Light Scalar Mesons in the Improved Ladder QCD

Abstract

The light scalar meson spectrum is studied using the improved ladder QCD with the UA(1) breaking Kobayashi-Maskawa-'t Hooft interaction by solving the Schwinger-Dyson and Bethe-Salpeter equations. The dynamically generated momentum-dependent quark mass is large enough in the low momentum region to give rise to the spontaneous breaking of chiral symmetry. Due to the large dynamical quark mass, the scalar mesons become the q bar{q} bound states. Since the parameters have been all fixed to reproduce the light pseudoscalar meson masses and the decay constant, there is no free parameter in the calculation of the scalar mesons. We obtain $M_{sigma} = 667$ MeV, $M_{a_0} = 942$ MeV and $M_{f_0} = 1336$ MeV. They are in good agreement with the observed masses of $sigma(600)$, $a_0(980)$ and $f_0(1370)$, respectively. We therefore conclude that these states are the members of the light scalar meson nonet. The mass of $K_0^{*}$ is obtained between that of $a_0$ and $f_0$ and the corresponding state is not observed experimentally. We also find that the strangeness content in the $sigma$ meson is about 5%.