# Presentation: 739969

## Thermal dissociation of  quarkonium bound states above Tc

**Marzia Nardi**
**INFN Torino**

_**May 9**__**th**__**,2006**_

## Work done by the Turin group:

*“**Heavy quark bound states above Tc”,*
- W.M.Alberico, A. Beraudo, A. De Pace, A. Molinari,
- Phys.Rev. D72:114011, 2005

## well known facts

-  J/ suppression = signature of QGP formation
-  a large fraction of observed J/’s come from excited c-cbar states (,’)
-  the dissociation temperature depends on the binding energy of the c-cbar state.
-  predictions for ‘step-like’ suppression pattern

## The quarkonium spectroscopy is successfully described as a Q-Qbar bound state by solving a 
Schroedinger equation with a Cornell potential:

Quarkonium states binding energy in the vacuum are known.

What about the high temperature/density case ?

- Schroedinger equation with a Cornell potential:
- Quarkonium states binding energy in the vacuum are known.
- What about the high temperature/density case ?

## Quarkonium states in dense and hot systems

- Same approach as for the zero-temperature case:
- solve the Schroedinger equation, the interacting potential being inspirated by lattice QCD calculation.
- First attempts in this direction used the color singlet free energy calculated on the lattice directly as the interacting potential and resulted in Tdiss(J/)~1-1.1Tc ,
- Tdiss() and Tdiss(’) < Tc.

## Recent lattice calculations of meson spectral functions seem to indicate that the J/ meson can survive, in a deconfined medium, up to about 2Tc.

- On the other hand, potential models using the internal energy (obtained from the free energy) as interaction potential give an higher value for Tdiss(J/).
- I will present the results on Tdiss for charmonium and bottomonium states based on potential extracted from lattice data in quenched approximation, 2- and 3-flavor QCD.

## Color singlet free energy from lattice

- From:
- [Nf=0] O. Kaczmarek et al., Phys.Lett. B 543, 41 (2002)
- [Nf=2] O. Kaczmarek et al., Phys.Rev D 71, 114510 (2005)
- [Nf=3] P.Petreczky et al., Phys.Rev.D 70, 054503 (2004)
- 1/2= 420 MeV [Nf=0,2]
- 1/2= 460 MeV [Nf=3]

## Heavy quark potential

- The internal energy U can be obtained from the free energy F by the ordinary thermodynamics relation:
***F = U - TS***
- where
***S = - ******∂F/∂T***
- F and U coincide at T=0

## The idea is to parameterize the lattice data for F to calculate the derivative with respect to T.

-  r<<1/T
-  T>>Tc :
- The running of the coupling constant is determined by the RGE; the energy scale is =1/r (=T) in the short (long) distance limit.
- We need a parameterization which includes these two limits

## We use: 

- where :  ****(r,T) = ****(****=cr/r+ctT)

## a1= 0.2719 [Nf=0]; 0.2687 [Nf=2]; 0.2354 [Nf=2]; 

## Effective Q-Qbar potential

## The Schroedinger equation can be solved to get the energy and radius of the bound states:

****= Q-Qbar reduced mass
- mc=1.3 GeV
- mb=4.3 GeV

## results: charmonium

- lines:
- mc=1.3 GeV
- bands:
- 1.15<mc<1.35 GeV
- Dissociation temperature for J/ :
- 1.7 – 2.3 Tc !

## mean square

- radii :

## The J/-c degeneracy can be removed by adding a spin-spin contact interaction:

- Energy shifts:
- corresponding to a J/-c split of 145 MeV at T=1.05 Tc (exp. value: 117 MeV), and 13 MeV at T=1.8 Tc

## results: bottomonium

- lines:
- mb=4.3 GeV
- bands:
- 4.1<mb<4.4 GeV

## Conclusions

-  Results obtained by lattice calculation are reproduced with a potential model
-  Interesting experimental consequences :         direct J/ suppression ?
- SPS : no
- RHIC : ?
- LHC : yes
-  Future work: ...