Composite and elementary nature of a resonance in the sigma model

TL;DR

This paper investigates the internal structure of the sigma meson, analyzing its composite and elementary components through a mixing model and scattering theory, revealing insights into its nature.

Contribution

It introduces a method to disentangle composite and elementary components of resonances within the sigma model using a two-level scattering approach.

Findings

The sigma meson has a mixed composite and elementary nature.

The mixing depends on model parameters like cutoff and elementary sigma mass.

The method clarifies the internal structure of scalar resonances.

Abstract

We analyze the mixing nature of the low-lying scalar resonance consisting of the pipi composite and the elementary particle within the sigma model. A method to disentangle the mixing is formulated in the scattering theory with the concept of the two-level problem. We investigate the composite and elementary components of the sigma meson by changing a mixing parameter. We also study the dependence of the results on model parameters such as the cut-off value and the mass of the elementary sigma meson.