Observation of $e^{+}{e}^{-}\to \gamma {\chi }_{c1}$ and search for $e^{+}{e}^{-}\to \gamma {\chi }_{c0}$, $\gamma {\chi }_{c2}$, and $\gamma {\eta }_c$ at $\sqrt{s}$ near 10.6 GeV at Belle

Using data samples of $89.5{\mathrm{fb}}^{-1}$, $711.0{\mathrm{fb}}^{-1}$, and $121.4{\mathrm{fb}}^{-1}$ collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider at center-of-mass energies 10.52, 10.58, and 10.867 GeV, respectively, we study the exclusive reactions $e^{+}{e}^{-}\to \gamma {\chi }_{cJ}$ ($J=0$, 1, 2) and $e^{+}{e}^{-}\to \gamma {\eta }_c$. A significant $\gamma {\chi }_{c1}$ signal is observed for the first time at $\sqrt{s}=10.58\mathrm{GeV}$ with a significance of $5.1\sigma$ including systematic uncertainties. No significant excesses for $\gamma {\chi }_{c0}$, $\gamma {\chi }_{c2}$, and $\gamma {\eta }_c$ final states are found, and we set 90% credibility level upper limits on the Born cross sections (${\sigma }_{\mathrm{B}}$) at 10.52 GeV, 10.58 GeV, and 10.867 GeV. Together with cross sections measured by BESIII at lower center-of-mass energies, the energy dependency of ${\sigma }_{\mathrm{B}}(e^{+}{e}^{-}\to \gamma {\chi }_{c1})$ is obtained.

Figure 1

The invariant mass distribution of ${\mu }^{+}{\mu }^{-}$ pairs from all the data samples before the application of the 5C kinematic fit. The solid curve is the fit, and the dotted line is the fitted background. The arrows show the boundaries of the defined $J/\psi$ signal region.

Figure 2

The ${\gamma }_{\mathrm{l}}J/\psi$ invariant mass spectra at $\sqrt{s}=10.52$ (bottom), 10.58 (middle), and 10.867 GeV (top) together with fit results. The points with error bars show the data and the solid curves are the fit functions; the dashed curves show the fitted backgrounds contributions. The arrows show the expected peak positions for the ${\chi }_{c0}$, ${\chi }_{c1}$, and ${\chi }_{c2}$ states.

Figure 3

The mass distributions for the sum of the five ${\eta }_c$ decay modes at $\sqrt{s}=10.52$ (bottom), 10.58 (middle), and 10.867 GeV (top). The points with error bars show the data and the curves show the best-fit results; the dashed curves show the backgrounds contributions. The insets show the ${\eta }_c$ region. The $J/\psi$ signals are produced via ISR.

Figure 4

Measured cross sections for $e^{+}{e}^{-}\to \gamma {\chi }_{c1}$ as a function of C. M. energy. Error bars contain both the statistical and systematic uncertainties. The curve shows the result of fit with a function proportional to $1/s^n$.