Study of the $h_c$($1^1{P}_1$) meson via $\ddot{I}ˆ(2S)\to \ddot{I}{€}^0{h}_c$ decays at BESIII

Abstract

Using 448 million $\ddot{I}ˆ(2S)$ events, the spin-singlet $P$-wave charmonium state $h_c$(1${}^1{P}_1$) is studied via the $\ddot{I}ˆ(2S)\to \ddot{I}{€}^0{h}_c$ decay followed by the $h_c\to {\hat{I}}^3\hat{I}{\cdot }_c$ transition. The branching fractions are measured to be ${\mathcal{B}}_{\mathrm{Inc}}(\ddot{I}ˆ(2S)\to \ddot{I}{€}^0{h}_c)\times {\mathcal{B}}_{\mathrm{Tag}}(h_c\to {\hat{I}}^3\hat{I}{\cdot }_c)=(4.22_{-0.26}^{+0.27}\pm 0.19)\times 10^{-4}$ , ${\mathcal{B}}_{\mathrm{Inc}}(\ddot{I}ˆ(2S)\to \ddot{I}{€}^0{h}_c)=(7.32\pm 0.34\pm 0.41)\times 10^{-4}$, and ${\mathcal{B}}_{\mathrm{Tag}}(h_c\to {\hat{I}}^3\hat{I}{\cdot }_c)=(57.66_{-3.50}^{+3.62}\pm 0.58)\%$, 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 $\hat{I}“=(0.78_{-0.24}^{+0.27}\pm 0.12)\mathrm{MeV}$. Using the center of gravity mass of the three $\ddot{I}{‡}_{cJ}$(1${}^3{P}_J$) mesons ($M(c.o.g.)$), the $1P$ hyperfine mass splitting is estimated to be $\hat{I}{”}_{\mathrm{hyp}}=M(h_c)-M(c.o.g.)=(0.03\pm 0.06\pm 0.15)\mathrm{MeV}/{\mathrm{c}}^2$, which is consistent with the expectation that the $1P$ hyperfine splitting is zero at the lowest-order.