Observation of the $h_c({}^{1}P_1)$ State of Charmonium

The $h_c{(}^1{P}_1)$ state of charmonium has been observed in the reaction $\psi (2S)\to {\pi }^0{h}_c\to (\gamma \gamma )(\gamma {\eta }_c)$ using $3.08\times {10}^6$ $\psi (2S)$ decays recorded in the CLEO detector. Data have been analyzed both for the inclusive reaction, where the decay products of the ${\eta }_c$ are not identified, and for exclusive reactions, in which ${\eta }_c$ decays are reconstructed in seven hadronic decay channels. We find $M(h_c)=3524.4\pm 0.6\pm 0.4\mathrm{MeV}$ which corresponds to a hyperfine splitting $\Delta M_{\mathrm{hf}}(1P)\equiv ⟨M{(}^3{P}_J)⟩-M{(}^1{P}_1)=+1.0\pm 0.6\pm 0.4\mathrm{MeV}$, and $\mathcal{B}\mathbf{(}\psi (2S)\to {\pi }^0{h}_c\mathbf{)}\times \mathcal{B}(h_c\to \gamma {\eta }_c)=(4.0\pm 0.8\pm 0.7)\times {10}^{-4}$.

Figure 1

Exclusive analysis: (a) Scatter plot of the reconstructed ${\eta }_c$ candidate mass vs the recoil mass against ${\pi }^0$ for data. The horizontal band in the vicinity of $M(J/\psi )$ and the diagonal band at larger ${\eta }_c$ candidate mass correspond to $\psi (2S)\to {\pi }^0{\pi }^{0}J/\psi$ and $\psi (2S)\to \gamma {\chi }_{c0}$, respectively. The dashed lines denote the region $M({\eta }_c)=2982\pm 50\mathrm{MeV}$. Data events (open histograms) and Monte Carlo background estimate (shaded histograms) of (b) reconstructed ${\eta }_c$ candidate mass projection for $M({\pi }^0\mathrm{\text{recoil}})=3524\pm 8\mathrm{MeV}$ and (c) recoil $h_c$ candidate mass spectrum for $M({\eta }_c)=2982\pm 50\mathrm{MeV}$. The peaks in (b) near $M=3.1$ and 3.25 GeV correspond to $\psi (2S)\to {\pi }^0{\pi }^{0}J/\psi$ and $\psi (2S)\to \gamma {\chi }_{c0}$, respectively. (d) Reconstructed ${\eta }_c$ candidate mass for data in the direct decay $\psi (2S)\to \gamma {\eta }_c$. The peak near $M=3.4\mathrm{GeV}$ is from the direct decay $\psi (2S)\to \gamma {\chi }_{c0}$.

Figure 2

Inclusive analysis: Recoil mass against ${\pi }^0$ for (a) Monte Carlo sample for $39.1\times {10}^6$ $\psi (2S)$ and (b) data for $3\times {10}^6$ $\psi (2S)$. See text for details.

Figure 3

Inclusive analysis: Efficiency-corrected fit yields versus $|\cos \theta |$ for data with $E_{\gamma }=503\pm 35\mathrm{MeV}$; (a) for $h_c$ yield, the curve corresponds to the best fit $\propto (1+{cos}^2\theta )$ and (b) for the nearly isotropic background yield.