heavy-quark diffusion, flow and recombination at rhic ralf rapp cyclotron institute + physics...
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Heavy-Quark Diffusion, Flow and
Recombination at RHIC
Ralf Rapp Cyclotron Institute + Physics Department
Texas A&M University College Station, USA
With: H. van Hees, V. Greco (…)
Strangeness in Quark Matter Conference 2006 Los Angeles, 30.03.06
1.) Introduction-I: The Virtue of HQ’s in URHICs
• , production follows
N-N collision-scaling
Valuable Probe of Medium:
bbcc
• distinguishable from gluons
• mass + charge-dependence of jet quenching (induced radiation?)
• elastic rescattering, (approach to) thermalization, collective flow: pQCD?! sQGP?!
• coalescence at low(er) pT: cq→ D (even in pp), cc →
[PHENIX ’04]
1.2 Intro-II: pQCD Jet Quenching
• enough quenching? (upscaled transport coefficient)• Gluon Plasma (maximal color charge)• pions over-quenched (pT ≤ 4GeV)• “drag” on heavy quarks → flow • consistency v2 ↔ RAA
Challenges:
[Armesto et al ’05][Gyulassy et al ’05]
1.3 Intro-III: Single-e± Elliptic Flow
coalescence assuming v2c=v2
q vs. jet quenching
• dynamical origin of re-interactions: radiative vs. elastic scattering, 3↔3 • bottom contribution• transition soft – intermediate hard …
Challenges:
[Armesto et al ’05]
jet-quench[Djordjevic et al ’04]
?
[Liu+Ko’06]
2.) Baseline Spectra in p-p, d-Au • Charm vs. Bottom
3.) Heavy-Quark Elastic Scattering in QGP • Brownian Motion and Thermal Relaxation • pQCD vs. Resonances
4.) Heavy-Quark and Electron Spectra at RHIC • Langevin Simulation, Hadronization • RAA and v2
5.) Heavy Quarkonia
• Charmonium pT-Spectra
6.) Summary
Outline
2.) Heavy-Flavor Baseline Spectra at RHIC Semileptonic Electrons D-Mesons
• bottom crossing at 5GeV !? (~pQCD [Cacciari et al ’05])• strategy: fix charm with D-mesons, adjust bottom in e±-spectra
QmDT γ=
2
2
p
fD
p)pf(
tf
∂∂+∂
∂=∂∂ γ• Brownian
Motion:
scattering rate diffusion constant
3.) Heavy-Quark Elastic Scattering in the QGP
Fokker Planck Eq.[Svetitsky ’88,…]Q
• e.g. T =400 MeV, s=0.4:therm~10 fm/c slow! (QGP ≤ 5 fm/c)
3.1 Perturbative QCD
g
c
dominated by t-channel gluon-ex.:
Microscopic Calculation of Diffusion:
q
c gT~,~dtd
DD
s μμσ
2
2
[Svetitsky ’88, Mustafa et al ’98, Molnar et al ’04Zhang et al ’04, Hees+RR ’04, Teaney+Moore‘04]
∫= kpkwkdp ),(3γ23 ),(
2
1∫= kpkwkdD
3.2 Open-Charm Resonances in QGP
h.c.2
v1 +/+= c)(qG DDDcq φΓL
• effective model with pseudo/scalar + axial/vector “D-mesons”
μμ γγγγΓ 551 ,,,=
“Light”-Quark Resonances
1.4Tc
[Asakawa+ Hatsuda ’03]
• parameters: mD=2GeV , GD , mc=1.5GeV, mq=0 • no. of D-states (chiral+HQ symm.): 8 per u and d, 4 for s• resonance cross section isotropic, pQCD forward
[van Hees+ RR ’04]
c
“D”
c
_q
_q
3.3 Heavy-Quark Thermalization Times in QGP
• decreased by factor ~3 with resonances
Charm: pQCD vs. Resonances
pQCD
“D”
• crelax ≥ (T>0.25GeV) ≈ 1fm/c
• bottom ≈ 3 charm
Charm vs. Bottom
• initialize heavy quarks (Glauber) in elliptic QGP fireball • realistic time evolution of bulk v0 , v2 • simulate HQ paths with drag and diffusion in QGP
4.) Heavy-Quark and Electron Spectra at RHIC 4.1 Relativistic Langevin Simulations for HQs
[van Hees, Greco+RR ’05]
Nuclear Modification Factor
• resonance effects large• bottom much less affected
• characteristic “leveling-off”• factor 3-4 from resonances
Elliptic Flow
4.2.1 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 for pT ~ 1-5 GeV• anti-correlation RAA ↔ v2 from coalescence (both up) • radiative E-loss at pT ≥ 5GeV ?!
