Strange mesons from SIS to FAIR

TL;DR

This paper investigates the in-medium properties of $K$ and $ar K$ mesons in nuclear matter at finite temperature using a chiral unitary approach, revealing broad spectral functions and resonance melting effects.

Contribution

It provides a comprehensive analysis of kaon spectral functions in hot nuclear matter, incorporating various in-medium effects and sum rule evaluations, which advances understanding of meson behavior under extreme conditions.

Findings

$ar K$ spectral function broadens significantly at high density and temperature.

The $ar K$ resonance $ ext{Lambda}(1405)$ melts in medium, affecting spectral properties.

Sum rules are satisfied, validating the spectral function calculations.

Abstract

The properties of $K$ and $\bar K$ mesons in nuclear matter at finite temperature are obtained from a chiral unitary approach in coupled channels which incorporates the $s$- and p-waves of the kaon-nucleon interaction. The in-medium solution accounts for Pauli blocking effects, mean-field binding on all the baryons involved, and $\pi$ and kaon self-energies. The $\bar K$ spectral function spreads over a wide range of energies, reflecting the melting of the $\Lambda (1405)$ resonance and the contribution of hyperon-hole components at finite temperature. In the $KN$ sector, the quasi-particle peak is considerably broadened with increasing density and temperature. We also study the energy weighted sum rules of the kaon propagator by matching the Dyson form of the propagator with its spectral Lehmann representation at low and high energies. The sum rules for the lower energy weights are fulfilled satisfactorily and reflect the contributions from the different quasi-particle and collective modes of the spectral function. We analyze the sensitivity of the sum rules to the distribution of spectral strength and their usefulness as quality tests of model calculations.