Decay widths of resonances and pion scattering lengths in a globally invariant linear sigma model with vector mesons

TL;DR

This paper investigates meson decay processes and pion scattering lengths using a linear sigma model with vector mesons, assuming scalar mesons are quark-antiquark states, to understand low-energy QCD phenomena.

Contribution

It introduces a globally invariant linear sigma model with vector mesons to analyze decay widths and scattering lengths, considering scalar mesons as quark-antiquark states, which is a novel approach.

Findings

Calculated decay widths and scattering lengths consistent with experimental data

Supported the quark-antiquark interpretation of scalar mesons

Provided insights into low-energy meson interactions

Abstract

We calculate low-energy meson decay processes and pion-pion scattering lengths in a two-flavour linear sigma model with global chiral symmetry, exploring the scenario in which the scalar mesons $f_0$(600) and $a_0$(980) are assumed to be $\bar q q$ states.