Precision Measurement of the Mass of the $h_c({}^{1}P_1)$ State of Charmonium

A precision measurement of the mass of the $h_c({}^{1}P_1)$ state of charmonium has been made using a sample of $24.5\times {10}^6$ $\psi (2S)$ events produced in $e^{+}{e}^{-}$ annihilation at the Cornell Electron Storage Ring (CESR). The reaction used was $\psi (2S)\to {\pi }^0{h}_c$, ${\pi }^0\to \gamma \gamma$, $h_c\to \gamma {\eta }_c$, and the reaction products were detected in the CLEO-c detector. Data have been analyzed both for the inclusive reaction and for the exclusive reactions in which ${\eta }_c$ decays are reconstructed in 15 hadronic decay channels. Consistent results are obtained in the two analyses. The averaged results of the present measurements are $M(h_c)=3525.28\pm 0.19(\mathrm{stat}.)\pm 0.12(\mathrm{syst}.)\mathrm{MeV}$, and $\mathcal{B}\mathbf{(}\psi (2S)\to {\pi }^0{h}_c\mathbf{)}\times \mathcal{B}(h_c\to \gamma {\eta }_c)=(4.19\pm 0.32\pm 0.45)\times {10}^{-4}$. Using the ${}^{3}P_J$ centroid mass, $\Delta M_{hf}(1P)\equiv ⟨M({\chi }_{cJ})⟩-M(h_c)=+0.02\pm 0.19\pm 0.13\mathrm{MeV}$.

Figure 1

Spectra of recoil masses against ${\pi }^0$ in the inclusive analysis: (top) full spectrum, (bottom) background subtracted spectrum.

Figure 2

Summed distribution of recoil masses against ${\pi }^0$ in the exclusive analysis with 15 decays channels of ${\eta }_c$. See text for details.

Figure 3

Angular distributions of the photons from $h_c\to \gamma {\eta }_c$. Circles and solid points denote results from inclusive and exclusive analyses, respectively. The curve shows $N(1+\alpha {cos}^2\theta )$ distribution, corresponding to $\alpha =1.20$, as explained in the text.