitative difference from J/y

8. 2.3 Upshot of Quarkonium Phenomenology
11/28/2018
Use temperature estimates from hydro/photons/dileptons to infer:
T0SPS (~240) < Tmelt(J/y,) ≤ T0RHIC (~350) < Tmelt() ≤ T0LHC (~550)
Remnants of confining force survive at SPS [hold J/y together]
Confining force screened at RHIC+LHC [“melts” J/y + (2S)]
Color-Coulomb screening at LHC [(1S) suppression]
Thermalizing charm quarks recombine at LHC [large J/y yield]
r [fm]
1.5 1
0.5
-0.5 -1
(2S)
J/, (2S)
(1S)
240
350
550

9. Outline 1.) Introduction 2.) Quarkonia ● Transport Coefficients
11/28/2018
Outline
1.) Introduction
2.) Quarkonia
● Transport Coefficients
● Phenomenology
3.) Open Heavy Flavor
● Brownian Motion of Heavy Quarks
4.) Many-Body Theory of Heavy Quarks + QGP
● T-Matrix Approach
● QGP Properties
5.) Conclusions

10. 3.1 Heavy-Flavor Transport in URHICs
| | | |
t [fm/c] D c
initial cond.
(nPDFs, …),
pre-equil. fields
c-quark diffusion
in QGP liquid
c-quark
hadronization
D-meson
diffusion in
hadron liquid
no “discontinuities” in interaction
 diffusion toward Tpc and hadronization same interaction (confining!)
[Moore+Teaney ‘05, van Hees et al ‘05, Gossiaux et al ‘08, Vitev et al ‘08, Das et al ‘09, Uphoff et al ’10,
M.He et al ‘11, Beraudo et al ‘11, Cao et al ’13, Bratkovskaya et al ‘14, …]

11. 3.2 Heavy-Flavor Transport
p2 ~ mQ T >> q2 ~ T2  Brownian Motion:
Fokker-
Planck Q
thermalization rate diffusion coefficient
g p =  d3q wQ(q,p) q
~  |TQj|2 (1-cosq) f j
Dp =  d3q wQ(q,p) q2
thermal relaxation time tQ = 1/g
Einstein relation: T = Dp / g mQ
spatial diffusion constant: Ds = T / g mQ , <x2> - <x>2 = 6 Ds t
relation to bulk medium: Ds (2pT) ~ h / s (4π)

12. 3.3 Heavy-Flavor Phenomemology at RHIC + LHC
Flow bump in RAA + large v2 ↔ strong coupling near Tpc (recombination)
Importance of T- + p-dependence of transport; Ds(2πT) ~ 2-4 near Tpc
High-precision v2: transition from elastic to radiative regime

13. 3.4 Spatial Charm-Quark Diffusion Coefficient
Ds = T / (mQ gQ(p=0))
HICs
T/Tc
suggests minimum of Ds(2pT) ~ 2-5 near Tpc
width: Gcoll ~ 3 / Ds ~ 1 GeV - no light quasi-particles!
upper limit from heavy-ion phenomenology

14. Outline 1.) Introduction 2.) Quarkonia ● Transport Coefficients
11/28/2018
Outline
1.) Introduction
2.) Quarkonia
● Transport Coefficients
● Phenomenology
3.) Open Heavy Flavor
● Brownian Motion of Heavy Quarks
4.) Many-Body Theory of Heavy Quarks + QGP
● T-Matrix Approach
● QGP Properties
5.) Conclusions

15. 4.1 Thermodynamic T-Matrix in QGP
i=Q,q,g
j=Q,q,g
Scattering
equation
Perturbative approximation (weak coupling): Tij  Vij
Strong coupling → resummation: Tij = Vij + ∫ Vij Di Dj Tij
Thermal parton propagators: Di = 1 / [w – wk –Si(w,k)]
Parton self-energies → self-consistency:
q ~ T << mQ  q(4)2 = q02 - q2  -q2
 3D reduction of Bethe-Salpeter equation
In-medium potential V?
j=q,g Si = ij

16. 4.2 Potential Extraction from Lattice Data
Free Energy -
QQ Spectral Function
Bayesian Approach T-Matrix Approach V
r [fm]
Potential close to free energy
small imaginary parts
Include large imaginary parts
Remnant of confining force!
[Burnier et al ’14]
[S.Liu+RR ’15, ‘17]

17. 4.3 Quarkonium Spectral Functions + Correlators
Charmonium Bottomonium
[S.Liu+RR ‘17]
J/y / ϒ(1S/2S) melting (300/500/250MeV) not inconsistent with pheno.

18. 4.4 Hamiltonian Approach to QGP
In-Medium Hamiltonian with ``bare” 2-body interactions
- effective in-medium mass
Interaction ansatz: Cornell potential with relativistic corrections
- color-Coulomb and string (“confining”) interaction
- decent spectroscopy in vacuum
Implement into Brueckner / Luttinger-Ward-Baym approach
[Liu+RR ‘16]

19. 4.5 QGP Equation of State + Spectral Functions
Thermodynamic
Potential
Selfconsistent SFs
G=G0+G0S G
S=GT
T=V+VGGT
T=194MeV
T=400MeV
Quark spectral
functions
 [GeV]
“Meson”
T-matrix
[S.Liu+RR ’16]
Near Tc light partons melt + broad hadronic resonances emerge

