Mott dissociation of pions and kaons in hot, dense quark matter

TL;DR

This paper investigates the Mott dissociation of pions and kaons in hot, dense quark matter using a unified Beth-Uhlenbeck approach within the PNJL model, highlighting phase shift behavior and the transition from meson gas to quark-gluon plasma.

Contribution

It introduces a comprehensive method to describe meson dissociation and phase shifts in hot dense matter, ensuring thermodynamic consistency and explaining phenomena like the 'horn' effect in heavy-ion collisions.

Findings

Phase shifts change at the Mott transition, signaling meson dissociation.

Total phase shift vanishes at high energies, removing mesonic correlations.

The approach unifies meson gas and quark-gluon plasma descriptions.

Abstract

We describe the Mott dissociation of pions and kaons within a Beth-Uhlenbeck approach based on the PNJL model, which allows for a unified description of bound, resonant and scattering states. Within this model we evaluate the temperature and chemical potential dependent modification of the phase shifts both in the pseudoscalar and scalar isovector meson channels for $N_f=2+1$ quark flavors. We show that the character change of the pseudoscalar bound states to resonances in the continuum at the Mott transition temperature is signaled by a jump of the phase shift at the threshold from $\pi$ to zero, in accordance with the Levinson theorem. In particular, we demonstrate the importance of accounting for the scattering continuum states, which ensures that the total phase shift in each of the meson channels vanishes at high energies, thus eliminating mesonic correlations from the thermodynamics at high temperatures. In this way, we prove that the present approach provides a unified description of the transition from a meson gas to a quark-gluon plasma. We discuss the occurrence of an anomalous mode for mesons composed of quarks with unequal masses which is particularly pronounced for $K^+$ and $\kappa^+$ states at finite densities a a possible mechanism to explain the "horn" effect for the $K^+/\pi^+$ ratio in heavy-ion collisions.