Revisiting the determining fraction of glueball component in $f_0$ mesons via radiative decays of $J/\psi$

Abstract

QCD theory predicts the existence of glueballs, but so far all experimental endeavors have failed to identify any such states. To remedy this discrepancy between QCD, which has proven to be a successful theory for strong interactions, and the failure of experimental searches for glueballs, one is tempted to accept the promising interpretation that the glueballs mix with regular $q\bar q$ states of the same quantum numbers. The lattice estimate of the masses of pure $0^{++}$ glueballs ranges from 1 to 2 GeV, which is the region of the $f_0$ family. Thus many authors suggest that the $f_0$ mesonic series is an ideal place to study possible mixtures of glueballs and $q\bar q$. In this paper, following the strategy proposed by Close, Farrar and Li, we try to determine the fraction of glueball components in $f_0$ mesons using the measured mass spectra and the branching ratios of $J/\psi$ radiative decays into $f_0$ mesons. Since the pioneering papers by Close et al., more than 20 years has elapsed and more accurate measurements have been done by several experimental collaborations, so it is time to revisit this interesting topic using new data. We suppose $f_0(500)$ and $f_0(980)$ to be pure quark states, while for $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$, to fit both the experimental data of $J/\psi$ radiative decay and their mass spectra, glueball components are needed. Moreover, the mass of the pure $0^{++}$ glueball is phenomenologically determined.