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.
Categories: hep-ph