Generalized Beth--Uhlenbeck approach to mesons and diquarks in hot, dense quark matter

TL;DR

This paper extends the Beth-Uhlenbeck approach to analyze mesons and diquarks in hot, dense quark matter within the NJL model, focusing on bound state dissociation and phase shifts in various phases.

Contribution

It introduces a generalized Beth-Uhlenbeck framework for mesons and diquarks at finite temperature and density, including mixing effects in the 2SC phase, and discusses bound state dissociation via phase shifts.

Findings

Phase shift analysis reveals Mott transition as a change by π at threshold.

Separation of phase shift into continuum and resonance parts clarifies bound state behavior.

Application to pressure contributions demonstrates the impact of mesonic correlations.

Abstract

An important first step in the program of hadronization of chiral quark models is the bosonization in meson and diquark channels. This procedure is presented at finite temperatures and chemical potentials for the SU(2) flavor case of the NJL model with special emphasis on the mixing between scalar meson and scalar diquark modes which occurs in the 2SC color superconducting phase. The thermodynamic potential is obtained in the gaussian approximation for the meson and diquark fields and it is given the Beth-Uhlenbeck form. This allows a detailed discussion of bound state dissociation in hot, dense matter (Mott effect) in terms of the in-medium scattering phase shift of two-particle correlations. It is shown for the case without meson-diquark mixing that the phase shift can be separated into a continuum and a resonance part. In the latter, the Mott transition manifests itself by a change of the phase shift at threshold by \pi\ in accordance with Levinson's theorem, when a bound state transforms to a resonance in the scattering continuum. The consequences for the contribution of pionic correlations to the pressure are discussed by evaluating the Beth-Uhlenbeck equation of state in different approximations. A similar discussion is performed for the scalar diquark channel in the normal phase. Further developments and applications of the developed approach are outlined.