Pions at finite temperature

The properties of pions in hot hadronic matter are analyzed with an effective chiral Lagrangian which includes vector and axial-vector mesons. To obtain the dispersion relation and the absorptive properties of the pions in hot matter, the real and imaginary parts of the pion self-energy are calculated to one-loop order. The dispersion relation is very similar to that of free pions even at $T\sim 160$ MeV. The mean free path is estimated from the imaginary part of the self-energy. The mass is obtained from the pole position of the propagator and from the screening limit of the pion self-energy. Even though the deviation of the mass at finite temperature is small, both masses decrease as $T$ increases. Pions remain massless in the chiral limit at finite temperature. Possible mixing of the pions with the $A_1$ mesons at finite temperature is discussed.