Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA With: F. Riek (Texas A&M), H. van Hees (Giessen), V. Greco (Catania), M. Mannarelli (Barcelona) Nonperturbative Heavy-Quark Interactions in the QGP
Jan 18, 2016
Ralf Rapp Cyclotron Institute + Physics Department
Texas A&M University College Station, USA
With: F. Riek (Texas A&M), H. van Hees (Giessen), V. Greco (Catania), M. Mannarelli (Barcelona)
Nonperturbative Heavy-Quark Interactions
in the QGP
1.) Introduction
• “Large” scale mQ >> QCD , T
• Low-energy/-momentum interactions:
- heavy-quark diffusion ↔ elastic scattering, Fokker-Planck
- quarkonia ↔ potential QCD
→ uniform framework
• s expansion inadequate
→ resummations, bound + scattering states
• theo. / pheno. constraints essential
(baselines prior to applications in heavy-ion collisions)
1.) Introduction
2.) T-Matrix Approach with Heavy Quarks
Potential Approach + Lippmann Schwinger Eq. Vacuum and pQCD Limits In-Medium Potentials Q-Q and Q-q Scattering in Medium
3.) Heavy-Quark Diffusion in QGP Fokker-Planck Equation Transport coefficients Electron Spectra at RHIC
4.) Conclusions
Outline
• 2-body potential VL in medium? Color-Magnetic Interaction?
Lippmann-Schwinger Equation
In-Medium Q-Q T-Matrix: -
2.) T-Matrix Approach with Heavy Quarks
)'q,k;E(T)k,E(G)k,q(Vdkk)'q,q(V)'q,q;E(T LQQLLL02
[Mannarelli+RR ’05, Cabrera+RR ‘06]
- Q-Q propagator: - bound + scattering states
• HQ potential concept well established in vacuum (EFT, lattice)
• 3-D reduction of Bethe-Salpeter Eq.
])(s/[)s(G QQkkQQ20 24 -
• Born approx. TQq = VQq recovers pQCD within ~20%
2.2 Color Magnetic Interaction and Constraints
Vacuum “Spectroscopy” Perturbative Q-q Scattering
• Color-Magnetic “Breit” Interaction VQ1Q2(r) → VQ1Q2(r) ( 1 – v1 · v2 )
[G.E. Brown ’52, Brown et al ‘04]
[van Hees et al ‘09][Riek et al ‘09]
• Q-Q and Q-q states ~ o.k.• spin-interactions O (1/mQ)
mc0 =1.4 GeV
- -
-
F1(r,T) = U1(r,T) – T S1(r,T)
• V1(r,T) ≡ X1(r,T) X1(r=∞,T) (X1
∞ / 2 : in-medium quark-mass?!)
(a) X1=F1 : relax << tint
(b) X1=U1 : relax >> tint
(c) Landau-Zener “mixing”
X1 = P U1 + (1-P) F1
P = exp[- 2 |H12|2 / vrel d/dr (F1-U1)]
|H12| ~ 1/relax
2.3 Lattice QCD Free Energy + In-Medium Potential
[Kaczmarek +Zantow ’05]
[Shuryak ‘08, Riek et al ‘09]
2.4 Charmonium T-Matrix in QGP
• ground state bound to ~ 2 Tc for V = U, VLZ
~ 1.2Tc for V = F
2.5 Heavy-Light Quark Scattering in QGP
• threshold S-wave resonances (meson+diquark) close to TC
QmDT
2
2
p
fD
p)pf(
tf
• Brownian
Motion:
thermalization rate diffusion coefficient
3.) Heavy-Quark Transport in the QGP
Fokker Planck Eq.[Svetitsky ’88,…]Q
k)p,k(wkdp Q3
23
21 k)p,k(wkdD Q
• Transition rate: wQ(p,k) ~ ∑ q,g ∫ fq,g(E;T) |TQq|2
• Heavy-quark selfenergy: Q
3.2 Charm-Quark Selfenergy + Drag
• charm quark widths c = -2 Imc ~ 250 MeV close to TC
• friction coefficients increase(!) with decreasing T→ TC!
