Nonperturbative Heavy-Quark Transport at RHIC Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA With: H. van Hees (Giessen), D. Cabrera (Madrid), V. Greco (Catania), M. Mannarelli (Barcelona) 417 th WE-Heraeus Seminar on “Characterization of the QGP with Heavy
Nonperturbative Heavy-Quark Transport at RHIC. Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA With: H. van Hees (Giessen), D. Cabrera (Madrid), V. Greco (Catania), M. Mannarelli (Barcelona) - PowerPoint PPT Presentation
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Nonperturbative Heavy-Quark Transport
at RHIC
Ralf Rapp Cyclotron Institute + Physics Department
Texas A&M University College Station, USA
With: H. van Hees (Giessen), D. Cabrera (Madrid), V. Greco (Catania), M. Mannarelli (Barcelona)
417th WE-Heraeus Seminar on “Characterization of the QGP with Heavy Quarks”
Physikzentrum Bad Honnef, 28.06.08
1.) Introduction
• Empirical evidence for sQGP at RHIC: - thermalization / low viscosity (low pT)
- energy loss / large opacity (high pT)
- quark coalescence (intermed. pT)
• Heavy Quarks as comprehensive probe:
- pT regimes connected via underlying HQ interaction?
- strong coupling: perturbation theory unreliable, resummations required
- simpler(?) problem: heavy quarkonia ↔ potential approach
- similar interactions operative for elastic heavy-quark scattering?
transport in QGP,hadronization
PRELIMINARY
Run-4
Run-7
resonance model[van Hees, Greco+RR ’05]
minimum-bias
1.) Introduction
2.) Heavy Quarkonia in QGP In-Medium T-Matrix with “lattice-QCD” potentials Charmonium Spectral + Correlation Functions In-Medium Mass and Width Effects
3.) Open Heavy Flavor in QGP Heavy-Light Quark T-Matrix HQ Selfenergies + Transport HQ and e± Spectra Implications for sQGP
4.) Conclusions
Outline
• Correlator: L=S,P
• Lippmann-Schwinger Equation
In-Medium Q-Q T-Matrix: -
2.) Quarkonia in QGP: Potential Models
)'q,k;E(T)k,E(G)k,q(Vdkk)'q,q(V)'q,q;E(T LQQLLL02
[Mannarelli+RR ’05, Cabrera+RR ‘06]
000QQLQQQQL GTGG)E(G
- quasi-particle propagator:
- bound+scatt. states, threshold effects large
• bound state + (free) continuum model too schematic for broad/dissolving states
2
J/
’
cont.
Ethr
])(s/[)s(G QQkkQQ20 24
[Karsch et al. ’87, …, Shuryak+Zahed ’04, Mocsy+Petreczky‘05, Alberico et al. ‘06, Wong et al. ’07, Laine et al. ‘07 …]
Determination of potential• fit lattice Q-Q free energy
• currently significant uncertainty• augment by magnetic interaction
QQQQQQQQQQ U)r(U)r(V,TSUF
• T-matrix for Q-q scatt. in QGP
• Casimir scaling for color chan. a
• in-medium heavy-quark selfenergy:
[Mannarelli+RR ’05]
aLQq
aL
aL
aL TGVdkVT 0
Nf=0[Wong ’05]
Nf=2[Shuryak+ Zahed ’04]
3.2.2 Charm-Light T-Matrix with lQCD-based Potential
• meson and diquark S-wave resonances up to 1.2-1.5Tc
• P-waves and (repulsive) color-6, -8 channels suppressed
[van Hees, Mannarelli, Greco+RR ’07]
Temperature Evolution + Channel Decomposition
3.2.3 Charm-Quark Selfenergy + Transport
• large charm-quark width c = -2 Imc ~ 250MeV close to Tc
Selfenergy Friction Coefficient
k|)p,k(T|Fkdp 23
• friction coefficients increase(!) with decreasing T→ Tc!
)kp(T)(fkd)p( a,LQqk
qa,LQ 3
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]
3.4 Single-Electron Spectra at RHIC
• heavy-quark hadronization: coalescence at Tc [Greco et al. ’04]
+ fragmentation
• hadronic correlations at Tc ↔ quark coalescence!
• charm bottom crossing at pT
e ~ 5GeV in d-Au (~3.5GeV in Au-Au)
• ~25% uncertainty due to differences in U1 potential
• suppression “early”, v2 “late”
3.5 Maximal “Interaction Strength” in the sQGP• potential-based description ↔ strongest interactions close to Tc
- minimum in /s at ~Tc
- hadronic correlations at Tc ↔ quark coalescence
• estimate 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
[RR+ van Hees ’08]
4.) Summary and Conclusions
• T-matrix approach with lQCD internal energy (UQQ): - S-wave charmonia survive up to Tdiss ≤ 2.5Tc - finite width can suppress J/ well below Tdiss!
• T-matrix for (elastic) heavy-light scattering: - large c-quark width + small diffusion - “hadronic” correlations dominant (meson + diquark) - maximum strength close to Tc ↔ minimum in /s ? - naturally merges into quark coalescence at Tc