20. 4.6 Transport Coefficients
Viscosity and Heavy-Quark Diffusion
Strongly coupled: (2pT) Ds ~ (4p) h/s
Perturbative: (2pT) Ds ~ 5/2 (4p) h/s
Transition as T increases

21. 4.5.2 Sensitivity to Heavy-Quark Transport
Strongly-coupled potential gives max. low-pT c-quark v2
Weakly-coupled potential (~ free energy) ruled out

22. 5.) Summary Quarkonia probe in-medium QCD force, survive into the QGP
 Regenerated J/y’s vs. suppressed ϒ’s in heavy-ion collisions
Open heavy flavor a more direct probe of in-medium force strength
 clear preference of strongly coupled potential (low-pT v2!)
Large scattering rates imply melting of light quasiparticles
Quantum many-body theory to connect heavy-flavor to bulk medium
properties to realize premise of Q’s as QGP probe
 strongly coupled solution toward Tpc predicts
(i) melting light partons (ii) hadron formation (iii) small Ds, h/s, …

23. 4.4.1 Selfconsistent Equation of State for QGP
Thermodynamic
Potential
Skeleton
Diagrams
n,n
Fully resummed Luttinger-Ward
functional (!)
Fit quark+ gluon “bare” masses
Broad hadronic resonances
emerge near Tpc
[S.Liu+RR ’16]

24. 2.2 In-Medium ϒ Suppression
11/28/2018
2.2 In-Medium ϒ Suppression 1P 2S 1S 1S 1P 2S
Binding energies control reaction rates
ϒ(1S) suppression sensitive to EB(T)
significant regeneration for ϒ(2S)

25. 3.8 Versatility of Equilibrium Benchmarks
Quarkonium equilibrium abundance in “chemical” transport
Heavy-quark equilibration controls quarkonium regeneration
Heavy-quark transport to satisfy detailed balance (2↔2, 2↔3)
Quark coalescence (energy conservation):
equilibrated quarks → equilibrated hadrons (!)
Constraints from lattice QCD

26. 2.1 Quarkonium Transport in URHICs
| | | |
fireball time
t [fm/c] c - c
production +
evolution of
cc wave pack.
~ Tpc:
c and c
hadronize
hadronic
kinetics
~ Tmelt:
y can
form
tform~1fm/c tceq ~5fm/c tyeq ~ 1/ Gy
QGP
c+c ↔ y -
c-quark
diffusion
in QGP
[Satz et al, Capella et al, Spieles et al, PBM et al, Thews et al, Grandchamp et al, Ko et al, Zhuang et al, Zhao et al,
Chaudhuri, Gossiaux et al, Young et al, Ferreiro et al, Strickland et al, Brambilla et al, …]

27. 3.5 y(2S) in dAu and pPb d-Au (0.2TeV) p-Pb (5.02TeV)
[ALICE]
[PHENIX]
- - EPS09
noticeable y and little J/y suppression, consistent with “comovers”
supports fireball formation with:
tFB G(y) ~ 1  Gavg(y) ~ MeV similar to thermal
tFB G(J/y) << 1  Gavg(J/y) < 20 MeV widths at T 200MeV
[Ferreiro ‘15]
[Du et al ‘15]

28. 2.3 Quarkonium Width Comparisons
Charmonium Bottomonium
J/y
(1S)
melted
Fair agreement for J/y
Larger spread for  states
Binding energies differ
(2S)
melted

29. 3.3 Properties of Charmonium Excess
• systematic softening of J/y
pT -spectra with increasing √s
→ nature of source changes
[Tsinghua]
excess concentrated at low pT • low-pT excess carries sizable v2

30. 4.1 Charm Thermalization + J/y Regeneration
→ Softening of charm-quark spectra facilitates regeneration
J/y Equilibrium Fraction Charm-Quark Diffusion Coeff.
(Nyeq )off-c / (Nyeq)thermal-c
1-exp[-t / tceq]
t / tceq
T / Tc
[Ko et al ‘12]
[Prino+RR ‘16]
Charmonium phenomenology
favors tceq ≤ 5 fm/c
(“strong” coupling)
Ds = tceq T/mQ ≤ (4-8) /(2pT)

31. 4.3 (1S): Rapidity Puzzle problem of large(r) suppression in
2.76 TeV ALICE data
beware of cold nuclear matter effects
Regeneration: Nbb ~ 1 for central PbPb
 canonical limit NY ~ (Nbb)1

32. 4.2 (1S) and (2S) Transport cont’d
… as implemented in current transport approaches
(1S)
[Tsinghua]
[Ko et al]
(2S) more sensitive sensitive to in-medium potential

33. 4.5 In-Medium Quarkonium Binding Energies

34. 2.4 Heavy-Quark Potential + Regeneration
Lattice-based potentials
[TAMU ‘11,’17]
[Kent St ‘17]
(1S) suppression at RHIC → regeneration at LHC
Regeneration dominant for (2S) in central PbPb at LHC?

35. 3.3 Heavy-Quark Interactions in QGP
Minimal / Desirable Ingredients and Features
Microscopic description of scattering amplitude
Realistic in-medium interaction kernel (screening)
Nonperturbative interactions
(color-Coulomb / pQCD not enough)
Resummation (strong coupling)
Hadronization approaching Tc from above
(bound states)
Elastic + radiative processes (low / high pT)
Realistic medium partons:
quasiparticles, widths, parton spectral functions, …? Equation of state?
Quantitatively rooted in constraints from lattice QCD
QGP Q
[Caron-Huot+Moore ’08]