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 spaicings, 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 → γ G)=0.449(44)~keV and the branching fraction Br(J/ψ → γ G) = 4.8(5)× 10⁻³, which are in agreement with the previous lattice results. We then extend the similar calculation to the process G→ γ φ and get the partial decay width Γ(G → γ φ)= 0.074(47)~keV, which implies that the combined branching fraction of J/ψ→γ G→ γγφ is as small as O(10⁻⁹) such that this process is hardly detected by the BESIII experiment even with the large J/ψ sample of O(10¹⁰). 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)~ O(10⁴) of the scalar glueball by assuming the stickiness of f₂(1270) to be one.