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

Abstract

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