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Thermal Corrections to $π$-$π$ Scattering Lengths in the Linear Sigma Model

In this article we explore the thermal evolution of the $π$-$π$ scattering lengths in the frame of the linear sigma model. We compute, using thermofield dynamics, all the one loop diagrams that contribute to $π$-$π$ scattering. We restrict ourselves to temperature correction only in the pion sector, due to the Boltzmann supression for the sigma meson. From this analysis we obtain the thermal behavior of $a_0^0$ and $a_0^2$, s-waves scattering lengths in the isospin channel I=0 and I=2 respectively. It turns out that $a_0^0$ grows whereas $a_0^2$ diminishes as function of temperature. We compare our results with other determinations of the thermal behavior of these magnitudes.