Thermal dissociation of quarkonium bound states above Tc

1
Thermal dissociation of quarkonium bound states
above Tc
May 9th,2006

• Marzia Nardi
• INFN Torino

2

• Work done by the Turin group
• Heavy quark bound states above Tc,
• W.M.Alberico, A. Beraudo, A. De Pace, A.
  Molinari,
• Phys.Rev. D72114011, 2005

3
well known facts

• J/y suppression signature of QGP formation
• a large fraction of observed J/ys come from
  excited c-cbar states (c,y)
• the dissociation temperature depends on the
  binding energy of the c-cbar state.
• predictions for step-like suppression pattern

4

• 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 ?

5
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/y)1-1.1Tc ,
• Tdiss(c) and Tdiss(y) lt Tc.

6

• Recent lattice calculations of meson spectral
  functions seem to indicate that the J/y 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/y).
• 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.

7
Color singlet free energy from lattice

• From
• Nf0 O. Kaczmarek et al., Phys.Lett. B 543, 41
  (2002)
• Nf2 O. Kaczmarek et al., Phys.Rev D 71, 114510
  (2005)
• Nf3 P.Petreczky et al., Phys.Rev.D 70, 054503
  (2004)
• s1/2 420 MeV Nf0,2
• s1/2 460 MeV Nf3

8
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 T0

9

• The idea is to parameterize the lattice data for
  F to calculate the derivative with respect to T.
• rltlt1/T
• TgtgtTc
• The running of the coupling constant is
  determined by the RGE the energy scale is m1/r
  (mT) in the short (long) distance limit.
• We need a parameterization which includes these
  two limits

10

• We use
• where a(r,T) a(mcr/rctT)

11

• a1 0.2719 Nf0 0.2687 Nf2 0.2354 Nf2

12
Effective Q-Qbar potential
13

• The Schroedinger equation can be solved to get
  the energy and radius of the bound states
• m Q-Qbar reduced mass
• mc1.3 GeV
• mb4.3 GeV

14
results charmonium

• lines
• mc1.3 GeV
• bands
• 1.15ltmclt1.35 GeV
• Dissociation temperature for J/y
• 1.7 2.3 Tc !

15

• mean square
• radii

16

• The J/y-hc degeneracy can be removed by adding a
  spin-spin contact interaction
• Energy shifts
• corresponding to a J/y-hc split of 145 MeV at
  T1.05 Tc (exp. value 117 MeV), and 13 MeV at
  T1.8 Tc

17
results bottomonium

• lines
• mb4.3 GeV
• bands
• 4.1ltmblt4.4 GeV

18
(No Transcript)
19
Conclusions

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