We explore the possibilities of categorizing SU(3)f representations of scalar mesons through J/ψ→ SV and γ S, with S (V) being the scalar(vector) mesons. We find that f₀(500) and f₀(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 θ = (84.2±13.9)∘ between f₀(500) and f₀(980), which supports the quark-antiquark (qq̄) hypothesis. For the scalar mesons in the range of 1-2 GeV, containing two of f₀(1370,\ 1500,\ 1700), we discuss the mixings between qq̄ and glueballs. Our numerical results suggest that f₀(1370 (1500)) has the a significant component of nn̄ (ss̄), while f₀(1710) is likely composed of the scalar glueball.
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Geng et al. (2024) studied this question.
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