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 phi 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 -> gamma G) = 0.578(86) keV and the branching fraction Br(J/psi -> gamma G) = 6.2(9) x 10-3, which are in agreement with the previous lattice results. We then extend the similar calculation to the process G -> gamma phi and get the partial decay width Gamma(G -> gamma phi) = 0.074(47) keV, which implies that the combined branching fraction of J/psi -> gamma G -> gamma gamma phi is as small as O(10-9)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\cal{O}(10<^>{-9})$$\end{document} such that this process is hardly detected by the BESIII experiment even with the large J/psi sample of O(1010)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\cal{O}(10<^>{10})$$\end{document}. With the vector meson dominance model, the two-photon decay width of the scalar glueball is estimated to be Gamma(G -> gamma gamma) = 0.53(46) eV, which results in a large stickiness S(G)similar to O(104)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S(G)\sim {\cal{O}}(10<^>{4})$$\end{document} of the scalar glueball by assuming the stickiness of f2(1270) to be one.