The radiative decay of scalar glueball from lattice QCD

We perform the first lattice QCD study on the radiative decay of the scalar glueball to the vector meson ϕ in the quenched approximation. The calculations are carried out on three gauge ensembles with different lattice spacings, which enable us to do the continuum extrapolation. We first revisit the radiative J/ψ decay into the scalar glueball G and obtain the partial decay width Γ(J/ψ → γG) = 0.578(86) keV and the branching fraction Br(J/ψ → γG) = 6.2(9) × 10⁻³, which are in agreement with the previous lattice results. We then extend the similar calculation to the process G → γϕ and get the partial decay width Γ(G → γϕ) = 0.074(47) keV, which implies that the combined branching fraction of J/ψ → γG → γγϕ is as small as \(\cal{O}(10^{-9})\) $$\mathcal{O}({10}^{-9})$$ such that this process is hardly detected by the BESIII experiment even with the large J/ψ sample of \(\cal{O}(10^{10})\) $$\mathcal{O}({10}^{10})$$ . With the vector meson dominance model, the two-photon decay width of the scalar glueball is estimated to be Γ(G → γγ) = 0.53(46) eV, which results in a large stickiness \(S(G)\sim {\cal{O}}(10^{4})\) $$S(G)\sim \mathcal{O}({10}^4)$$ of the scalar glueball by assuming the stickiness of f₂(1270) to be one.