The lightest scalar meson in a simple approach

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.