Observation of theP11state of charmonium

The spin-singlet $P$-wave state of charmonium, $h_c{(}^1{P}_1)$, has been observed in the decay $\psi (2S)\to {\pi }^0{h}_c$ followed by $h_c\to \gamma {\eta }_c$. Inclusive and exclusive analyses of the $M(h_c)$ spectrum have been performed. Two complementary inclusive analyses select either a range of energies for the photon emitted in $h_c\to \gamma {\eta }_c$ or a range of values of $M({\eta }_c)$. These analyses, consistent with one another within statistics, yield $M(h_c)=[3524.9\pm 0.7(\mathrm{stat})\pm 0.4(\mathrm{sys})]\mathrm{MeV}/c^2$ and a product of the branching ratios ${\mathcal{B}}_{\psi }(\psi (2S)\to {\pi }^0{h}_c)\times {\mathcal{B}}_h(h_c\to \gamma {\eta }_c)=[3.5\pm 1.0(\mathrm{stat})\pm 0.7(\mathrm{sys})]\times {10}^{-4}$. When the ${\eta }_c$ is reconstructed in seven exclusive decay modes, $17.5\pm 4.5$ $h_c$ events are seen with an average mass $M(h_c)=[3523.6\pm 0.9(\mathrm{stat})\pm 0.5(\mathrm{sys})]\mathrm{MeV}/c^2$, and ${\mathcal{B}}_{\psi }{\mathcal{B}}_h=[5.3\pm 1.5(\mathrm{stat})\pm 1.0(\mathrm{sys})]\times {10}^{-4}$. If combined, the inclusive and exclusive data samples yield an overall mass $M(h_c)=[3524.4\pm 0.6(\mathrm{stat})\pm 0.4(\mathrm{sys})]\mathrm{MeV}/c^2$ and product of branching ratios ${\mathcal{B}}_{\psi }{\mathcal{B}}_h=[4.0\pm 0.8(\mathrm{stat})\pm 0.7(\mathrm{sys})]\times {10}^{-4}$. The $h_c$ mass implies a $P$-wave hyperfine splitting $\Delta M_{\mathrm{HF}}(1P)\equiv ⟨M(1^{3}P)⟩-M(1^1{P}_1)=[1.0\pm 0.6(\mathrm{stat})\pm 0.4(\mathrm{sys})]\mathrm{MeV}/c^2$.