The radiative decay of scalar glueball from lattice QCD

Abstract

We perform the first lattice QCD study on the radiative decay of the scalar glueball to the vector meson $\varphi$ 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 $J/\psi$ decay into the scalar glueball $G$ and obtain the partial decay width $\Gamma (J/\psi \to \gamma G)=0.578(86)\text{keV}$ and the branching fraction $\text{Br}(J/\psi \to \gamma G)=6.2(9)\times 10^{-3}$. We then extend the similar calculation to the process $G\to \gamma \varphi$ and get the partial decay width $\Gamma (G\to \gamma \varphi )=0.074(47)\text{keV}$, which implies that the combined branching fraction of $J/\psi \to \gamma G\to \gamma \gamma \varphi$ is as small as $\mathcal{O}(10^{-9})$ such that this process is hardly detected by the BESIII experiment even with the large $J/\psi$ sample of $\mathcal{O}(10^{10})$. With the vector meson dominance model, the two-photon decay width of the scalar glueball is estimated to be $\Gamma (G\to \gamma \gamma )=0.53(46)\text{eV}$, which results in a large stickiness $S(G)\sim \mathcal{O}(10^4)$ of the scalar glueball by assuming the stickiness of $f_2(1270)$ to be one.

13 pages,11 figures. This version is to be published in SCPMA

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