Scalar mesons and glueball in a quark model allowing for gluon anomalies

This paper is a sequel of a previous one (Scalar mesons in a chiral quark model with glueball, Eur. Phys. J. A 8, 567 (2000)) where an attempt to construct an effective $U(3)\times U(3)$-symmetric meson Lagrangian with a scalar glueball was made. The glueball was introduced by using the dilaton model on the base of scale invariance. The scale invariance breaking because of current quark masses and the scale anomaly of QCD, reproduced by the dilaton potential, was taken into account. However, in the previous paper, the scale invariance breaking because of the terms like $h_{\phi}\phi_0^2$ and $h_{\sigma}\bar\sigma_0^2$, where $\phi_0$ and $\bar\sigma_0$ are the pseudoscalar and scalar isosinglets, was not taken into account. These terms are produced by the part of the 't Hooft interaction that is connected with gluon anomalies. Allowing for the scale invariance breaking by these terms has a decisive effect on the quarkonium-glueball mixing and noticeably changes the widths of glueball strong decays. Taking account of this additional source of the scale invariance breaking and its implications are the subject of the present work. It is also shown that in the decay of a glueball into four pions, the channel with two $\rho$-resonances dominates