Radiative X(3872) Decays in Charmonium-Molecule Hybrid Model

We study the radiative decays of the X(3872) in the charmonium-molecule model combined with the quark potential model. We obtain Γ(X(3872)→J/ψγ)=29.2keV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Gamma(X(3872) \to J/\psi \, \gamma) = 29.2\,{\rm keV}}$$\end{document} and Γ(X(3872)→ψ′γ)=6.3keV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Gamma(X(3872) \to \psi' \, \gamma) = 6.3\,{\rm keV}}$$\end{document}. The ratio of these two is 0.22, which is much smaller than the BABAR observation. We find that the result is very sensitive to the amount of the χc1(1P)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\chi_{c1}(1P)}$$\end{document} component in the X(3872).