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Heavy-Quark Thermalization and Resonances in the QGP. Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA With: H. van Hees (Texas A&M), V. Greco (Texas A&M, Catania) Quark Matter 2005 Conference Budapest (Hungary), 06.08.05. - PowerPoint PPT Presentation
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Heavy-Quark Thermalization
and Resonances in the QGP
Ralf Rapp Cyclotron Institute + Physics Department
Texas A&M University College Station, USA
With: H. van Hees (Texas A&M), V. Greco (Texas A&M, Catania)
Quark Matter 2005 Conference Budapest (Hungary), 06.08.05
1.) Introduction: Single-e± Spectra pre-QM05
Coalescence assuming v2(c) = v2(q) and/or jet quenching?
• dynamical origin of strong re-interactions• consistency v2 ↔ RAA
• open-bottom “contamination” • induced radiation vs. elastic scattering• …
Challenges:
pT [GeV/c]
RA
A
Djordjevic etal. ‘04
Armesto etal.‘05
jet-quench[Djordjevic etal ’04]
2.) Baseline Spectra in p-p, d-Au Charm vs. Bottom
3.) Heavy-Quark Elastic Scattering in QGP pQCD vs. Resonances Brownian Motion and Thermal Relaxation
4.) Heavy-Quark and Electron Spectra at RHIC Langevin Simulation, Hadronization RAA and v2
5.) Heavy Quarkonia Charmonium pT-Spectra
6.) Conclusions
Outline
2.) Heavy-Flavor Baseline Spectra at RHIC Single-Electron Decays D-Mesons
• bottom crossing at 5GeV !? (pQCD: ~4GeV [Cacciari etal ’05])• strategy: fix charm with D-mesons, adjust bottom in e±-spectra
TEtpp peetpf /2/)]([ 220
2
1),(
)1()( 22 teD
t
2
2
p
fD
p)pf(
tf
• Brownian Motion:
kpkwkdp ),(323 ),(
2
1 kpkwkdD
scatt. rate
diff. const.
3.) Elastic Heavy-Quark Scattering in the QGP
• e.g. T=400MeV, s=0.4 = 0.1 fm-1 ↔ therm~10fm/c slow!
3.1 Perturbative QCDg
c
q
c
• dominated by t-channel gluon-ex in gc→gc: gT~,~dtd
DD
s
2
2
Fokker Planck Eq.
[Svetitsky ’88,Mustafa etal ’98, Molnar etal ’04Zhang etal. ’04,Teaney+Moore‘04]
3.2 Open-Charm Resonances in QGP
h.c.2
v1 c)(
qG DDDcq L
• effective model with pseudo/scalar + axial/vector “D-mesons”
551 ,,,
“Light”-Quark Resonances
1.4Tc
[Asakawa+ Hatsuda ’03]
• parameters: mD(0)=2GeV , GD ,
mc=1.5GeV, mq=0 • number of D-states: 4 per u and d, 2 for s• cross section isotropic • more microscopic → [M.Mannarelli’s talk]
[van Hees+ RR ’04]
c
“D”
c
_q
_q
3.3 Heavy-Quark Thermalization Times in QGP
• substantially smaller for resonances
Charm: pQCD vs. Resonances
pQCD
“D”
• crelax ≥ (T>0.25GeV) ≈ 1fm/c
• bottom does not thermalize (10%)
Charm vs. Bottom
→ stochastic implementation of heavy quarks in expanding fireball with realistic time evolution of bulk v0 , v2
4.) Heavy-Quark and Electron Spectra at RHIC 4.1 Relativistic Langevin Simulations
[van Hees,Greco+RR ’05]
Nuclear Suppression Factor
• pQCD elastic scatt. moderate • resonance effects substantial
• characteristic “leveling-off”• factor ~4 from resonances
Elliptic Flow
frag2
2333
)p(f)p(f|)q(|qd)(
pdg
pd
dNE ccqqDD
D
4.2 Single-Electron v2 and RAA at RHIC fq from, K
coalescence+ fragment.
