Heavy-Flavor Interactions in Medium
Ralf Rapp
Cyclotron Institute +
Dept. of Physics & Astronomy
Texas A&M University
College Station, TX
USA
Workshop on
Heavy-Quark Physics in Heavy-Ion Collisions
ECT* (Trento, Italy), 16.-20.03.15
1.) Introduction: A “Calibrated” QCD Force
V [½ GeV]
r [½ fm]
• Vacuum charm-/bottomonium spectroscopy well described
• Confinement ↔ linear part of potential
• non-perturbative treatment in medium
lattice QCD, potential/T-matrix approach, AdS/CFT, …
• relate quarkonia kinetics and heavy-flavor diffusion
[Kaczmarek
et al ‘03]
1.2 Objectives with Heavy Flavor in URHICs
Determine modifications of QCD force in medium
+ infer consequences for the many-body system
• Open heavy-flavor diffusion: Brownian motion
- Scattering rates in QGP: widths, quasiparticles? (mQT)
- Transport/thermalization: type of interaction (non/pert.,dofs, …)
• Quarkonia kinetics
- Screening of confining (≥Tc?) + Coulomb (≥2Tc?) force
- ϒ states: sequential melting
- ψ states: sequential recombination
Outline
1.) Introduction
2.) Heavy-Quark Interactions in QGP
3.) Open Heavy-Flavor Transport
4.) Quarkonia: ψ Puzzle(s)
5.) Conclusions
2.1 Free and Internal Energy in Lattice QCD
F1(r,T) = U1(r,T) – T S1(r,T)
Free Energy
- potential
• “weak” QQ
• small DmQ ~ F1(∞,T)/2
Internal Energy
- potential, U = ‹H ›
• “strong” QQ
int
• large DmQ ~ U1(∞,T)/2
• F, U, S thermodynamic quantities
• Entropy: many-body effects
2.2 Reconstructed Potential from Lattice QCD
• static potential from
Wilson loop correlator:
Real Part
Imaginary Part
• real part ~ singlet free energy
• imaginary part ~ HTL perturbative
 strongly coupled QGP?
[Burnier et al ’14]
2.3 Thermodynamic T-Matrix in QGP
• Lippmann-Schwinger equation
In-Medium
Q-Q T-Matrix:
T ( E ; q , q' )  V  ( q , q' )   k 2 dk V  ( q , k ) G Q0 Q ( E , k ) T ( E ; k , q' )
• thermal 2-particle propagator:
G Q0 Q ( E , k ;T


)  T  D Q ( z , k ) D Q ( E  z , k )
• selfenergy:
 Q (  ,k ) 
  TQ p (    p ) f p (  p )
p  q ,g
• In-medium potential V?
Q

q,g
=
[Cabrera+RR ’06,
Riek+RR ‘10]
2.3.2 Free Energy from T-Matrix
• Free Energy
• Euclidean T-matrix in static limit
[Beraudo et al ’08]
[S.Liu+RR
in progress]
• Spectral Function
[S.Liu+RR ’15]
• Key ingredients:
imaginary parts + their  dependence
• heavy-quark selfenergies from
previous T-matrix calculations
2.3.3. Free + Internal Energy from T-Matrix
• potential ansatz:
lattice data
U
V
F
1.2 Tc
r [fm]
1.5 Tc
r [fm]
2 Tc
r [fm]
• remnant of long-range “confining” force in QGP
• smaller in-medium quark mass relative to internal energy
2.3.4 Brueckner Theory of Heavy Flavor in QGP
Input
lattice-QCD
free energy
2-body
potential
Quark
selfenergy
Process
Q→Q
0-modes
QQ
T-matrix
Qq
T-matrix
Output
Test
quark-no.
susceptibility
lattice
data
spectral fcts./
eucl. correlat.
