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

Abstract

In this article we explore the thermal evolution of the $\pi$-$\pi$ scattering lengths in the frame of the linear sigma model. We compute, using thermofield dynamics, all the one loop diagrams that contribute to $\pi$-$\pi$ 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.

Comments: 8 pages. Keywords: Finite temperature field theory; scattering lengths; linear sigma model. A new reference has been added. Written in RevTex4. The paper is being accepted for publication in Phys. Rev. D. The size of the manuscript was reduced considerably