Categorizing $SU(3{)}_f$ representations of scalar mesons by $J/\ddot{I}ˆ$ decays

Abstract

The scalar mesons are established for a long time, but their nature is still an open question. In this paper, we investigate the potential of categorizing their $SU(3{)}_f$ representations via $J/\ddot{I}ˆ\to SV$ and ${\hat{I}}^{3}S$, offering a criterion that may illuminate this issue. Here, $S$ ($V$) denotes scalar (vector) mesons. Using the $SU(3{)}_f$ symmetry with the current data, we find that $f_0(500)$ and $f_0(980)$ are mostly made of singlet and octet $SU(3{)}_f$ representations, respectively, with the singlet-octet mixing angle of $\hat{I}¸=(82.9\pm 4.4{)}^{\circ }$. This conclusion is consistent with the caculations of the quark-antiquark ($q\bar{q}$) hypothesis. For the scalar mesons in the range of 1-2 GeV, we discuss the mixings between $q\bar{q}$ and glueballs. Our numerical results suggest that $f_0(1710)$ is likely composed of the scalar glueball. We urge our experimental colleagues to measure $J/\ddot{I}ˆ\to \ddot{I}a_0(980,1450,1710),$ $K^{\ast }(892{)}^{\pm }{K}^{\ast }(700,1430,1950{)}^{\mp }$ and $\ddot{I}‰f_0(500)$, which provide useful information in the $SU(3{)}_f$ analysis.

12 pages, 7 figures, 5 tables