Abstract
We study the three-flavor chirally and dilatation invariant extended linear sigma model with (pseudo)scalar and (axial-)vector mesons as well as a scalar dilaton field whose excitations are interpreted as a glueball. The model successfully describes masses and decay widths of quark-antiquark mesons in the low-energy region up to 1.6 GeV. Here we study in detail the vacuum properties of the scalar-isoscalar ${J}^{PC}={0}^{++}$ channel and find that (i) a narrow glueball is only possible if the vacuum expectation value of the dilaton field is (at tree level) quite large (i.e. larger than what lattice QCD and QCD sum rules suggest) and (ii) only solutions in which ${f}_{0}(1710)$ is predominantly a glueball are found. Moreover, the resonance ${f}_{0}(1370)$ turns out to be mainly $(\overline{u}u+\overline{d}d)/\sqrt{2}$ and thus corresponds to the chiral partner of the pion, while the resonance ${f}_{0}(1500)$ is mainly $\overline{s}s$.
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