- evolution
QQ
(rate equation)
exp.
data
Q spectra + v2
(Langevin)
Outline
1.) Introduction
2.) Heavy-Quark Interactions in QGP
3.) Open Heavy-Flavor Transport
4.) Quarkonia: ψ Puzzle(s)
5.) Conclusions
3.1 Heavy-Light Scattering Amplitudes
New Potential V
U-Potential
c-q-
• “confining” force induces “Feshbach resonances” in Qq T-matrix
• strength comparable to internal-energy (U) potential
3.2 Charm-Quark Relaxation Rates
• heavy-light T-matrix → HQ transport: g Q p   | TQ q |2 ( 1  cos  ) f q , g
Diffusion Coefficient
gc [1/fm]
Relaxation Rate
p [GeV]
[S.Liu+RR in prep]
• tc ≈ 3 fm/c close to Tc at low p
• 3-mom. + temperature dependence reflect core properties of QCD!
3.3 D-Meson Transport in Hadronic Matter
g D   | M D h | ( 1  cos  ) f
2
gD [fm-1]
h
• effective D-h scattering amplitudes
[He,Fries+RR ’11]
• consistent with:
- unitarized HQET (pion gas) [Cabrera
et al ‘11]
- recent works in HRG using similar
methods [Tolos+Torres-Ricon ’13,
Ozvenchuk et al ‘14]
gD [fm-1]
• hadron gas at ~Tc: tD ≈ 10fm/c
3.4 Summary of Charm Diffusion in Matter
Ds =T/mg : Hadronic Matter vs. QGP vs. Lattice QCD
[He et al ’11,
Riek+RR ’10,
Ding et al ‘11,
Gavai et al ‘11]
AdS/QCD
• shallow minimum near Tc
• Quark-Hadron continuity?
[Gubser ‘07]
3.5 Heavy-Flavor Transport in URHICs
0
|
0.5
|
t [fm/c]
5
|
D
c
• initial cond.
(shadowing,
• c-quark diffusion
Cronin),
in QGP liquid
pre-equil. fields
10
|
• c-quark
hadronization
• D-meson
diffusion in
hadron liquid
• no “discontinuities” in interaction
 diffusion toward Tpc and hadronization same interaction (confining!)
3.6 Heavy-Flavor Electrons at √s=62GeV
• uncertainties in pp baseline
• interplay of Cronin (pA!) + collective flow
• sizable medium effects in RCP + v2
Outline
1.) Introduction
2.) Heavy-Quark Interactions in QGP
3.) Open Heavy-Flavor Transport
4.) Quarkonia: ψ Puzzle(s)
5.) Conclusions
4.) Charmonium: y(3686)
• easily dissociated in hadronic matter:
p, r, ... + y →DD, y → DmedDmed
[Grandchamp
+RR ‘02]
[PBM+Stachel ‘00]
• hadronic y dissociation at SPS important ingredient for
transport models [Sorge et al ‘97, …]
4.2 Charmonia in d+Au Fireball
• construct fireball + evolve rate equat.
→ y suppression from hot medium
• similar in spirit to comover approach
[Ferreiro ‘14]
• formation time effects?!
[X.Du+RR, in prep]
[Y.Liu, Ko et al ‘14]
4.3.1 Sequential Recombination of Charmonia in AA
Time Evolution
pT Spectra
• smaller binding → smaller Tdiss → y forms later than J/ψ !
• harder blast wave for ψ formed at later times (hadronic phase!)
[X.Du+RR, in prep]
4.3.2 Sequential Recombination vs. Dissociation
ψ / J/ψ Double Ratio
RAA ψ / RAA J/ψ
Nuclear Modification Factor
• ψ blast wave fills pt = 3-6 GeV region, primordial for pt > 6 GeV
• helps explain CMS double-ratio puzzle
• more complex in practice …
[X.Du+RR, in prep]
5.) Conclusions
• Heavy-quark potential in QGP from lQCD F: Bayesian, T-matrix
- Large imaginary parts
- Remnants of confinement generate strong coupling
• “Critical” consequences for heavy-flavor diffusion
• Continuity + minimum of transport coefficient through Tpc
• No principal difference between diffusion forces + hadronization
• Sequential recombination of charmonia?!
