Charmonium properties in deconfinement phase in anisotropic lattice QCD

Abstract

$J/\ensuremath{\Psi}$ and ${\ensuremath{\eta}}_{c}$ above the QCD critical temperature ${T}_{c}$ are studied in anisotropic quenched lattice QCD, considering whether the $c\overline{c}$ systems above ${T}_{c}$ are spatially compact (quasi-)bound states or scattering states. We adopt the standard Wilson gauge action and $O(a)$-improved Wilson quark action with renormalized anisotropy ${a}_{s}/{a}_{t}=4.0$ at $\ensuremath{\beta}=6.10$ on ${16}^{3}\ifmmode\times\else\texttimes\fi{}(14--26)$ lattices, which correspond to the spatial lattice volume $V\ensuremath{\equiv}{L}^{3}\ensuremath{\simeq}(1.55\text{ }\text{ }\mathrm{fm}{)}^{3}$ and temperatures $T\ensuremath{\simeq}(1.11--2.07){T}_{c}$. We investigate the $c\overline{c}$ system above ${T}_{c}$ from the temporal correlators with spatially extended operators, where the overlap with the ground state is enhanced. To clarify whether compact charmonia survive in the deconfinement phase, we investigate spatial boundary-condition dependence of the energy of $c\overline{c}$ systems above ${T}_{c}$. In fact, for low-lying $S$-wave $c\overline{c}$ scattering states, it is expected that there appears a significant energy difference $\ensuremath{\Delta}E\ensuremath{\equiv}E(\mathrm{APBC})\ensuremath{-}E(\mathrm{PBC})\ensuremath{\simeq}2\sqrt{{m}_{c}^{2}+3{\ensuremath{\pi}}^{2}/{L}^{2}}\ensuremath{-}2{m}_{c}$ (${m}_{c}$: charm quark mass) between periodic and antiperiodic boundary conditions on the finite-volume lattice. In contrast, for compact charmonia, there is no significant energy difference between periodic and antiperiodic boundary conditions. As a lattice QCD result, almost no spatial boundary-condition dependence is observed for the energy of the $c\overline{c}$ system in $J/\ensuremath{\Psi}$ and ${\ensuremath{\eta}}_{c}$ channels for $T\ensuremath{\simeq}(1.11--2.07){T}_{c}$. This fact indicates that $J/\ensuremath{\Psi}$ and ${\ensuremath{\eta}}_{c}$ would survive as spatially compact $c\overline{c}$ (quasi-)bound states below $2{T}_{c}$. We also investigate a $P$-wave channel at high temperature with maximal entropy method and find no low-lying peak structure corresponding to ${\ensuremath{\chi}}_{c1}$ at $1.62{T}_{c}$.