Radiative and hadronic transitions of the charmoniumP11state

Hadronic transitions of the charmonium ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ ($=h_c$) state into $\frac{J}{\psi }$ are considered in the QCD multipole expansion. Using the decay rate of ${\chi }_{\mathrm{cJ}}\to \frac{J}{\psi }+\gamma$ and a quantum-mechanical sum rule, we estimate $\Gamma \left(h_c\mathrm{}\right(1P)\mathrm{}\to \frac{J}{\psi }{\pi }^0)>\mathrm{}1.6\mathrm{}$ keV, which is close to the recent measurement by E760, $\Gamma \left(h_c\mathrm{}\right(1P)\mathrm{}\to \frac{J}{\psi }{\pi }^0)\sim 1$ keV. Other transitions of $h_c$ are also considered in the same context.