Scalar glueball: analysis of the (IJ^{PC}=00^{++})-wave

Abstract

Basing on the previously performed K-matrix analysis of experimental data, we investigate, in the framework of the propagator matrix (D-matrix) technique, the 1100-1900 MeV mass region, where overlapping resonances $f_0(1300)$, $f_0(1500)$, $f_0(1530_{-250}^{+90})$, and $f_0(1780)$ are located. Necessary elements of the D-matrix technique are developed. The D-matrix analysis confirms previous K-matrix results: in the region 900-1900 MeV five scalar/isoscalar states are located. Four of them are members of the two $q\bar{q}$-nonets, while one state is an extra for the $q\bar{q}$ systematics, being a good candidate for the lightest scalar glueball. The D-matrix analysis shows that this extra state, a candidate for the lightest scalar glueball, is dispersed, due to a mixing with $q\bar{q}$- states, over three resonances: $f_0(1300)$, $f_0(1500)$, and $f_0(1530_{-250}^{+90})$. The broad resonance $f_0(1530^{+}{90}_{-250})$ is a descendant of the lightest glueball carrying about 50% of the gluonium component, the rest of the gluonium is shared between $f_0(1300)$ and $f_0(1500)$.

Comments: 41 pages including 8 figures