The eLSM at nonzero density

TL;DR

This paper extends the Linear Sigma Model to include the four-quark state $f_{0}(500)$ and explores chiral symmetry restoration at high density, providing insights into nuclear matter properties.

Contribution

The paper introduces a method to incorporate the $f_{0}(500)$ four-quark state into the eLSM in a chiral invariant way and studies chiral restoration in dense matter.

Findings

Inclusion of $f_{0}(500)$ affects nuclear matter saturation.

Chiral symmetry restoration can be homogeneous or inhomogeneous at high density.

The extended model provides a framework for dense QCD matter analysis.

Abstract

The extended Linear Sigma Model (eLSM) is an effective model of QCD which includes in the mesonic sector (pseudo)scalar and (axial-)vector quarkonia mesons as well as one dilaton/glueball field and in the baryonic sector the nucleon doublet and its chiral partner in the mirror assignment. The chiral partner of the pion turns out to be the resonance $f_{0}(1370),$ which is then predominantly a quarkonium state. As a consequence, $f_{0}(500)$ is predominately not a quarkonium state but a four-quark object and is at first not part of the model. Yet, $f_{0}(500)$ is important in the baryonic sector and affects nuclear matter saturation, the high-density behavior, and nucleon-nucleon scattering. In these proceedings, we show how to enlarge the two-flavour version of the eLSM in order to include the four-quark field $f_{0}(500)$ in a chiral invariant manner. We then discuss homogeneous and inhomogeneous chiral restoration in a dense medium.