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]

QQ

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!