Systematization of tensor mesons and the determination of the $2^{++}$ glueball

Abstract

It is shown that new data on the $(J^{PC}=2^{++})$-resonances in the mass range $M\sim1700-2400 $MeV support the linearity of the $(n,M^2)$-trajectories, where $n$ is the radial quantum number of quark--antiquark state. In this way all vacancies for the isoscalar tensor $q\bar q$-mesons in the range up to 2450 MeV are filled in. This allows one to fix the broad $f_2$-state with $M=2000\pm30 $MeV and $\Gamma=530\pm40 $MeV as the lowest tensor glueball. PACS numbers: 14.40.-n, 12.38.-t, 12.39.-Mk