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Thermal conductivity of hot pionic medium due to pion self-energy for $πσ$ and $πρ$ loops

The thermal conductivity of pionic medium has been evaluated with the help of its standard expression from the relaxation time approximation, where inverse of pion relaxation time or pion thermal width has been obtained from the imaginary part of pion self-energy. In the real-time formalism of thermal field theory, the finite temperature calculations of pion self-energy for $πσ$ and $πρ$ loops have been done. The numerical value of our thermal conductivity increases with temperature very softly, though at particular temperature, our estimation has to consider a large band of phenomenological uncertainty.