Pion dissociation and Levinson's theorem in hot PNJL quark matter

TL;DR

This paper investigates pion dissociation in hot quark matter using the PNJL model, emphasizing the importance of scattering states and Levinson's theorem for accurate thermodynamic descriptions.

Contribution

It introduces a unified approach to describe bound, resonant, and scattering states in pion dissociation, highlighting the role of scattering continuum and Levinson's theorem.

Findings

Spectral broadening alone is insufficient to describe pion Mott dissociation.

The continuum of scattering states significantly impacts thermodynamics.

Levinson's theorem clarifies the relation between bound states and scattering states.

Abstract

Pion dissociation by the Mott effect in quark plasma is described within the generalized Beth-Uhlenbeck approach on the basis of the PNJL model which allows for a unified description of bound, resonant and scattering states. As a first approximation, we utilize the Breit-Wigner ansatz for the spectral function and clarify its relation to the complex mass pole solution of the pion Bethe-Salpeter equation. Application of the Levinson theorem proves that describing the pion Mott dissociation solely by means of spectral broadening of the pion bound state beyond T_Mott leaves out a significant aspect. Thus we acknowledge the importance of the continuum of scattering states and show its role for the thermodynamics of pion dissociation.