Quarkonium correlators and spectral functions

1
Quarkonium correlators and spectral
functions at finite
temperature
Péter Petreczky

• Introduction screening in QGP and quarkonium
  melting
• Quarkonium correlators and spectral functions
• Quarkonium spectral functions in potential
  models
• Summary

ECT, Trento, May 25-29, 2009
2
Color screening in lattice QCD
RBC-Bielefeld Collaboration
Does this imply quarkonium melting ? Matsui and
Satz PLB 178 (86) 416 see also Digal et al, PLB
514 (01) 57 PRD 64 (01) 094015,
3
Meson correlators and spectral functions
LGT
Imaginary time Real time
Experiment, dilepton rate
MEM
4
Quarkonium spectral functions above deconfinement
interactions
P.P., Teaney, PRD 73 (2006) 014508
calculate the area under the peak using lattice
QCD !
E.g. free theory

quark number susceptibility
5
Charmonia spectral functions at T0
Jakovác, P.P., Petrov, Velytsky, PRD 75 (07)
014506

For the spectral
function is sensitive to lattice cut-off Strong
default model dependence in the continuum region
6
Charmonia correlators at Tgt0
temperature dependene of
If there is no T-dependence in the spectral
function,
Datta, Karsch, P.P., Wetzorke, PRD 69 (04) 094507
7
Charmonia correlators at Tgt0
zero mode contribution is not present in the time
derivative of the correlator Umeda, PRD 75 (2007)
094502
P.P., arXiv0810.0258 
8
Charmonia correlators at Tgt0
zero mode contribution is not present in the time
derivative of the correlator Umeda, PRD 75 (2007)
094502
P.P., arXiv0810.0258 
9
Estimating the zero mode contribution
P.P., arXiv0810.0258 
10
Heavy quark susceptibility in quasi-particle
picture
P.P., arXiv0810.0258 
11
Zero mode contribution in quasi-particle picture
P.P., arXiv0810.0258 
12
Charmonium spectral functions at finite
temperature
Jakovác, P.P., Petrov, Velytsky, PRD 75 (07)
014506
no large T-dependence but details are not resolved
13
Quarkonium spectral functions in potential models
? MJ/? , s0 nonrelativistic
? ?? s0 perturbative
many gluon exchanges important near threshold
S-wave
P-wave
use lattice data on the quark anti-quark free
energy to construct the potential
PRD77 (08) 014501, EPJC ST 155 (08) 101
Mócsy, P.P., PRL 99 (07) 211602,
14
?c

• resonance-like structures disappear already by
  1.2Tc
• strong threshold enhancement above free case
  indication of correlations

15
?c

• resonance-like structures disappear already by
  1.2Tc
• strong threshold enhancement above free case
  indication of correlations
• height of bump in lattice and model are similar
• The correlators do not change significantly
  despite
• the melting of the bound states

16
ground state bottomonium survives deconfinement
other states dissolved medium modification of
the 1S peak is small agreement found with lattice
correlators
17

• all P-states disappear already by 1.2Tc
• but the derivatives of the of the correlators don
  not show any significant T-dependence

18
Quarkonium binding energy and thermal width
Using lattice data on the static quark anti-quark
free energy in 21f QCD the binding energy of
different quarkonium states can be estimated
Kharzeev, McLerran, Satz, PLB356 (95) 349
Mócsy, P.P., PRL 99 (07) 211602
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Summary and outlook

• The temperature dependence of quarkonium
  correlators in Euclidean time
• is dominated by the zero mode contribution and
  are not sensitive to the change
• in the spectral function related to melting of
  the bound states
• Spectral functions extracted from the lattice
  data using MEM are compatible with
• the threshold enhancement
• The zero mode contribution can be very well
  described by a quasi-particle model
• Potential models at finite temperature predict
  melting of all charmonium states,
• yet are consistent with lattice data on the
  Eulcidean correlators
• Most quarkonium states dissolve in QGP
• at temperatures not much larger than the
• transition temperature

20
Back-up slides
The color octet correlator only fixes the
relative color orientation of static quark
anti-quark pair.
Juge et al, hep-lat/0103008
Perturbative relation between to the color
singlet free energy at high temperatures