The lightest scalar meson in a simple approach

TL;DR

This paper investigates the properties of the lightest scalar meson, $f_{0}(500)$, using a quantum field theoretical toy model to analyze its spectral function, mass, and decay width, revealing complex structure beyond simple models.

Contribution

It introduces a simple effective Lagrangian approach to study the $f_{0}(500)$ resonance, emphasizing the importance of pole analysis on the Riemann sheet for understanding its nature.

Findings

The $f_{0}(500)$ cannot be accurately described by a Breit--Wigner function.

A more complex spectral structure is necessary to model the resonance.

The spectral function is obtained from the pole position on the second Riemann sheet.

Abstract

We study basic properties of scalar hadronic resonances within a quantum field theoretical toy model. In particular, we focus on the spectral function, the mass and the decay width of the resonance $f_{0}(500)$. In this work, this meson is understood as a seed state in an effective Lagrangian which couples to pions. With such a setup we use the position of the pole on the second Riemann sheet in order to obtain its spectral function. We confirm that $f_{0}(500)$ cannot be described by an ordinary Breit--Wigner function, and that a more complicated structure is needed.