$0^{++}$-Glueball/$q\bar{q}$-State Mixing in the Mass Region near 1500 MeV

Abstract

Basing on the results of the K-matrix fit of $(I{J}^{PC}=00^{++})$ wave, we analyze the analytic structure of the amplitude and $q\bar{q}$/glueball content of resonances in the mass region 1200-1900 MeV, where an extra state for $q\bar{q}$-systematics exists being a good candidate for the lightest scalar glueball. Our analysis shows that the pure glueball state dispersed over three resonances: $f_0(1300)$, $f_0(1500)$ and $f_0(1530_{-250}^{+90})$, while the glueball admixture in $f_0(1750)$ is small. The broad resonance $f_0(1530_{-250}^{+90})$ is the descendant of the lightest pure glueball. The mass of pure glueball is $1630\pm \genfrac{}{}{0ex}{}{70}{30}$ MeV, in agreement with Lattice calculation results.

Comments: LaTex, 12 pages, 2 figures