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 • The confinement force gets weaken • The chiral symmetry is partially restored T=0.87Tc T=0.93Tc 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. QCD phase transitionTc ～ 150 MeV very high temperature If the range of the qqbar potential becomes smaller than the size of the hadron,the hadron becomes unbound ! ⇒ J/ψ suppression J/ψ 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 spectral function “maximize” The spectral representation • The recent lattice QCD results suggest that The narrowJ/ψ 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/ψ and ηc. 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 providesome 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 (PBC case) In the lowest lying state,each of c and cbar has ～zero spatial momentum. (APBC case) L～1.55 fm case In the lowest lying state,each of c and cbar has pmin～690 MeV. 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. ※ mc～1.3GeV 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 . • β = 2Nc/g2 = 6.10 • as－1= 2.03 GeV (as～0.097 fm) [L～1.55 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 ρ～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(τ). “Effective mass plot” serves as a convenient tool. The “effective mass” meff(τ) is a “weighted average” of the energies of states, which contribute to particular time-slice t. A flat region(plateau) in meff(τ) plot indicates that G(τ) is dominated by a single state contribution in this plateau retion.

9. Numerical Result for J/ψ(JP=1-) Effective mass plot Plateaux(single state saturation) Temperature dependence of the pole-mass No BC dependence is seen for the lowest lying state(plateau) ! No BC dependence is seen. J/ψ remains as a compact state up to 2.07 Tc

10. If a compact state does not exist, the plateau is raised.(An example: Θ+(1540)) Standard BC Hybrid 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 parameterleads to mN=1.74GeV, mK=0.79 GeV • Expected shift of the NK threshold for L=2.15 fm is

11. Numerical Result for ηc (JP=0-) Effective mass plot Plateaux(single state saturation) Temperature dependence of the pole-mass No BC dependence is seen for the lowest lying state(plateau) ! No BC dependence is seen. ηc remains as a compact state up to 2.07 Tc

12. Level inversion • A significant pole-mass reduction of J/ψ of ～100 MeV above 1.3 Tc • An inversion of M(J/ψ) and M(ηc) 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/ψ and ηc, 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” ?