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

Productions and decays of spin-singlet $S,P-$wave charmonium states, $\eta_{c}^{'}$ 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 $B (\psi^{'} \rightarrow h_{c} + \pi^{0}) \approx 0.3 \%$, $B ( \psi^{'} \rightarrow \eta^{'} + \gamma ) \approx 0.34 \%$, $\Gamma (\eta_{c}^{'} \rightarrow J/\psi + \gamma) \approx 0.26$ keV and $\Gamma (h_{c} \rightarrow J/\psi + \pi^{0}) \approx 2.5$ keV.