Understanding the $f_0(980)$ and $a_0(980)$ masses as well as their widths

TL;DR

This paper investigates the nature of light scalar mesons $f_0(980)$ and $a_0(980)$, showing they are dynamically generated states influenced by confinement and decay interactions, and discusses evidence for a lighter scalar boson $E(38)$.

Contribution

It introduces a unitarised quark-meson model demonstrating that these mesons are dynamical states, highlighting the role of strong decay interactions and $SU(3)_{ m flavour}$ symmetry breaking.

Findings

$f_0(980)$ and $a_0(980)$ are generated by quark confinement and decay interactions.

Evidence for a lighter scalar boson $E(38)$ is presented.

The mesons exhibit large $SU(3)_{ m flavour}$ symmetry breaking effects.

Abstract

The low and approximately equal masses of the scalar mesons $f_0(980)$ and $a_0(980)$, as well as their relatively small decay widths, are impossible to understand in terms of standard $P$-wave quark-antiquark states. Here, these mesons are studied in a unitarised quark-meson model, together with the other light isoscalar scalar $f_0(500)$, as members of a complete scalar nonet below about 1 GeV. They are shown to be dynamical states generated by a combination of quark-confinement and strong-decay interactions, resulting in a large breaking of $SU(3)_{\rm flavour}$ symmetry. This is illustrated with several pole trajectories in the complex-energy plane as a function of the model's decay coupling constant. Also, experimental evidence is presented of a still much lighter scalar boson called $E(38)$, which may correspond to a novel kind of mesons predicted by V. N. Gribov, as an observable manifestation of a condensate of light quarks.