1. Overview of Potential models at finite temperature Péter Petreczky
Physics Department and RIKEN-BNL
Brief history :
Potential models with screening and quarkonium dissociation in the quark gluon plasma ( ):
J/psi melts at T<1.2Tc, Upsilon melts at T~2Tc, excited charmonium states melt around Tc
(Matsui, Satz, 1986, ….)
Lattice calculations of quarkonium correlators and spectral functions ( ):
J/psi survives till T~1.6Tc, Upsilon does not melt, excited charmonium states melt around Tc
(Umeda 2002, Asakawa, Hatsuda, 2003, Datta et al, 2003)
Role of zero mode contribution and threshold enhancement ( ) :
zero mode contribution mock melting of 1P quarkonium states (Umeda , 2006, Mocsy, P.P, 2007),
threshold enhancement leads to almost T-independent quarkonium correlators ( Mocsy, P.P, 2007)
QWG2008, Nara, December 2-5, 2008

2. Color screening in QCD and quarkonia melting
Confined
Deconfined r
V(r)
T/TC
1/r [fm-1]
(1S)
J/(1S)
c(1P)
’(2S)
b’(2P)
’’(3S)
Matsui and Satz, 1986
Color screening reduces the effective range
of interactions in QGP
Other medium effects (e.g. Landau damping)
produce an imaginary part for the potential
(Laine et al, 2006, Blaizot 2007, Brambilla et al, 2008,
Escobeto and Soto, 2008)
use quarkonia
as thermometer
of the matter created in
RHIC

3. Color screening in QCD and quarkonia melting
RBC-Bielefeld Collaboration, 2+f lattice QCD

4. Meson correlators and spectral functions
LGT
Imaginary time Real time
Study the ratio
MEM
If there is no T-dependence in
the spectral function

5. many gluon exchanges important near threshold
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
compare to lattice QCD results
Mócsy, P.P., PRL 99 (07) ,
PRD77 (08) , EPJC ST 155 (08) 101

6. 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

7. 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

8. 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

9. Quarkonium binding energy and thermal width
Using lattice data on the static quark anti-quark free energy in 2+1f QCD
the binding energy of different quarkonium states can be estimated
Mócsy, P.P., PRL 99 (07)
Kharzeev, McLerran, Satz, PLB356 (95) 349

10. Quarkonium binding energy in different models
Alberico et al,
PRD72 (05)
binding energy decreases with T, but there are large uncertanties from modeling of V

11. Quarkonium width in different models
Park et al, PRC76 (07)
Zhao, Rapp, PLB664 (08) 253
NLO pQCD + in-medium binding energy
quasi-free dissociation
in-medium binding energy
quark
gluon
Reduced binding energy => larger width;
thermal width increases with T above
deconfinement

12. Spectral functions with complex potential
Burnier, Laine, Vepsalainen JHEP 0801 (08) 043
The imaginary part of the potential washes out the bound state peak making it a
mere threshold enhancement even for b-quarks !
Large threshold enhancement is observed

13. Summary
Lattice and perturbative calculations show that in-medium modification of the potential
is sufficiently strong to lead to quarkonium dissociation in the deconfined phase
Residual interaction of quark and anti-quark are important  threshold enhancement
very small T-dependence of Euclidean correlators
conclusions reached in lattice calculations of the Euclidean correlators and
spectral functions about the survival of 1S state (Umeda et al, 2002; Asakawa,
Hatsuda, 2003, Datta et al, 2003) were premature ! MEM is not sufficiently accurate
Potential model calculations based on lattice results on singlet free energy reproduce
the temperature (in)dependence of the Euclidean time correlators
Crosscheck : threshold enhancement effects weaken with decreasing quark masses 
larger T-dependence for quarkonium correlators
(consistent with lattice calculations of Datta et al)
Lattice calculations based on “wave function method” indicate survival of charmonium
states till 2.3Tc (Umeda et al, 2000, 2008)
Problems : even highly excited states, e.g. 2P states survive to such high T
the notion of well defined states is problematic due to finite width effect
Crosscheck : consider the light quark case where no bound states are expected, c.f. lattice
calculations of fluctuations of conserved charges.

14. Outlook
Combine EFT techniques in the weak coupling regime with available lattice
data on the static meson correlators to obtain a reliable potential model type
of framework with all medium effect included.
Calculate charm fluctuations to find the relevant degrees of freedom : bound
states or free quark. Determine the quasi-particle properties at high T
Extend the lattice “wave function analysis” to light quark sector to check the
consistency of the approach

15. Backup slides