Pion and sigma meson dissociation in a modified NJL model at finite temperature

TL;DR

This paper studies how pion and sigma mesons dissolve into resonances in hot quark matter using a modified NJL model, focusing on the Mott transition and effects of confinement modeling at finite temperature.

Contribution

It introduces a modified NJL model with a low-momentum cutoff linked to the quark mass gap to analyze meson dissociation and in-medium phase shifts at finite temperature.

Findings

Identification of the Mott temperature where mesons become resonances.

Modeling confinement increases the quark-antiquark continuum threshold.

In-medium phase shifts align with the Levinson theorem.

Abstract

We investigate pion and sigma meson correlations in hot quark matter within a modified NJL model. Special emphasis is on the transformation of mesonic bound states to resonances (Mott dissociation) when due to the partial chiral symmetry restoration with increasing temperature the threshold of quark-antiquark continuum states drops below the meson mass at the corresponding Mott temperature. The description is based on evaluating the polarization functions for quark-antiquark (meson) correlations as a function of the temperature and the results can be represented by introducing modulus and phase of the complex propagator functions for the mesonic states. We study the effect of modelling confinement by introducing a low-momentum cutoff in loop integrals. We make the ansatz that this cutoff is identified with the dynamically generated quark mass gap and find an increase of the continuum threshold which makes the otherwise unbound sigma meson a bound state in the vacuum. We discuss the in-medium behavior of the mesonic phase shifts including the Mott effect and find accordance with the Levinson theorem.