Selfenergy Thermalization Rate
)kp(T)(fkd)p( a,LQqk
qa,LQ 3 k|)p,k(T|Fkdp 23
3.3 Comparison of Drag Coefficients
(Thermal Relaxation Rate)
• T-matrix rate ~ constant (melting resonances)• relax = 1/ ~ 7 fm/c
T [GeV]
[1
/fm
]
[Gubser ’06]
[Peshier ‘06; Gossiaux+Aichelin ’08]
[van Hees+RR ’04]
[van Hees,Mannarelli, Greco+RR ’07]
3.4 T-Matrix Approach vs. e± Spectra at RHIC
• max. interaction at ~Tc
↔ hadronic correlations ↔ quark coalescence
[van Hees,Mannarelli,Greco+RR ’07]
Spatial Diffusion Coeff.
4.) Summary and Conclusions
• In-Medium Q-q + Q-Q T-Matrix → heavy-quark diffusion and quarkonia in QGP on same footing
• Constraints essential: - lQCD based potential (F-U relaxation), Eucl. correlators - vacuum, pQCD
• “hadronic” correlations close to Tc ↔ quark coalescence
↔ max. coupling strength at ~Tc ↔ min. /s !?
• Radiative diffusion? Light-quark sector? Non-pert. gluons? …
• RHIC non-photonic e± Ds (2T) ≈ 5
- v2 - RAA correlation essential
- scrutinize medium evolution, Fokker-Planck, d-Au …
3.1 HQ Langevin Simulations: Hydro vs. Fireball Elastic pQCD + Hydrodynamics [Moore+Teaney ’05]
• b=6.5 fm Tc=165 MeV ≈ 9 fm/c
•Tc=180 MeV bulk-v2 ~5.5%QGP ≈ 5 fm/c
Resonance Model + Expanding Fireball
[van Hees,Greco +RR ’05]
Ds (2T) ≈ 6
v2max ~ 5-6%RAA~ 0.3
2.3 AdS/CFT-QCD Correspondence
[Gubser ‘07]
pdtdp 2
2 SYMc
CFT/ADS Tm
cCFT/ADS m
T)..(2
5012
• match energy density (d.o.f = 120 vs. ~40) and coupling constant (heavy-quark potential) to QCD
3-momentum independent
[Herzog et al, Gubser ‘06]
≈ (4-2 fm/c)-1 at T=180-250 MeV
Lat-QCD
TQCD ~ 250 MeV
3.) Phenomenology at RHIC• Medium evolution - hydrodynamics or parameterizations thereof
- realistic bulk-v2 (~5-6%)
- stop evolution after QGP; hadronic phase?
• Hadronization - fragmentation: c → D + X
- coalescence: c + q → D, adds momentum and v2
- chemistry (e.g. c enhancement)
• Semileptonic electron decays - approx. conserve v2 and RAA of parent meson
- charm/bottom composition in p-p
[Hirano et al ’06]
[Martinez et al, Sorensen et al ‘07]
[Greco et al, Dong et al ‘04]
3.3 Heavy-Quark Spectra at RHIC
• T-matrix approach ≈ effective resonance model • other mechanisms: radiative (2↔3), …
• relativistic Langevin simulation in thermal fireball background
pT [GeV]
Nuclear Modification Factor Elliptic Flow
pT [GeV]
[Wiedemann et al.’05,Wicks et al.’06, Vitev et al.’06, Ko et al.’06]
4.) Maximal “Interaction Strength” in the sQGP• potential-based description ↔ strongest interactions close to Tc
- consistent with minimum in /s at ~Tc
- strong hadronic correlations at Tc ↔ quark coalescence
• semi-quantitative estimate for diffusion constant:
[Lacey et al. ’06]
weak coupl. s ≈n <p> tr=1/5 T Ds
strong coupl.s≈ Ds= 1/2 T Ds
s≈ close toTc
3.2.2 The first 5 fm/c for Charm-Quark v2 + RAA Inclusive v2
• RAA built up earlier than v2
Time Evolution
2.2.2 “Lattice QCD-based” Potentials• accurate lattice “data” for free energy: F1(r,T) = U1(r,T) – T S1(r,T)• V1(r,T) ≡ U1(r,T) U1(r=∞,T)
[Cabrera+RR ’06; Petreczky+Petrov’04]
[Wong ’05; Kaczmarek et al ‘03]
• (much) smaller binding for V1=F1 , V1 = (1-U1 + F1
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]
2.1.3 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
3.2 Model Predictions vs. PHENIX Data
Single-e± Spectra [PHENIX ’06]
• coalescence increases both RAA and v2
• pQCD radiative E-loss with upscaled transport coeff.
• Langevin with elastic pQCD + resonances + coalescence
• Langevin with upscaled pQCD elastic