Heavy quark bound states in QGP

1
Heavy quark bound states in QGP
N. Ishii (Univ. of Tokyo) with H. Iida
(YITP, Kyoto Univ.)T. Doi
(RIKEN BNL)H. Suganuma (Kyoto Univ.)K.
Tsumura (Kyoto Univ.)
2
QCD at finite T
QCD vacuum is expected to change its properties
at finite temperature/density.

• The hadronic phase(confinement phase)
• color charge is confined
• spontaneous chiral sym. breaking (massive
  constituent quark)

• Quark Gluon Plasma phase
• color deconfinement(isolated quarks gluons)
• restored chiral symmetry (massless current
  quark)

low temperature
QCD phase transitionTc 150 MeV
high temperature
3
QCD above Tc
The confinement force no longer exists.The qqbar
potential becomes of Yukawa type The Debye
screening mass mD(T) increases with increasing
T.The range of the qqbar potential becomes
shorter.
very high temperature
QCD phase transitionTc 150 MeV
If the range of the qqbar potential becomes
smaller than the size of the hadron,the hadron
becomes unbound ! ? J/? suppression J/? melts
slightly after the QCD phase transition !

• T.Hashimoto et al., PRL57,2123(86)
• T.Matsui et al., PLB178,416(86)

4
Recent Lattice QCD results

• The recent lattice QCD results suggest that The
  narrow J/? peak survives at much higher
  temperature.
• M.Asakawa et al., PRL92,012001(04).
• T.Umeda et al., EPJC39,9(05).
• S.Datta et al., PRD69,094507(04)
  JPG31,S351(05).
• The maximum entropy method (MEM) is used to
  extract the spectral function directly from the
  lattice QCD temporal correlators for ccbar
  systems.
• Sharpe peakes are found to survive up to 2 Tc
  for J/? and ?c.

From M.Asakawa et al., PRL92,012001(04)
by MEM
cf) M.Asakawa et al., PPNP46,459(01)
? The physical origins of the inconsistency
between these lattice QCD calculations and
the effective model predictions are not fully
understood yet.
5
The our aim
Since the effective model arguments are
convincing enough, one may wonder if the lattice
QCD results might have some uncertainty !
? All of these lattice QCD calculations may
suffer from a possible problem that the observed
ccbar state is actually a trivial
scattering state of c and cbar rather than
a nontrivial compact (quasi-)bound state.
It is difficult to distinguish these two on the
lattice. A narrow peak does not immediately imply
a spatially compact bound state
? The MEM itself might provide some uncertainty.
Our aim is to confirm the lattice QCD
MEM resultsby means of a more
standard method examining the spatial boundary
condition dependence.
6
The boundary conditions
To distinguish a compact (quasi-)bound statefrom
a mere scattering state of c and cbar,we
consider two spatial boundary conditions (PBC)
Periodic BC the ordinary
one(APBC) Anti-Periodic BC BC dependence shows
a clear difference
? CASE 1 (compact bound state)If the state is
a compact bound state, and if the lattice can
accommodate it,it is not sensitive to the change
of the spatial BC. ? CASE 2 (scattering
state)If the state is a mere scattering state of
c and cbar,it is sensitive to the change of
spatial BC. Due to the finiteness of
the lattice, the lowest energy differs one from
the other.
If it is a compact state, its energy is unchanged.
? mc1.3GeV is assumed.
If it is a scattering state, the energy is raised
by about 340 MeV !
7
Anisotropic lattice QCD

• The standard Wilson gauge action on 163xNt
  lattice
• Nt 14-26 are used for T (1.11-2.07)Tc .
• ß 2Nc/g2 6.10
• as-1 2.03 GeV (as0.097 fm) L1.55 fm
• The anistotropic lattice (as/at 4) for
  precision measurements.
• 999 gauge config. are used.
• 20,000 sweeps are skipped for thermalization
• gauge configs are separated by 500 sweeps
• O(a) improved Wilson (clover) action for quark.
• Spatially extended operator is used to enhance
  the ground state overlap.
• Gaussian extention with size ?0.2-0.3 fm
  achieves the optimum operator.

Effective number of datais increased by factor
of 4 ! Anisotropic lattice serves asan essential
tool to study the temporal correlation at large
T.
8
Effective mass plot
To calculate the pole-mass from lattice QCD,we
have to find a region where a single-state
contribution dominate the temporal correlator
G(t). Effective mass plot serves as a
convenient tool. The effective mass meff(t) is
a weighted average of the energies of states,
which contribute to particular time-slice t.
A flat region(plateau) in meff(t) plot indicates
that G(t) is dominated by a single state
contribution in this plateau retion.
9
Numerical Result for J/?(JP1-)
J/? remains as a compact state up to 2.07 Tc
10
If a compact state does not exist, the plateau is
raised. (An example T(1540))
Hybrid BC
Standard BC
The plateau is shifted above by the expected
amount. (1) No compact 5Q resonance exists in
the region as (2) The state observed in the
negative parity channel turns out to be an NK
scattering state.

• The hopping parameter leads to mN1.74
  GeV, mK0.79 GeV
• Expected shift of the NK threshold for L2.15 fm
  is

11
Numerical Result for ?c (JP0-)
?c remains as a compact state up to 2.07 Tc
12
Level inversion

• A significant pole-mass reduction of J/? of 100
  MeV above 1.3 Tc
• An inversion of M(J/?) and M(?c) is seen.

13
Summary

• There is an inconsistency in the charmonium state
  above Tc between the effective model prediction
  and the recent lattice QCD results using MEM.
  Since the effective model arguments are
  convincing enough, one may wonder if the lattice
  QCD results might involve some uncertainty !
• Are these narrow peak really non-trivial ccbar
  bound states ?
• Does MEM involve any uncertainty ?
• To confirm the lattice QCD results, we have
  performed more standard lattice QCD analysis
  using the spatial BC dependence (APBC vs PBC).
• For J/? and ?c, we have seen NO BC DEPENDENCE,
  which implies that these two charmonium remain as
  spatially compact (quasi-)bound states up to 2
  Tc.
• One conjectures that a possible resolution may be
  provided by a proper definition of the heavy
  quark potential for potential models. (Such an
  ambiguity already exists below Tc)
• What is the proper definition of heavy quark
  potential ?