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

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.