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Quarkonium Correlators in Medium. Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA Quarkonium Working Group Workshop QWG ‘07 Deutsches Elektronen Synchrotron (Hamburg), 19.10.07. _. Q-Q Potential Scattering Rates - PowerPoint PPT Presentation
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Quarkonium Correlators in Medium
Ralf Rapp Cyclotron Institute + Physics Department
Texas A&M University College Station, USA
Quarkonium Working Group Workshop QWG ‘07Deutsches Elektronen Synchrotron (Hamburg), 19.10.07
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
Q-Q Potential
Scattering Rates
Q Selfenergy
_
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
Outline
2.1 Euclidean Correlator + Timelike Spectral Function
)T/sinh(])T/[cosh(
)T,(d)T,(2
21
0
Early Example: Dileptons (, )
integrate
• schematic at the time[RR ‘01] [Wetzorke
et al ‘01]
2.1.2 Lattice QCD Computations: G / Grecon + SFs
• accurate “data” from lattice QCD
)(~)T,(G,]T/[
)]T/([)T,(d)T,(G
vacrecon
sinhcosh
221
0
• 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]
c
c
[Datta et al ‘04]
• Correlator: L=S,P
• Lippmann-Schwinger-Eq. for Q-Q T-Matrix: -
2.2 Potential-Model Approaches for Spectral Fcts.
)'q,k;E(T)k,E(G)k,q(Vdkk)'q,q(V)'q,q;E(T LQQLLL02
[Mannarelli+RR ’05,Cabrera+RR ‘06]
000QQLQQQQL GTGG)E(G
- 2-quasi-particle propagator:
- bound+scatt. states, nonperturbative threshold effects (large!)
• Schrödinger Eq. for bound state + free continuum () = F
2 (m) + 2 -thrfthr
- improved for rescattering
2
J/
’
cont.
[Shuryak et al ’04, Wong ’05, Alberico et al ’05, Mocsy+Petreczky ’05]
[Mocsy et al ’06, Laine ’07, Wong et al ’07, Alberico et al ‘07] Ethr
])(/s/[)s(G QkkQQ20 4
2.3.1 Uncertainties I: “Lattice QCD-based” Potentials
• (much) smaller binding for V1=F1 , V1 = (1-U1 + F1
• free vs. internal energy: F1 (r;T) = U1(r;T) – T S(r;T)
[Cabrera+RR ’06; Petreczky+Petrov’04]
[Wong ’05; Kaczmarek et al ‘03]
2.3.2 Uncertainties II: Heavy-Quark Masses in the QGP
[Kaczmarek +Zantow ‘05]
• close to Tc: - increasing heavy-quark mass?!
- entropy contribution?
• quarkonium mass: m= 2mc* - B
• asymptotic energies F∞ = U∞ - TS∞
U∞
F∞
3.) T-Matrix Approach
3.1 Baseline Results
3.2 In-Medium HQ Masses
3.3 Width Effects
[Cabrera+RR ‘06]
3.1 Baseline Results: V1=U1, mc=1.7GeV fix, small, Grec= Gvac
Q-Q T-Matrix - cc
• slightly overbound at 1.1Tc
(or mc too small)• dissolves at >2.5Tc
• quickly dissolves above Tc
• ~40% variation in S-wave (1.1Tc overbound), P-wave: zero modes needed
3.2 T-Matrix with in-medium mc* - I
• lattice U1-potential, mc* from U1 subtraction
c
• upward shift due to large mc* at 1.1Tc
• ~stable m=2mc*-B above → correlator within ~20%
• lattice U1-potential, adjust mc* close to Tc + zero modes; S-Waves:
3.2.2 T-Matrix with in-medium mc* - II
J
c
T-Matrix ApproachLattice QCD
[Cabrera+RR in prep] [Aarts
et al. ‘07]
• fair agreement!
• lattice U1-potential, adjust mc* close to Tc + zero modes; P-Waves:
3.2.3 T-Matrix with in-medium mc* - II
c1
c0
T-Matrix ApproachLattice QCD
[Aarts et al. ‘07]
[Cabrera +RR in prep]
• fair agreement!
3.2.4 Temperature Dependence of Charm-Quark Mass
• significant deviation only close to Tc
])(/s/[)s(G QkkQQ24
3.3 Finite-Width Effects• c-quark width in propagator
• dominant process depends on BJ/ Lifetime
_
[Grandchamp+RR ‘01]
[Cabrera+RR ‘06]
• moderate width → small enhancement
• effect on correlator
c
• balance direct - regenerated• sensitive to: mc* , Ncc
4.) Observables at RHIC: Centrality + pT Spectra
[X.Zhao+ RR in prep]
• updated predictions including 3-momentum dependencies
5.) Summary
• potential models useful tool to interpret finite-T lQCD
• importance of nonperturbative threshold effects
• consistency of bound+scatt. 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 ≤ 1fm/c possibly relevant
• 3-Stage Dissociation: nuclear (pre-eq) -- QGP -- HG
Stot = exp[-nuc L] exp[-QGP QGP ] exp[-HGHG ]
• Regeneration in QGP + HG: - microscopically: backward reaction (detailed balance!)
key ingredients: reaction rate equilibrium limit ( -width) )m,m,N( ccc
(links to lattice QCD)
)NN(d
dN eq
4.) Suppression + Regeneration in Heavy-Ion Collisions
[PBM etal ’01, Gorenstein etal ’02,Thews etal ’01,Grandchamp+RR ’01, Ko etal ’02, Cassing etal ‘03] J/ + g c + c + X←→ -
- for thermal c-quarks and gluons:
- nuc(SPS) ≈ 4.5mb - RHIC d-Au data → nuc≈ 0-3mb
• nontrivial “flat” dependence• similar interplay in rapidity!? (need accurate dNc/dy)
3.3.2 Observables II: Excitation Function + Rapidity
J/ Suppression vs. Regeneration
[Grandchamp +RR ’01]
• direct J/ essentially survive (even at RHIC)
Sequential ’+ c Suppression
[Karsch,Kharzeev+Satz ‘06]