Heavy Flavor in the sQGP

1
Heavy Flavor in the sQGP
Ralf Rapp Cyclotron Institute Physics
Department Texas AM University College
Station, USA With H. van Hees, D. Cabrera
(Madrid), X. Zhao, V. Greco (Catania), M.
Mannarelli (Barcelona) 24. Winter Workshop on
Nuclear Dynamics South Padre Island (Texas),
09.04.08
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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
• - connect pT regimes via underlying HQ
  interaction?
• - strong coupling perturbation theory becomes
  unreliable,
• resummations
  required
• - simpler(?) problem heavy quarkonia ?
  potential approach
• - similar interactions operative for elastic
  heavy-quark scattering?

3
Outline
1.) Introduction 2.) Heavy Quarkonia in QGP
? Charmonium Spectral Correlation Functions
? In-Medium T-Matrix with lattice-QCD
potential 3.) Open Heavy Flavor in QGP ?
Heavy-Light Quark T-Matrix ? HQ Selfenergies
Transport ? HQ and e Spectra ?
Implications for sQGP 4.) Constituent-Quark
Number Scaling 5.) Conclusions
4
2.1 Quarkonia in Lattice QCD

• direct computation of
• Euclidean Correlation Fct.

spectral function

• accurate lattice data for Euclidean Correlator

hc
cc
Datta et al 04

• S-wave charmonia little changed to 2Tc Iida
  et al 06, Jakovac et al 07,
• 
  
  Aarts et al 07

5
2.2 Potential-Model Approaches for Spectral Fcts.
J/y
s/w2
Karsch et al. 87, , Wong et al. 05,
MocsyPetreczky 06, Alberico et al. 06,
Y

• bound state free continuum model
• too schematic for broad / dissolving states

cont.
w

• Lippmann-Schwinger Equation

Ethr
MannarelliRR 05,CabreraRR 06
- 2-quasi-particle propagator - boundscatt.
states, nonperturbative threshold effects (large)

• Correlator
  LS,P

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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(r8,T)

• (much) smaller binding for
• V1F1 , V1 (1-a) U1 a F1

CabreraRR 06 PetreczkyPetrov04
Wong 05 Kaczmarek et al 03
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2.3 Charmonium Spectral Functions in QGP
withinT-Matrix Approach (lattice U1 Potential)
Fixed mc1.7GeV
In-medium mc (U1 subtraction)
hc
hc

• gradual decrease of binding, large rescattering
  enhancement
• hc , J/y survive until 2.5Tc , cc up to 1.2Tc

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2.4 Charmonium Correlators above Tc

• lattice U1-potential, in-medium mc, zero-mode
  Gzero Tc(T)

CabreraRR in prep.
T-Matrix Approach
Lattice QCD
Aarts et al. 07
hc
cc1

• qualitative agreement

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3.) Heavy Quarks in the QGP

• Brownian
• Motion

Fokker Planck Eq.
Svetitsky 88,
Q
scattering rate diffusion constant
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3.2 Potential Scattering in sQGP
MannarelliRR 05

• T-matrix for Q-q scatt. in QGP
• Casimir scaling for color chan. a
• in-medium heavy-quark selfenergy

• Determination of potential
• fit lattice Q-Q free energy
• currently
• significant
• uncertainty

_
Shuryak Zahed 04
Wong 05
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3.2.2 Charm-Light T-Matrix with lQCD-based
Potential
Temperature Evolution Channel Decomposition
van Hees, Mannarelli, GrecoRR 07

• meson and diquark S-wave resonances up to
  1.2-1.5Tc
• P-waves and (repulsive) color-6, -8 channels
  suppressed

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3.2.3 Charm-Quark Selfenergy Transport
Selfenergy
Friction Coefficient

• charm quark widths Gc -2 ImSc 250MeV close
  to Tc
• friction coefficients increase(!) with
  decreasing T? Tc!

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3.3 Heavy-Quark Spectra at RHIC

• relativistic Langevin simulation in thermal
  fireball background

Nuclear Modification Factor
Elliptic Flow
pT GeV
pT GeV

• T-matrix approach effective resonance model
• other mechanisms radiative (2?3),

Wiedemann et al.05,Wicks et al.06, Vitev et
al.06, Ko et al.06
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3.5 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 pTe 5GeV in d-Au
• (3.5GeV in Au-Au)
• 30 uncertainty due to
• lattice QCD potential
• suppression early, v2 late

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3.6 Maximal Interaction Strength in the sQGP

• potential-based description ? strongest
  interactions close to Tc
• - consistent with minimum in h/s at Tc
• - strong hadronic correlations at Tc ? quark
  coalescence
• semi-quantitative estimate for diffusion
  constant

weak coupl. h/s 4/15 n ltpgt ltr1/5 T Ds
strong coupl. h/s 1/4p Ds(2pT) 1/2 T Ds
? h/s (2-4)/4p close to Tc
Lacey et al. 06
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4.) Constitutent-Quark Number Scaling of v2