[van Hees, Greco +RR ’05]
• coalescence increases both RAA and v2 , resonances essential• bottom contribution reduces effects• induced gluon radiation?
Elliptic Flow Nuclear Suppression FactorMinimun-BiasAu-Au 200GeV
Minimun-BiasAu-Au 200GeV
5.) J/ pt-Spectra in Au-Au at RHIC
• total yields different by factor 3
• large sensitivity to radial flow (t,max=0.5-0.65)
[Thews+Mangano ’05]
[Greco,Ko+RR ’04]
Quark Coalescence at Tc
6.) Summary
• “D”-meson resonances in QGP (lQCD spectral fcts., potentials) c(b)-quark thermalization ~4(12)fm/c (elastic scattering), (factor ~3 faster than pQCD)
• Langevin simulation for RHIC + coalescence/fragmentation: - electrons: v2 ≤ 11% , RAA ≥ 0.45 (MinBias), “compromised” by bottom - predictions similar to new PHENIX data
• sQGP elastic scattering (resonances) prevalent over radiation at low / medium pt !?
• (more) uncertainties: hadronic phase (lifetime), smaller mc (?), bottom contribution, softer fragmentation
• impact on quarkonia, dileptons (intermediate mass)
3.) Resonances in QGP: Microscopic Description Lattice Q-Q Free Energy
TSUF QQQQ
QQQ mU 2
[BielefeldGroup ’04]
Applications
• → Schröd.-Eq. → bound states (sQGP)!
• scattering states? imaginary parts? → Lippmann-Schwinger Equation
QQU[Shuryak,Zahed, Brown ’04]
Selfconsistency Problem[Mannarelli+RR ’05]
q-q T-Matrix -
Quark-Selfenergy
3.2 Selfconsistent T-Matrix and Selfenergy [Mannarelli+RR ’05]
• assume mq(gluon)=0.1GeV
• transition from bound (1.2Tc) to resonance states! • quark-width ≈0.3GeV≈(2/3fm)-1 (≈ mass ↔ liquid!?) • colored states, equat. of state?
q-q T-Matrices -
Quark Self-
Energy
T=1.2Tc
T=1.5Tc
T=1.75Tc
T=1.5Tc
Individual Charm- and Bottom-Electron RAA and v2
2.4.2 Langevin-Simul. at RHIC: Heavy-Quark v2
Resonances vs. pQCD Charm-pQCD (s, D=1.5T)
[van Hees,Greco+RR ’05]
• characteristic “leveling-off”• factor ~4 from resonances • more sensitive to res.-coupling
• hydro with Tc=165, ≈ 9fm/c
• s and Debye mass independent[Moore and Teaney ’04]
2.4.1 Langevin-Simul. at RHIC: Heavy-Quark RAA
[van Hees,Greco+RR ’05]
Resonances vs. pQCD Charm-pQCD (s, D=1.5T)s , g
1 , 3.5
0.5 , 2.5
0.25,1.8
[Moore and Teaney ’04]
• hydro with Tc=165MeV, ≈ 9fm/c
• s and Debye mass independent
• expanding fireball ≈ hydro • pQCD elastic scatt. moderate • resonance effects substantial
c-Quark Drag and Diffusion Coefficients in QGP
• substantially smaller for resonances
Thermalization Times [van Hees+RR ’04]
pQCD
“D”
Coordinate Space Diffusion
• ‹x2› - ‹x›2 = Dx t ≈ (5 fm)2
~ fireball size at Tc
• QGP-suppression prevalent• no “jump” in theory
• QGP-regeneration dominant• sensitive to: mc
* , (Ncc )2 ↔ rapidity, √s, A
4.4 Charmonium in A-A
SPS RHIC
[Grandchamp etal. ’03]
Pb(158AGeV)-Pb
[Grandchamp +RR ’03]
J/ Excitation Function
same net suppression at SPS + RHIC!
3.4.3 Scrutinizing Charmonium Regeneration II: J/ Elliptic Flow
Suppression only Thermal Coalescence at Tc
[Wang+Yuan ’02]
[Greco etal ’04]
MB Au-Au
• factor ~5 different! • transition in pt!?