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The pion at finite temperature

Properties of the pion are studied at finite temperature with the help of the PCAC and the QCD sum rule. The pionic mode is treated consistently with the thermal pions which consist of the ground state at finite temperature. The temperature dependence of the pion decay constant is estimated for $m_{q}=0$. No consistent solution is found above the critical temperature $T_{c} = \sqrt{2} f_π^{T=0} $. The QCD sum rule shows that the finite quark mass makes the critical temperature move up to a temperature where the dilute pion gas approximation is no more valid. It also suggests that the pion decay constant and the continuum threshold decrease by $\sim 15\%$ and $\sim 10\%$, respectively, and that the pion mass slightly ($\sim 3\%$) increases at $T=160MeV$, where the pion gas approximation seems to break down.