Production of singletP-wavecc¯andbb¯states

No spin-singlet $b\overline{b}$ quarkonium state has yet been observed. In this paper we discuss the production of the singlet P-wave $b\overline{b}$ and $c\overline{c}$ ${}^1{P}_1$ states $h_b$ and $h_c.$ We consider two possibilities. In the first the ${}^1{P}_1$ states are produced via the electromagnetic cascades ${\rm Y}\mathrm{}\left(3S\right)\mathrm{}\to {\eta }_b\mathrm{}\left(2S\right)+\overrightarrow{\gamma }{h}_b+\gamma \overrightarrow{\gamma }{\eta }_b+\gamma \gamma \gamma$ and ${\psi }^{\prime }\to {\eta }_c^{\prime }+\overrightarrow{\gamma }{h}_c+\gamma \overrightarrow{\gamma }{\eta }_c+\gamma \gamma \gamma .$ 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: ${\rm Y}\mathrm{}\left(3S\right)\mathrm{}\to h_b+{\pi }^0\to {\eta }_b+{\pi }^0+\gamma$ and ${\psi }^{\prime }\to h_c+{\pi }^0\to {\eta }_c+{\pi }^0+\gamma .$ For a million ${\rm Y}\mathrm{}\left(3S\right)\mathrm{}$ or ${\psi }^{\prime }’\mathrm{s}$ produced we expect these processes to produce several hundred events.