Production of singlet P-wave $c\bar{c}$ and $b\bar{b}$ states

No spin-singlet $b\bar{b}$ quarkonium state has yet been observed. In this paper we discuss the production of the singlet P-wave $b\bar{b}$ and $c\bar{c}$ ${}^1{P}_1$ states $h_b$ and $h_c$. We consider two possibilities. In the first the ${}^1{P}_1$ states are produced via the electromagnetic cascades $\ups(3S) \to \eta_b(2S) + \gamma \to h_b + \gamma \gamma \to \eta_b +\gamma\gamma\gamma $and$\psi’\to \eta_c’ + \gamma \to h_c + \gamma \gamma \to \eta_c + \gamma\gamma\gamma$. A more promising process consists of single pion transition to the ${}^1{P}_1$ state followed by the radiative transition to the $1^1{S}_0$ state: $\text{ups}(3S)\to h_b+{\pi }^0\to {\eta }_b+{\pi }^0+\gamma$ and $\psi’ \to h_c + \pi^0 \to \eta_c + \pi^0 +\gamma$\mathrm{.}Foramillion$\ups(3S)$or$\psi’$'s produced we expect these processes to produce several hundred events.