4.2.2 Single-e± at RHIC: Resonances + Q-q Coalescence
frag2
2333
−+= ∫ ∫ ψπ
σ μμ
)p(f)p(f|)q(|qd)(
pdg
pddN
E ccqqDDD rrr fq from π, K
Nuclear Modification Factor Elliptic Flow
[Greco et al ’03]
4.2.3 Formfactor Effect on Resonance Formation
• formfactor affects higher pT
• rather far from equilibrium
Charm-Quark RAA
• replace (renormalized) point vertex by formfactor (=1GeV)
c
“D”
c
_q
_q
Charm-Quark v2
5.) J/ψ pT-Spectra in Au-Au at RHIC
• total yields different by up to factor 3• rather sensitive to radial flow (t,max=0.5-0.65)
• Cronin effect for quantitative RAA
[Greco,van Hees+RR in prep][Greco,Ko+RR ’04]
• Recombination via Quark Coalescence at Tc
Zero vs. Maximal Reinteraction “Realistic” Input from Langevin
pQCD scatt.
resonance scatt.
J/ψ Elliptic Flow
largest sensitivity!
6.) Summary
• “D”-/”B”- resonances in sQGP (elastic scattering) - accelerate c-/b-quark thermalization (factor ~3 over pQCD) - coalescence increases both v2 and RAA (consistency!)
• existence of resonances (q-Q, q-q) to be scrutinized
• complete treatment incl. elastic + radiative processes - discriminate with angular correlations (tagged Q-jets)?
• consistency with / impact on: - light-parton spectra - quarkonia (v2!) - IM dileptons (vs. QGP radiation)
• pQCD energy loss ↔ Gluon-Plasma, color charge resonances ↔ Quark-Gluon Plasma, nonpert. dynamics
2.4.1 Langevin-Simul. at RHIC: Heavy-Quark RAA
[van Hees,Greco+RR ’05]
Resonances vs. pQCD Charm-pQCD (s, μD=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
4.1.2 HQ Langevin-Simulations with Hydro + pQCD
Elliptic Flow
[Moore+Teaney ’04]
• Charm-pQCD cross sections with variable s , μD=1.5T fix
• Hydrodynamic bulk evolution with Tc=165MeV, ≈ 9fm/c
s , g
1 , 3.5
0.5 , 2.5
0.25,1.8
• correlation: small RAA ↔ large v2
• realistic coupling / decoupling ?
Nuclear Modification
4.2.3 Semi-Central e± RAA at RHIC
[van Hees,Greco +RR ’05]
• coalescence favored
• Elliptic QGP fireball with D-/B-resonances, coal./frag. and decay
Coal. + Frag. Fragmentation only
4.2.3 Light-Parton Jet-Quenching RHIC
[Armesto et al.]• problems below ~4-5GeV
• pion quenching in pQCD
3.4.3 Scrutinizing Charmonium Regeneration II: J/ψ Elliptic Flow
Suppression only Thermal Coalescence at Tc
[Wang+Yuan ’02]
[Greco etal ’04]
MB Au-Au
• factor ~5 different! • transition in pt!?
5.) Resonances in QGP from Lattice QCD 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
_
5.2 Lattice Spectral Functions vs. T-Matrix in QGP
Evidence for Resonances in sQGP!? more studies required …
[Datta etal ’03]
LQCD Spectral Function:Charmonium
[Mannarelli+RR ’05]
Q-Q T-Matrix (ladder approx.) based on Lattice Potential
_
QQV
• reasonable qualitative agreement
• Parton Cascade with fixed σ(q,g-c), forward/isotropic, coalescence
• similar to Langevin; Xsection effect on pT-spectra moderate • no bottom
4.3 Single-e± at RHIC: Transport Calculations
[Zhang,Chen+Ko ‘05]
Elliptic Flow pT-Spectra
[MPC, AMPT]
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/ψ Excitation Function
same net suppression at SPS + RHIC!