Continuum extrapolation of finite temperature meson correlation functions in quenched lattice QCD

We explore the continuum limit $a\to 0$ of meson correlation functions at finite temperature. In detail we analyze finite volume and lattice cut-off effects in view of possible consequences for continuum physics. We perform calculations on quenched gauge configurations using the clover improved Wilson fermion action. We present and discuss simulations on isotropic $N_{\sigma }^3\times 16$ lattices with $N_{\sigma }=32,48,64,128$ and $128^3 \times N_\tau$latticeswith$N_\tau=16,24,32,48$ corresponding to lattice spacings in the range of $0.01fm\text{lsim}a\text{lsim}0.031fm$ at $T\simeq 1.45T_c$. Continuum limit extrapolations of vector meson and pseudo scalar correlators are performed and their large distance expansion in terms of thermal moments is introduced. We discuss consequences of this analysis for the calculation of the electrical conductivity of the QGP at this temperature.