Modified Breit-Wigner formula for mesonic resonances describing OZI decays of confined $q\bar{q}$ states and the light scalar mesons

TL;DR

This paper introduces a modified Breit-Wigner formula derived from a unitarised meson model to describe mesonic resonances and OZI decays, providing insights into light scalar mesons without extra degrees of freedom.

Contribution

A new resonance spectrum expansion formula that relates resonance parameters directly to confinement spectrum and quark-pair creation mechanisms.

Findings

Provides a unified description of mesonic resonances in scattering.

Explains the origin of light scalar mesons without additional assumptions.

Connects resonance parameters to underlying quark dynamics.

Abstract

A general expression resembling Breit-Wigner formulae is derived for the description of resonances which appear in meson-meson scattering. Starting point is a unitarised meson model, but reduced to a simpler form and freed from the specific assumption about the confining force. The parameters of the resulting ``Resonance-Spectrum Expansion'' are directly related to the confinement spectrum and the mechanism of $^3P_0$ valence-quark-pair creation for OZI-allowed hadronic decay, and not to the central positions and widths of resonances. The method also provides a straightforward explanation for the origin of the light scalar mesons without requiring extra degrees of freedom.