Categorizing $SU(3)_f$ representations of scalar mesons by $J/\psi$ decays

• DOI: 10.48550/arxiv.2403.07701
• Publication Date: 2024-03-12
• Authors: Chao-Qiang Geng; Chia-Wei Liu; Xiao Yu; Ao-Wen Zhou
• Keywords: High Energy Physics - Phenomenology; High Energy Physics - Experiment (hep-ex); High Energy Physics - Phenomenology (hep-ph); FOS: Physical sciences; High Energy Physics - Experiment

We explore the possibilities of categorizing $SU(3)_f$ representations scalar mesons through $J/\psi\to SV$ and $\gamma S$, with $S$ ($V$) being scalar(vector) mesons. find that $f_0(500)$ $f_0(980)$ are singlet octet states, respectively; which both belong to a nonet flavor symmetry. In addition, we determine singlet-octet mixing angle $\theta = (84.2\pm13.9)^{\circ}$ between $f_0(980)$, supports quark-antiquark ($q\bar{q}$) hypothesis. For in range 1-2 GeV, containing two $f_0(1370,\ 1500,\ 1700)$, discuss mixings $q\bar{q}$ glueballs. Our numerical results suggest $f_0(1370 (1500))$ has significant component $n\bar{n}$ ($s\bar{s}$), while $f_0(1710)$ is likely composed glueball.