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:

QQ

• 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

QQ

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]