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

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.