• CQNS difficult to recover with local v2,q(p,r)
• Resonance Recombination Model
• resonance scatt. qq ? M close to Tc using
  Boltzmann eq.
• quark phase-space distrib. from relativistic
  Langevin, hadronization at Tc

Molnar 04, GrecoKo 05, PrattPal 05
-
RavagliRR 07

• energy conservation
• thermal equil. limit
• interaction strength
• adjusted to v2max 7
• no fragmentation
• KT scaling at both
• quark and meson level

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5.) Summary and Conclusions

• T-matrix approach with lQCD internal energy
  (UQQ)
• S-wave charmonia survive up to 2.5Tc,
• consistent with lQCD correlators spectral
  functions
• T-matrix approach for (elastic) heavy-light
  scattering
• large c-quark width small diffusion
• Hadronic correlations dominant (meson
  diquark)
• - maximum strength close to Tc ? minimum in
  h/s !?
• - naturally merge into quark coalescence at
  Tc
• Observables quarkonia, HQ suppressionflow,
  dileptons,
• Consequences for light-quark sector? Radiative
  processes?
• Potential approach?

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3.5.2 The first 5 fm/c for Charm-Quark v2 RAA
Inclusive v2

• RAA built up earlier than v2

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3.2.4 Temperature Dependence of Charm-Quark Mass

• significant deviation only close to Tc

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2.3.3 HQ Langevin Simulations Hydro vs. Fireball

Elastic pQCD (charm) Hydrodynamics
MooreTeaney 04
as , g 1 , 3.5 0.5 , 2.5 0.25,1.8

• Tc165MeV,
• t 9fm/c
• sgQ (as/mD)2
• as and mDgT
• independent
• (mD1.5T)

• as0.4, mD2.2T
• ? D(2pT) 20
• ? hydro
• fireball
• expansion

van Hees,GrecoRR 05
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3.6 Heavy-Quark Single-e Spectra at LHC

• relativistic Langevin simulation in thermal
  fireball background
• resonances inoperative at Tgt2Tc , coalescence at
  Tc

• harder input spectra, slightly more suppression
  ? RAA similar to RHIC

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2.5 Observables at RHIC Centrality pT Spectra

• update of 03 predictions - 3-momentum
  dependence
• -
  less nucl. absorption c-quark thermalization

X.ZhaoRR in prep

• direct regenerated (cf. )
• sensitive to tctherm , mc , Ncc

Yan et al. 06
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3.2 Model Comparisons to Recent PHENIX Data
Single-e Spectra PHENIX 06

• pQCD radiative E-loss with
• 10-fold upscaled transport coeff.
• Langevin with elastic pQCD
• resonances coalescence
• Langevin with 2-6 upscaled
• pQCD elastic

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3.2.2 Transport Properties of (s)QGP
x2-x2 Dst , Ds 1/g
Spatial Diffusion Coefficient
Charm-Quark Diffusion
Viscosity-to-Entropy Lattice QCD
Nakamura Sakai 04

• small spatial diffusion ? strong coupling

• E.g. AdS/CFT correspondence h/s1/4p, DHQ1/2pT
• ? resonances DHQ4-6/2pT , DHQ h/s
  (1-1.5)/p

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2.4 Single-e at RHIC Effect of Resonances

• hadronize output from Langevin HQs (d-fct.
  fragmentation, coalescence)
• semileptonic decays D, B ? enX

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2.4.2 Single-e at RHIC Resonances Q-q
Coalescence
fq from p, K
Greco et al 03
Elliptic Flow
Nuclear Modification Factor

• less suppression and more v2
• anti-correlation RAA ? v2 from coalescence
  (both up)
• radiative E-loss at high pT?!

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2.3 Heavy-Quark Spectra at RHIC

• Relativistic Langevin Simulation
• stochastic implementation of HQ motion in
  expanding QGP-fireball
• hydrodynamic evolution of bulk-matter bT , v2

van Hees,GrecoRR 05
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2.1.3 Thermal Relaxation of Heavy Quarks in QGP

Charm pQCD vs. Resonances
Charm vs. Bottom
pQCD
D

• tctherm tQGP 3-5 fm/c
• bottom does not thermalize

• factor 3 faster with
• resonance interactions!

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5.3.2 Dileptons II RHIC
RR 01
QGP

• low mass thermal! (mostly in-medium r)
• connection to Chiral Restoration a1 (1260)? pg
  , 3p
• int. mass QGP (resonances?) vs. cc ? ee-X
  (softening?)

-