Using 448 million $\psi (2S)$ events, the spin-singlet $P$-wave charmonium state $h_c(1{}^1{P}_1)$ is studied via the $\psi (2S)\to {\pi }^0{h}_c$ decay followed by the $h_c\to \gamma {\eta }_c$ transition. The branching fractions are measured to be ${\mathcal{B}}_{\text{Inc}}(\psi (2S)\to {\pi }^0{h}_c)\times {\mathcal{B}}_{\text{Tag}}(h_c\to \gamma {\eta }_c)=(4.22_{-0.26}^{+0.27}\pm 0.19)\times {10}^{-4}$, ${\mathcal{B}}_{\text{Inc}}(\psi (2S)\to {\pi }^0{h}_c)=(7.32\pm 0.34\pm 0.41)\times {10}^{-4}$, and ${\mathcal{B}}_{\text{Tag}}(h_c\to \gamma {\eta }_c)=(57.66_{-3.50}^{+3.62}\pm 0.58)\%$, where the uncertainties are statistical and systematic, respectively. The $h_c(1{}^1{P}_1)$ mass and width are determined to be $M=(3525.32\pm 0.06\pm 0.15)\mathrm{MeV}/{\mathrm{c}}^2$ and $\mathrm{\Gamma }=(0.78_{-0.24}^{+0.27}\pm 0.12)\mathrm{MeV}$. Using the center of gravity mass of the three ${\chi }_{cJ}(1^3{P}_J)$ mesons [$M(\mathrm{c}.\mathrm{o}.\mathrm{g}.)$], the $1P$ hyperfine mass splitting is estimated to be ${\mathrm{\Delta }}_{\mathrm{hyp}}=M(h_c)-M(\mathrm{c}.\mathrm{o}.\mathrm{g}.)=(0.03\pm 0.06\pm 0.15)\mathrm{MeV}/{\mathrm{c}}^2$, which is consistent with the expectation that the $1P$ hyperfine splitting is zero at the lowest order.

• Received 20 April 2022
• Accepted 11 October 2022

DOI:https://doi.org/10.1103/PhysRevD.106.072007

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Published by the American Physical Society