Octet baryons at finite temperature: QCD sum rules versus chiral symmetry

Correlators of the octet baryons in the hot pion gas are studied in the framework of the QCD sum rule. The condensates appearing in the OPE side of the correlators become $T$ dependent through the interaction with thermal pions. We present an explicit demonstration that the $O\left(T^2\right)$ dependence of the condensates is completely compensated by the change of the pole residue and the $\pi +B\to B^{\prime }$ scattering effect in the spectral functions. Therefore the baryon masses are constant to this order, although ${〈\overline{u}u〉}_T\simeq {〈\overline{u}u〉}_0(1-\frac{T^2}{8f_{\pi }^2})$, which is consistent with the chiral symmetry constraint by Leutwyler and Smilga.