Vacuum Properties of Mesons in a Linear Sigma Model with Vector Mesons and Global Chiral Invariance

TL;DR

This paper develops a linear sigma model with vector mesons to analyze meson vacuum properties, emphasizing the importance of chiral symmetry and exploring quark content assignments for scalar mesons against experimental data.

Contribution

It introduces a globally chiral invariant linear sigma model with vector mesons and compares two quark content scenarios for scalar mesons, highlighting the model's successes and limitations.

Findings

Model describes vacuum properties well except for sigma decay width.

Scalar meson quark content assignment affects decay widths and scattering lengths.

Additional scalar degrees of freedom are needed for a complete description.

Abstract

We present a two-flavour linear sigma model with global chiral symmetry and vector and axial-vector mesons. We calculate pion-pion scattering lengths and the decay widths of scalar, vector, and axial-vector mesons. It is demonstrated that vector and axial-vector meson degrees of freedom play an important role in these low-energy processes and that a reasonable theoretical description requires globally chirally invariant terms other than the vector meson mass term. An important question for meson vacuum phenomenology is the quark content of the physical scalar f0(600) and a0(980) mesons. We investigate this question by assigning the quark-antiquark sigma and a0 states of our model with these physical mesons. We show via a detailed comparison with experimental data that this scenario can describe all vacuum properties studied here except for the decay width of the sigma, which turns out to be too small. We also study the alternative assignment f0(1370) and a0(1450) for the scalar mesons. In this case the decay width agrees with the experimental value, but the pion-pion scattering length $a_{0}^{0}$ is too small. This indicates the necessity to extend our model by additional scalar degrees of freedom.