Temperature and volume dependence of pion-pion scattering lengths

Author:

Qing-Wu Wang, Hua-Zhong Guo

Keyword:

High Energy Physics - Phenomenology, High Energy Physics - Phenomenology (hep-ph)

journal:

date:

2023-12-03 00:00:00

Abstract

The s-wave pion-pion scattering lengths $ a_0 $ and $ a_2 $ are studied at finite temperature and in finite spatial volume under the framework of the Nambu--Jona-Lasinio model. With the proper time regularization, the behavior beyond the pseudo transition temperature is presented. The scattering length $ a_0$ shows singularity near the Mott temperature and $ a_2$ is a continuous but non-monotonic function of temperature. We present the finite volume effect on the scattering length and have found that $a_0$ can be negative and its singularity disappears at small volume size which may hint the existence of chiral phase transition as volume decreases.

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