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

The thermal properties of glueballs are studied using SU(3) anisotropic lattice QCD with ${\beta }_{\mathrm{lat}}=6.25,$ the renormalized anisotropy $\xi \equiv a_s{/a}_t=4\mathrm{}$ over the lattice of the size ${20}^3\times N_t$ 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 $G\left(t\right)\mathrm{}$ for the lowest $0^{++}$ and $2^{++}$ glueballs, using more than 5500 gauge configurations at each temperature $T.\mathrm{}$ We then perform the pole-mass measurement of the thermal glueballs from $G\left(t\right).$ For the lowest $0^{++}$ glueball, we observe a significant pole-mass reduction of about 300 MeV in the vicinity of $T_c$ or $m_G\left(T\simeq T_c\right)\simeq {0.8m}_G\left(T\sim 0\right),$ while its size remains almost unchanged as $\rho \mathrm{}\left(T\right)\mathrm{}\simeq 0.4\mathrm{fm}.$ Finally, for completeness, as an attempt to take into account the effect of the thermal width $\Gamma \mathrm{}\left(T\right)\mathrm{}$ at finite temperature, we perform a more general new analysis of $G\left(t\right)\mathrm{}$ based on its spectral representation. As an ansatz to the spectral function $\rho \left(\omega \right),$ 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 $\Gamma \mathrm{}\left(T\right)\mathrm{}\sim 300\mathrm{MeV}$ 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.