Using 448 million $\psi(2S)$ events, the spin-singlet $P$-wave charmonium state $h_c$(1$^1P_1$) is studied via the $\psi(2S) \rightarrow \pi^0 h_c$ decay followed by the $h_c \to \gamma \eta_c$ transition. The branching fractions are measured to be $\mathcal{ B}_{ \rm Inc}(\psi(2S) \rightarrow \pi^0h_c) \times \mathcal{ B}_{ \rm Tag}(h_c \rightarrow \gamma \eta_c) = (4.22 ^{ +0.27}_{ -0.26} \pm 0.19) \times 10^{ -4}$ , $\mathcal{ B}_{ \rm Inc}(\psi(2S) \rightarrow \pi^0h_c) = (7.32 \pm 0.34 \pm 0.41) \times 10^{ -4}$, and $\mathcal{ B}_{ \rm Tag}(h_c \rightarrow \gamma \eta_c) = (57.66 ^{ +3.62}_{ -3.50} \pm 0.58)\%$, where the uncertainties are statistical and systematic, respectively. The $h_c$(1$^1P_1$) mass and width are determined to be $M = (3525.32 \pm 0.06 \pm 0.15)~\rm{ MeV}/c^{ \rm{ 2}}$ and ${ \mathit \Gamma} = (0.78 ^{ +0.27}_{ -0.24} \pm 0.12)~\rm{ MeV}$. Using the center of gravity mass of the three $\chi_{ cJ}$(1$^3 P_J$) mesons ($M(\rm c.o.g.)$), the $1P$ hyperfine mass splitting is estimated to be $\Delta_{ \rm hyp} = M(h_c) - M(\rm c.o.g.) = (0.03 \pm 0.06 \pm 0.15) ~ \rm{ MeV}/c^{ \rm{ 2}}$, which is consistent with the expectation that the $1P$ hyperfine splitting is zero at the lowest-order.
Categories: hep-ex
