Temperature dependence of the gluon condensate and the $ρ$ -meson mass from QCD sum rules

We determine the temperature (T) dependence of the $\rho$-meson mass and the gluon condensate below the deconfinement phase transition by means of QCD sum rules. In the chiral limit we derive sum rule induced scaling relations for the vacuum parts of the Gibbs averaged scalar operators contributing to the operator product expansion of the $\rho^0$ current-current correlator at finite temperature. The scaling with $\lambda\equiv \sqrt{s_0(T)/s_0(0)}$, $s_0$ being the T-dependent perturbative QCD continuum threshold in the spectral integral, is simple for renormalization group invariant operators, and becomes nontrivial for a set of operators which mix and scale anomalously under a change of the renormalization point. In contrast to previous works on thermal QCD sum rules with this approach the gluon condensate exhibits a sizable T-dependence which is qualitatively in accord with lattice data. The $\rho$-meson mass rises slowly with temperature, and there is no indication of its breakdown up to T=160 MeV.