Vector Meson Dominance and $g_{\rho\pi\pi}$ at Finite Temperature from QCD Sum Rules

A Finite Energy QCD sum rule at non-zero temperature is used to determine the $q^2$- and the T-dependence of the $\rho \pi \pi$ vertex function in the space-like region. A comparison with an independent QCD determination of the electromagnetic pion form factor $F_{\pi}$ at $T \neq 0$ indicates that Vector Meson Dominance holds to a very good approximation at finite temperature. At the same time, analytical evidence for deconfinement is obtained from the result that $g_{\rho \pi \pi}(q^{2},T)$ vanishes at the critical temperature $T_c$, independently of $q^{2}$. Also, by extrapolating the $\rho \pi \pi$ form factor to $q^2 = 0$, it is found that the pion radius increases with increasing $T$, and it diverges at $T=T_c$.