Theoretical Aspects of Heavy Quarkonia in HeavyIon Collisions

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Theoretical Aspects of Heavy Quarkonia in
Heavy-Ion Collisions
Ralf Rapp Cyclotron Institute Physics
Department Texas AM University College
Station, USA with D. Cabrera (Madrid), L.
Grandchamp, X. Zhao (Texas AM) Tamura
Symposium University of Texas at Austin, 21.11.08
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1.) Introduction Quarkonia in URHICs

• Production - shadowing (nucl. PDF)
• - pT broadening (Cronin)
• Pre-Equilibrium - formation time
  (Lorentz-dilated)
• - nuclear
  absorption
• -
  pre-equilibrium medium

• Equilibrium Matter
• - bound-state properties (mass/binding energy)
• - dissolution temperature (inelastic width ?
  formation!)
• - relation to QGP / hadronic matter
• phase transition? order parameter?
• Expanding Medium
• - collectivity (elastic Y-parton scattering?)
• - regeneration c c ? Y X ? open-charm flow
  

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Outline
1.) Introduction 2.) Heavy Quarkonia in
Medium ? Lattice QCD, Color Screening and
Quark Mass ? Spectral/Correlation Functions
Potential Models ? Inelastic Reactions
Rates Momentum Dependence 3.) Phenomenology at
SPS RHIC ? Rate Equation Approach ?
Suppression vs. Regeneration at SPS RHIC ?
Momentum and Tdiss Dependence 4.) Conclusions
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2.1 Quarkonia in Lattice QCD

• direct computation of
• Euclidean Correlation Fct.

spectral function

• accurate lattice data for Euclidean Correlator

hc
Datta et al 04
Asakawa et al 03, Iida et al 06, Jakovac et
al 07, Aarts et al 07

• S-wave charmonia little changed to 2Tc
• Bound states survive? Spectral functions?!
  
  

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2.2 Potential Models for Spectral Functions

• well established in vacuum (EFT, lattice)
• Schrödinger equation in medium
• correlators quark rescatt. in continuum

MocsyPetreczky 06, Alberico et al 06, Wong
07, Laine 07,

• Lippmann-Schwinger Equation

MannarelliRR 05,CabreraRR 06
In-Medium Q-Q T-Matrix
-
-
- Q-Q propagator - boundscattering states
(threshold effects!)

• 2-body potential VL at finite temperature?

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2.2.1 Color Screening Quarkonium Binding in QGP
e.g. screened Cornell pot.
Charmonium
Bottomonium
Tc
Tc
m gT GeV
MatsuiSatz 86, Karsch,MehrSatz 88, Wong
04,
m gT GeV

• quarkonium binding substantially reduced above Tc

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2.2.2 Heavy-Quark Free Energy in Lattice QCD

• F1(r,T) U1(r,T) T S1(r,T)
• V1(r,T) X1(r,T) - X1(r8,T)
• X18 / 2 in-medium quark-mass correction (?)
• 2 extreme potential choices
• (a) X1 F1
• gt weak potential, eB(1.1Tc) 50 MeV
• small quark-mass correction
• (b) X1U1
• gt strong potential, eB(1.1Tc) 500 MeV
• large quark-mass correction
• approximate compensation in
• bound-state mass Ey 2mc0 X18 - eB

KaczmarekZantow 05
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2.2.3 In-Medium Charm-Quark Mass
KaczmarekZantow 05
F?

• large variation close to Tc mass
  interpretation?!
• heavy-quark mass from HQ susceptibility?
  Petreczky 08

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2.2.4 Charmonium Spectral Function Correlators
I Weak Potential V(r,T) F1
hc
Mocsy Petreczky 07

• low threshold (2mc 2.7GeV), ground state
  Tdiss 1.2 Tc
• gt early melting scenario compatible with
  lattice QCD

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2.2.5 Charmonium Spectral Function Correllators
IIStrong Potential V(r,T) U1
CabreraRR 06
hc
mc1.7GeV fix, Gy 40 MeV
hc
mc1.8-1.5 GeV Gy 40 MeV
decreasing 2mc (and eB) stabilizes correlator,
Tdiss2.5Tc
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2.3 Quarkonium Widths in QGP
? sensitive to binding energy (i.e.,
color screening)!
GrandchampRR 01
BhanotPeskin 79
J/y Dissociation
? Dissociation

