Search for ${\mathrm{\eta }}_{\mathrm{c}}^{\prime }$ and ${\mathrm{h}}_{\mathrm{c}}$(${\mathrm{P}}_1^1$) states in ${\mathrm{e}}^{+}$${\mathrm{e}}^{\mathrm{-}}$ annihilation

The production and decay of spin-singlet S-, P-wave charmonium states ${\mathrm{\eta }}_{\mathrm{c}}^{\prime }$ and ${\mathrm{h}}_{\mathrm{c}}$(${\mathrm{P}}_1^1$) in ${\mathrm{e}}^{+}$ ${\mathrm{e}}^{\mathrm{-}}$ annihilation are considered in the QCD multipole expansion neglecting the nonlocality in time coming from the color-octet intermediate states. Our approximation is opposite to the Kuang-Yan model. The results are B(ψ′→${\mathrm{h}}_{\mathrm{c}}$+${\mathrm{\pi }}^0$)≈0.3%, B(ψ′→η′+γ)≈0.34%, Γ(${\mathrm{\eta }}_{\mathrm{c}}^{\prime }$→J/ψ+γ)≈0.26 keV, and Γ(${\mathrm{h}}_{\mathrm{c}}$→J/ψ+${\mathrm{\pi }}^0$)≈2.5 keV.