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 m odel with glueball, fur. Phys. J. A 8, 567 (2000)) where an attempt to cons truct an effective U(3) x U(3)-symmetric meson Lagrangian with a scalar glu eball was made. The glueball was introduced by using the dilaton model on t he base of scale invariance. The scale invariance breaking because of curre nt quark masses and the scale anomaly of QCD reproduced by the dilaton pote ntial, was taken into account. However, in the previous paper, the scale in variance breaking because of the terms like h(phi)phi (2)(0) and h(sigma)<( <sigma>)over bar>(2)(0), where phi (0) and <(<sigma>)over bar>(0) are the p seudoscalar and scalar isosinglets, was not taken into account. These terms are produced by the part of the 't Hooft interaction that is connected wit h gluon anomalies. Allowing for the scale invariance breaking by these term s has a decisive effect on the quarkonium-glueball mixing and noticeably ch anges the widths of glueball strong decays. Taking account of this addition al source of the scale invariance breaking and its implications are the sub ject 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.