Quarkonium Correlators in Medium

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Quarkonium Correlators in Medium
Ralf Rapp Cyclotron Institute Physics
Department Texas AM University College
Station, USA Quarkonium Working Group Workshop
QWG 07 Deutsches Elektronen Synchrotron
(Hamburg), 19.10.07
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1.) Introduction Quarkonia Probing the QGP

• immerse -pair into the QGP
• ? Vacuum properties change

• color screening (reduced binding)
  
• dissociation reactions (and reverse!)
• heavy-quark mass (? mass, decay rates,
  threshold)

• Experiment Heavy-Ion Collisions
• yields no access to spectral shape (?)
• mass ? equilibrium number exp(-M/T)
• pT-spectra, v2(pT)

Theory - in-medium -spectral functions
- Euclidean correlators lattice
QCD ? effective models
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Outline
1.) Introduction 2.) Potential Models
Spectral Functions 2.1 SFs Correlators,
Lattice Results 2.2 Potential Models
(Schrödinger/T-Matrix) 2.3 Uncertainties in
Potential HQ Mass 3.) T-Matrix Approach
3.1 Baseline Results 3.2 In-Medium HQ Masses
3.3 Width Effects 4.) Charmonia at RHIC 5.)
Summary Outlook
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2.1 Euclidean Correlator Timelike Spectral
Function
Early Example Dileptons (r, w)
integrate
Wetzorke et al 01
RR 01

• schematic at the time

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2.1.2 Lattice QCD Computations G / Grecon SFs

• accurate data from lattice QCD

hc
cc
Datta et al 04

• S-wave charmonia little changed to 2Tc, P-wave
  signal enhanced(!)
• similar in other lQCD studies Iida et al 06,
  Jakovac et al 07, Aarts et al 07

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2.2 Potential-Model Approaches for Spectral Fcts.
s/w2

• Schrödinger Eq. for bound
• state free continuum
• sy(w) Fy2 d(w - my ) w2 Q(w -Ethr) fythr
• - improved for rescattering

J/y
Shuryak et al 04, Wong 05, Alberico et al 05,
MocsyPetreczky 05
Y
cont.
w
Mocsy et al 06, Laine 07, Wong et al 07,
Alberico et al 07
Ethr

• Lippmann-Schwinger-Eq.
• for

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

• Correlator
  LS,P

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2.3.1 Uncertainties I Lattice QCD-based
Potentials

• free vs. internal energy F1 (rT) U1(rT)
  T S(rT)

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

CabreraRR 06 PetreczkyPetrov04
Wong 05 Kaczmarek et al 03
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2.3.2 Uncertainties II Heavy-Quark Masses in the
QGP

• quarkonium mass my 2mc - eB
• asymptotic energies F8 U8 - TS8

U8
Kaczmarek Zantow 05
F8

• close to Tc - increasing heavy-quark mass?!
• - entropy contribution?

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3.) T-Matrix Approach
3.1 Baseline Results 3.2 In-Medium HQ Masses
3.3 Width Effects
CabreraRR 06
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3.1 Baseline Results V1U1, mc1.7GeV fix, Gy
small, Grec Gvac
hc
cc

• slightly overbound at 1.1Tc
• (or mc too small)
• dissolves at gt2.5Tc

• quickly dissolves above Tc

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3.2 T-Matrix with in-medium mc - I

• lattice U1-potential, mc from U1 subtraction

hc

• upward shift due to large mc at 1.1Tc
• stable my2mc-eB above ? correlator within 20

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3.2.2 T-Matrix with in-medium mc - II

• lattice U1-potential, adjust mc close to Tc
  zero modes S-Waves

CabreraRR in prep
T-Matrix Approach
Aarts et al. 07
Lattice QCD
J/y
hc

• fair agreement!

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3.2.3 T-Matrix with in-medium mc - II

• lattice U1-potential, adjust mc close to Tc
  zero modes P-Waves

Cabrera RR in prep
T-Matrix Approach
Aarts et al. 07
Lattice QCD
cc0
cc1

• fair agreement!

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3.2.4 Temperature Dependence of Charm-Quark Mass

• significant deviation only close to Tc

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3.3 Finite-Width Effects

• c-quark width in propagator
• dominant process depends on eB

J/y Lifetime
GrandchampRR 01
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4.) Observables at RHIC Centrality pT Spectra

• updated predictions including 3-momentum
  dependencies

X.Zhao RR in prep

• balance direct - regenerated
• sensitive to mc , Ncc

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5.) Summary

• potential models useful tool to interpret
  finite-T lQCD
• importance of nonperturbative threshold effects
• consistency of boundscatt. states mc
  mandatory (T-matrix)
• significant uncertainties (U1 vs. F1 , mc)
• S-wave charmonia survival to 2-3Tc in line with
  lQCD correlators
• no conclusive interpretation yet
• threshold reduction compensates decreasing
  binding
• quarkonium lifetimes of tY 1fm/c possibly
  relevant

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4.) Suppression Regeneration in Heavy-Ion
Collisions

• 3-Stage Dissociation nuclear (pre-eq) --
  QGP -- HG
• Stot exp-snuc r L
  exp-GQGP tQGP exp-GHG tHG
• Regeneration in QGP HG
• - microscopically backward reaction (detailed
  balance!)

- snuc(SPS) 4.5mb - RHIC d-Au data ? snuc
0-3mb
PBM etal 01, Gorenstein etal 02,Thews etal
01, GrandchampRR 01, Ko etal 02, Cassing etal
03
- for thermal c-quarks and gluons
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3.3.2 Observables II Excitation Function
Rapidity
J/y Suppression vs. Regeneration
Sequential Y cc Suppression

Grandchamp RR 01
Karsch,KharzeevSatz 06

• direct J/y essentially survive
• (even at RHIC)

• nontrivial flat dependence
• similar interplay in rapidity!?
• (need accurate dNc/dy)