Search for $η_{c}^{'}$ and $h_{c} (^{1}P_{1})$ states in the $e^+ e^-$ annihilations

Abstract

Productions and decays of spin-singlet $S,P-$wave charmonium states, $η_{c}^{'}$ and $h_{c} (^{1}P_{1})$, in the $e^+ e^-$ annihilations are considered in the QCD multipole expansion with neglecting nonlocality in time coming from the color-octet intermediate states. Our approximation is opposite to the Kuang-Yan's model. The results are $B (ψ^{'} \rightarrow h_{c} + π^{0}) \approx 0.3 \%$, $B ( ψ^{'} \rightarrow η^{'} + γ) \approx 0.34 \%$, $Γ(η_{c}^{'} \rightarrow J/ψ+ γ) \approx 0.26$ keV and $Γ(h_{c} \rightarrow J/ψ+ π^{0}) \approx 2.5$ keV.