Spontaneous breakdown and the scalar nonet

Abstract

In the context of the QCD quark model and on the basis of dynamical Bethe-Salpeter ladder graphs, we suggest that (i) the existence of the scalar $\overline{q}q$ hadron multiplet, like the pseudoscalar $\overline{q}q$ multiplet, is a direct consequence of dynamical spontaneous breakdown of chiral symmetry with a chiral-limiting nonstrange mass scale of ${m}_{\ensuremath{\sigma}\mathrm{NS}}^{\mathrm{CL}}=2{m}_{\mathrm{dyn}}\ensuremath{\approx}630$ MeV, (ii) the lifting of the nonstrange $\ensuremath{\sigma}\ensuremath{-}\ensuremath{\delta}$ degeneracy is expected from the $s$-wave quark-gluon annihilation diagram, and (iii) the observed $\ensuremath{\delta}\ensuremath{-}{S}^{*}$ mixing from the existence of the $p$-wave scalar quark-annihilation diagram. The resulting predicted ${0}^{++}$ $\overline{q}q$ nonet is then $\ensuremath{\sigma}(750 \mathrm{MeV})$, $\ensuremath{\kappa}(800)$, ${S}^{*}(980)$, and $\ensuremath{\delta}(985)$, in agreement with data for the resonant masses, the mixing angle, and also decay widths except for the $\ensuremath{\kappa}(800)$.