(↔ pA)
3.) Quarkonium Transport in Heavy-Ion Collisions
• Inelastic Reactions:
detailed balance: J/y + g
• Rate
Equation:
dN y
dt
[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, …]
→
c
+
c
+X
←
  y ( N y  N yeq )
D
-
D
J/y
c-
c
J/y
• Theoretical Input: Transport coefficients
- chemical relaxation rate y
- equililbrium limit Nyeq(eyB, mc* ,tceq)
• Phenomenological Input:
- J/y,cc,y’+c,b initial distributions [pp, pA]
- space-time medium evolution [AA: hydro,...]
Observables
3.1 Thermal Charmonium Properties
(a) Equilibrium Y number:
N yeq
 V FB 3 g c2
d 3q y
 ( 2p )3 f ( my ,T )
• gc from fixed cc- number: N c c  1 V FB g c nc ( m *c ,T ) I 1 / I 0 
2
• interplay of mc* and m y  2 m *c  e yB
• constrain spectral shape by
lattice-QCD correlators
q
y
eyB
mc*
(b) Inelastic Y Width
 Nyeq
q
• controlled by s (parameter)
y
3.3 Inclusive J/y at SPS + RHIC
Strong Binding (U)
Weak Binding (F)
[Zhao+RR ‘10]
• Fix two main parameters:
s~0.3, charm relax. tceq = 4(2) fm/c for U(F) vs. ~5(10) from T-matrix
3.4 J/y Excitation Function: BES at RHIC
PHENIX (forward y)
STAR (central y)
• suppression pattern varies little (expected from transport) [Grandchamp
+RR ’02]
• quantitative pp + pA baseline critical to extract systematics
3.5 J/y Predictions at LHC
[Zhao+RR ‘11]
• regeneration becomes dominant
• uncertainties in scc+shadowing
• low pT maximum confirms
regeneration
• too much high-pT suppression?
3.6 (1S) and (2S) at LHC
Weak Binding
Strong Binding
(1S)
→
(2S)
→
[Grandchamp et al ’06,
Emerick et al ‘11]
• sensitive to color-screening + early evolution times
• clear preference for strong binding (U potential)
• similar results by [Strickland ‘12]
• possible problem in rapidity dependence
3.7 Summary of Phenomenology
• Quarkonium discoveries in URHICs:
- increase of J/y RAA SPS, RHIC → LHC
- low-pT enhancement
- sizable v2
- increasing suppression of ’ (eB’ ~ eBJ/y )
• Fair predictive power of theoretical modeling
- based on description of SPS+RHIC with 2 main parameters
• Implications
- T0 SPS (~230) < Tdiss(J/y,’) < T0RHIC (~350) < T0LHC(~550) ≤ Tdiss()
- confining force screened at RHIC+LHC
- marked recombination of diffusing charm quarks at LHC
3.2.2 J/y at LHC: v2
[He et al ’12]
• further increase at mid-y
3.1.2 J/y pT Spectra + Elliptic Flow at RHIC
(strong binding)
• shallow minimum at low pT
• high pT:
formation time, b feeddown, Cronin
• small v2 limits regeneration,
but does not exclude it
3.2.2 D-Meson Thermalization at LHC
• to be determined…
3.3.4 Time Evolution of J/y at LHC
Strong Binding (U)
Weak Binding (F)
• finite “cooking-time” window, determined by inelastic width
[Zhao+RR ‘11]
4.3 J/y at Forward Rapidity at RHIC
[Zhao+
RR ‘10]
3.2 Incomplete c-Quark Thermalization
• Relaxation time ansatz:
Nyeq (t) ~ Nytherm(t) · [1-exp(-t/tceq)]
Microscopic Calculation
Impact on Regeneration
[Zhao+RR ‘11]
[Song,Han,
Ko ‘12]
• regeneration sensitive to charm-quark spectra
3.6.1 Heavy-Flavor Electrons at √s=62GeV
Hydro Tune
• importance of flow + Cronin effect
at lower energies