Glueball properties at finite temperature in SU(3) anisotropic lattice QCD

Abstract

The thermal properties of glueballs are studied using SU(3) anisotropic lattice QCD with ${\ensuremath{\beta}}_{\mathrm{lat}}=6.25,$ the renormalized anisotropy $\ensuremath{\xi}\ensuremath{\equiv}{a}_{s}{/a}_{t}=4$ over the lattice of the size ${20}^{3}\ifmmode\times\else\texttimes\fi{}{N}_{t}$ with ${N}_{t}=24,$ 26, 28, 30, 33, 34, 35, 36, 37, 38, 40, 43, 45, 50, 72 at the quenched level. To construct a suitable operator for the lowest-state glueball on the lattice, we adopt the smearing method, providing an illustration of its physical meaning in terms of the operator size. First, we construct the temporal correlators $G(t)$ for the lowest ${0}^{++}$ and ${2}^{++}$ glueballs, using more than 5500 gauge configurations at each temperature $T.$ We then perform the pole-mass measurement of the thermal glueballs from $G(t).$ For the lowest ${0}^{++}$ glueball, we observe a significant pole-mass reduction of about 300 MeV in the vicinity of ${T}_{c}$ or ${m}_{G}(T\ensuremath{\simeq}{T}_{c})\ensuremath{\simeq}{0.8m}_{G}(T\ensuremath{\sim}0),$ while its size remains almost unchanged as $\ensuremath{\rho}(T)\ensuremath{\simeq}0.4\mathrm{fm}.$ Finally, for completeness, as an attempt to take into account the effect of the thermal width $\ensuremath{\Gamma}(T)$ at finite temperature, we perform a more general new analysis of $G(t)$ based on its spectral representation. As an ansatz to the spectral function $\ensuremath{\rho}(\ensuremath{\omega}),$ we adopt the Breit-Wigner form, and perform the best-fit analysis of the temporal correlator as a straightforward extension to the standard pole-mass analysis. The result indicates a significant broadening of the peak as $\ensuremath{\Gamma}(T)\ensuremath{\sim}300\mathrm{MeV}$ as well as a rather modest reduction of the peak center of about 100 MeV near ${T}_{c}$ for the lowest ${0}^{++}$ glueball. The temporal correlators of the color-singlet modes corresponding to these glueballs above ${T}_{c}$ are also investigated.