Thermal Behaviour of $\pi-\pi$ Scattering Lengths in the Nambu--Jona-Lasinio model

TL;DR

This paper investigates how pion-pion scattering lengths and thermal masses evolve with temperature using the Nambu--Jona-Lasinio model, employing one-loop Thermofield Dynamics and meson chain resummation.

Contribution

It provides a detailed calculation of thermal corrections to pion scattering lengths and masses within the NJL model, including a novel meson propagator resummation approach.

Findings

Thermal corrections increase with temperature.

Pion thermal mass shows significant temperature dependence.

Results are consistent with previous theoretical approaches.

Abstract

We calculate the thermal evolution of $\pi-\pi$ scattering lengths, in the frame of the Nambu--Jona-Lasinio model. The thermal corrections were calculated at the one loop level using Thermofield Dynamics. We present also results for the pion thermal mass. Our procedure implies the modeling of a propagating scalar meson as a resumation of chains of quark bubbles, which is presented explicitly. We compare our results with previous analysis of this problem in the frame of different theoretical approaches.