Transcript 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),

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
1.) Introduction: Quarkonia Probing the QGP
• immerse QQ -pair into the QGP
 Vacuum properties change:
_
Q-Q Potential
• color screening (reduced binding)
Scattering Rates
• dissociation reactions (and reverse!)
• heavy-quark mass (→ mass, decay rates, threshold) Q Selfenergy
Experiment: Heavy-Ion Collisions
• yields; no access to spectral shape (?)
• mass ↔ equilibrium number ~ exp(-M/T)
• pT-spectra, v2(pT)
Theory: - in-medium QQ-spectral functions
- Euclidean correlators: lattice QCD ↔ effective models
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
2.1 Euclidean Correlator + Timelike Spectral Function

cosh(  [  1 / 2T ])
  ( ,T )   d   (  ,T )
sinh(  / 2T )
0
Early Example: Dileptons (r, )
integrate
[RR ‘01]
• schematic at the time
[Wetzorke
et al ‘01]
2.1.2 Lattice QCD Computations: G / Grecon + SFs

cosh[  (  1 / 2T )]
G ( ,T )   d   (  ,T )
, Grecon( ,T )  ~  vac (  )
sinh [  / 2T ]
0
• 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]
2.2 Potential-Model Approaches for Spectral Fcts.
et al ’04, Wong
• Schrödinger Eq. for bound [Shuryak
’05, Alberico et al ’05,
Mocsy+Petreczky ’05]
state + free continuum
y() = Fy2 d(  my )+ 2 Q( -Ethr) fythr
/2
J/y
Y’
cont.

- improved for rescattering
[Mocsy et al ’06, Laine ’07, Wong et al ’07, Alberico et al ‘07]
Ethr
• Lippmann-Schwinger-Eq.
- T-Matrix:
for Q-Q
[Mannarelli+RR ’05,Cabrera+RR ‘06]
TL( E ;q ,q' )  VL( q ,q' )   k 2dk VL( q ,k ) GQ0 Q ( E ,k ) TL( E ;k ,q' )
- 2-quasi-particle propagator: GQ0 Q ( s )  k /[ s / 4  ( k   Q )2 ]
- bound+scatt. states, nonperturbative threshold effects (large!)
• Correlator: GL( E )   GQ0 Q   GQ0 Q  TL GQ0 Q
L=S,P
2.3.1 Uncertainties I: “Lattice QCD-based” Potentials
• free vs. internal energy: F1 (r;T) = U1(r;T) – T S(r;T)
• (much) smaller binding for
V1=F1 , V1 = (1-) U1 +  F1
[Cabrera+RR ’06;
Petreczky+Petrov’04]
[Wong ’05;
Kaczmarek
et al ‘03]
2.3.2 Uncertainties II: Heavy-Quark Masses in the QGP
• quarkonium mass: my= 2mc* - eB
• asymptotic energies F∞ = U∞ - TS∞
U∞
[Kaczmarek
+Zantow ‘05]
F∞
• close to Tc: - increasing heavy-quark mass?!
- entropy contribution?
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, Gy small, Grec= Gvac
hc
• slightly overbound at 1.1Tc
(or mc too small)
• dissolves at >2.5Tc
- T-Matrix
Q-Q
cc
• 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
hc
• upward shift due to large mc* at 1.1Tc
• ~stable my=2mc*-eB above → correlator within ~20%
3.2.2 T-Matrix with in-medium mc* - II
• lattice U1-potential, adjust mc* close to Tc + zero modes; S-Waves:
T-Matrix Approach
[Cabrera+RR
in prep]
Lattice QCD
J/y
hc
• fair agreement!
[Aarts
et al. ‘07]
3.2.3 T-Matrix with in-medium mc* - II
• lattice U1-potential, adjust mc* close to Tc + zero modes; P-Waves:
T-Matrix Approach
cc0
[Cabrera +RR
in prep]
Lattice QCD
cc1
• fair agreement!
[Aarts
et al. ‘07]
3.2.4 Temperature Dependence of Charm-Quark Mass
• significant deviation only close to Tc
3.3 Finite-Width Effects
GQQ ( s )  k /[ s / 4  ( k   Q )2 ]
• dominant process depends on eB
J/y Lifetime
• c-quark width in propagator
_
[Grandchamp+RR ‘01]
• effect on correlator
hc
• moderate width
→ small enhancement
[Cabrera+RR ‘06]
4.) Observables at RHIC: Centrality + pT Spectra
• updated predictions including 3-momentum dependencies
• balance direct - regenerated
• sensitive to: mc* , Ncc
[X.Zhao+
RR in prep]
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 Y ≤ 1fm/c possibly relevant
4.) Suppression + Regeneration in Heavy-Ion Collisions
• 3-Stage Dissociation: nuclear (pre-eq) -- QGP -- HG
Stot = exp[-nuc r L] exp[-GQGP QGP ] exp[-GHG HG ]
- nuc(SPS) ≈ 4.5mb
- RHIC d-Au data → nuc≈ 0-3mb
• Regeneration in QGP + HG:
- microscopically: backward reaction (detailed balance!)
J/y + g
→
c
+
c
+X
←
[PBM etal ’01, Gorenstein etal ’02,Thews etal ’01,
Grandchamp+RR ’01, Ko etal ’02, Cassing etal ‘03]
- for thermal c-quarks and gluons:
key ingredients:
(links to lattice QCD)
dNy
d
  Gy ( Ny  Nyeq )
reaction rate
(y -width)
equilibrium limit
( N cc , my ,mc )
3.3.2 Observables II: Excitation Function + Rapidity
J/y Suppression vs. Regeneration
[Grandchamp
+RR ’01]
• nontrivial “flat” dependence
• similar interplay in rapidity!?
(need accurate dNc/dy)
Sequential Y’+ cc Suppression
[Karsch,Kharzeev+Satz ‘06]
• direct J/y essentially survive
(even at RHIC)