Ψ(2S) Decay to J/Ψ(1S) + 2 π or J/Ψ(1S) + σ + 2 π

We estimate the decay rate of the Ψ(2S) to J/Ψ(1S) + 2 π and J/Ψ(1S) + σ + 2 π. This is based on the mixed hybrid theory that was developed for the Ψ(2S) and was used to estimate the ratio Ψ(2S)→J/Ψ(1S)+σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\Psi }(2S)\rightarrow J/{\Psi }(1S) + \sigma $\end{document} to Ψ(2S)→J/Ψ(1S)+2π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\Psi }(2S) \rightarrow J/{\Psi }(1S) + 2 \pi $\end{document} in 2011. A main motivation of the present work is to predict the possible experimental detection of the decay of Ψ(2S) to J/Ψ(1S) + σ+2π, or possibly to J/Ψ(1S)+2π+glueball.