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. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.