• GY 100 MeV ?
• 60 J/y destroyed in Dt2fm/c

• very sensitive to color screening
• at RHIC tY 50 ? 5 fm/c

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2.3.2 Finite-Width Effects on Euclidean
Correlators
-

• c-quark width in cc propagator

hc
CabreraRR 06

• width GY 40 ? 100 MeV ? few- enhancement
• further stabilization with increasing T

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2.3.3 Momentum Dependence of Inelastic Width

• dashed lines gluo-dissociation
• solid lines quasifree dissociation
• similar to full NLO calculation

Park et al 07
ZhaoRR 07
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3.) Quarkonium Production in URHICs

• 3-Stage Dissociation nuclear (pre-eq) --
  QGP -- HG
• Stot exp-snuc r L
  exp-GQGP tQGP exp-GHG tHG

? solve rate equation in hydro/fireball/transport
background
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3.1 Charmonium at CERN-SPS

• sabs(J/y,y) 4.4,7.9 mb, T0 190-210 MeV
  (MB-central)
• suppression controlled by as 0.25 in quasifree
  dissociation rate

Centrality Dependence Momentum
Dependence

• gauge anomalous J/y suppression (mostly in
  QGP)
• pt dependence ? Cronin effect (p-A)
• (quasifree rate slightly suppresses pt2)

ZhaoRR 07
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3.2 Charmonium at RHIC Centrality Dependence

• fireball with T0340-370 MeV (MB-central)
• schematic relaxation for c-quark equilibration
• Nyeq (t) Nytherm(t) 1-exp(-t/tceq)

• 21 hydro with fixed c-quark
• distribution pQCD vs. thermal

Yan,ZhuangXu 06
GrandchampRR 03, ZhaoRR 07

• 50 regeneration in central Au-Au
• regeneration sensitive to c-quark equilibration?

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3.2.2 Charmonium at RHIC Momentum Dependence
Au-Au 200AGeV

• regeneration part ? blast-wave at Tc

• regeneration at low pT

ZhaoRR 07, 08
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3.2.3 Charmonium at RHIC Dissociation Temperature
Suppression only (Hydro)
Including Regeneration
Tdiss 2.0 Tc 1.2 Tc
threshold melting
finite width
ZhaoRR 08

• finite width and regeneration
• inhibit step structure

Gunji et al. 07
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3.3 Upsilon at RHIC
No Color-Debye Screening With
Color-Debye Screening
Grandchamp et al. 05

• ?(1S,2S) suppression unambiguous QGP signature
  ?!
• NB 50 feed-down on ?(1S)

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4.) Summary and Conclusions

• Interplay of color-screening and heavy-quark
  mass (width)
• essential to understand quarkonia in QGP
• lQCD-based potential VQQ F1 ? pQGP
  (Tdiss(y) 1.2Tc)
• 
  VQQ U1 ? sQGP (Tdiss(y) 2.5Tc)
• Charmonium in heavy-ion collision
• - gauge suppression at SPS (dissociation
  width)
• - up to 50 regeneration at RHIC, consistent
  with pt spectra
• - no steps for finite width, regeneration
• Intimate relations to open charm
• - mc ? eB , charm-quark diffusion ?
  regeneration
• Bottomonium
• - suppression very sensitive to color screening
  (width!)
• - regeneration (very) small at RHIC

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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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3.4 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 pTe 5GeV in d-Au
• (3.5GeV in Au-Au)
• 25 uncertainty due to
• differences in U1 potential
• suppression early, v2 late

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3.3 Heavy-Quark Spectra at RHIC

• relativistic Langevin simulation in elliptic
  expanding fireball background

Nuclear Modification Factor
Elliptic Flow
pT GeV
pT GeV

• T-matrix approach effective resonance model
• similar to coll. dissoc. AdilVitev 07
  radiative E-loss? (2?3),

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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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2.2.3 In-Medium Charm-Quark Mass
KaczmarekZantow 05
Petreczky 08

• large variation close to Tc
• mass interpretation!?

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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
• when using
• F1 ? pQCD!

_
Shuryak Zahed 04
Wong 05