Vector Meson Dominance and gρππg_{\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 $T=T_c$.Comment: 7 pages, Latex, 3 figures to be delivered from the authors by request, to appear in Phys. Lett.

The ρ\rho Meson and the Thermal Behavior of an Effective Hadronic Coupling Constant

Vector Meson Dominance ideas together with a Finite Energy QCD sum rule allows for the determination of the $q^{2}$- and the $T$- dependence of the effective hadronic coupling constant $g_{\rho \pi \pi}$ in the space-like region. It turns out that $g_{\rho \pi \pi}(q^{2},T)$ vanishes at the critical temperature $T_{c}$, independently of $q^{2}$. A comparison with a previous independent QCD determination of the electromagnetic pion form factor at finite temperature supports the validity of Vector Meson Dominance at finite temperature. We find also thet the pion radius increases with $T$, having a divergent behavior at $T_{c}$.Comment: 4 pages, Latex.One figure, to be requested by from the author