New Members in the $0^{+}$ ($0^{++})$ Family

Abstract

Recent BES data on $J/\psi \to \varphi \pi \pi$ indicate that there is a possible new spin-0 state ($f_0(1790)$) with a mass of $m=1790_{-30}^{+40}\mathrm{MeV}/{\mathrm{c}}^2$. Assuming it to be an iso-singlet $0^{+}(0^{++})$, we propose a new mixing scheme to describe this and the other three known iso-singlet $f_0(1370)$, $f_0(1500)$, $f_0(1710)$ states by adding iso-singlet hybrid states to the usual basis of two iso-singlet quarkonia and one glueball. Since there are two iso-singlet hybrid states, $(u\bar{u}+d\bar{d})g/\sqrt{2}$ and $s\bar{s}g$, this new basis implies existence of another iso-singlet state $X$. Using known data, we estimate the ranges of the mixing parameters. We find two sets of solutions with X mass predicted to be about 1820 MeV and 1760 MeV, respectively. We also study implications on the decay properties of these new states.

Comments: 16 pages, 1 figure, 3 tables. More reference added and text re-arranged