Search for $\psi(4S)\to\eta J/\psi$ in $B^\pm \to \eta J/\psi K^\pm$ and $e^+ e^- \to \eta J/\psi$ processes

We search for the?ψ(4S)?state in?$B^\pm \ra \eta J/\psi K^\pm$?and?$e^+e^- \ra \eta J/\psi$?based on the Belle measurements with the assumed mass?M=(4230±8)?MeV/c2?and width?Γ=(38±12)?MeV. No significant signal is observed in the?ηJ/ψ?mass spectra. The 90\% confidence level upper limit on the product branching fraction?$\BR(B^\pm \ra \psi(4S)K^\pm)\BR(\psi(4S) \ra \eta J/\psi)<6.8\times 10^{-6}$?is obtained in$B^\pm \ra \eta J/\psi K^\pm$?decays. By assuming the partial width of?ψ(4S)→e+e??being 0.63 keV, the branching fraction limit?$\BR(\psi(4S) \ra \eta J/\psi) < 1.3\%$?is obtained at the 90\% confidence level in$e^+e^- \ra \eta J/\psi$, which is consistent with the theoretical prediction.