Behaviour of S-Wave poles Near Threshold and the Scalar Meson Nonet Below 1 GeV

TL;DR

This paper analyzes the behavior of S-wave poles near threshold in meson-meson scattering, revealing that light scalar mesons originate from semi-bound states rather than confinement spectrum poles, using a four-parameter scattering model.

Contribution

It introduces a four-parameter model for non-exotic meson scattering that explains the origin and behavior of light scalar mesons near threshold.

Findings

Light scalar mesons originate from semi-bound states, not confinement poles.

S-wave poles exhibit identical threshold behavior regardless of origin.

The model accommodates all non-exotic mesons as resonances or bound states.

Abstract

We describe the behaviour at threshold of S-wave poles of the scattering matrix within a four-parameter model for non-exotic meson-meson scattering. This model accommodates all non-exotic mesons, hence also the light scalar mesons, as resonances and bound states characterised by complex singularities of the scattering amplitude as a function of the total invariant mass. The majority of the full S-matrix mesonic poles stem from an underlying confinement spectrum. However, the light scalar mesons K0*(830), a0(980), f0(400--1200), and f0(980) do not, but instead originate in 3P0-barrier semi-bound states. We show that the behaviour of the corresponding poles is identical at threshold.