Measurement of the ${\eta }_b(1S)$ mass and the branching fraction for ${\rm Y}(3S)\to \gamma {\eta }_b(1S)$

We report evidence for the ground state of bottomonium, ${\eta }_b(1S)$, in the radiative decay ${\rm Y}(3S)\to \gamma {\eta }_b$ in $e^{+}{e}^{-}$ annihilation data taken with the CLEO III detector. Using $6\times {10}^6$ ${\rm Y}(3S)$ decays, and assuming $\Gamma ({\eta }_b)=10\pm 5\mathrm{MeV}/c^2$, we obtain $\mathcal{B}({\rm Y}(3S)\to \gamma {\eta }_b)=(7.1\pm 1.8\pm 1.3)\times {10}^{-4}$, where the first error is statistical and the second is systematic. The statistical significance is $\sim 4\sigma$. The mass is determined to be $M({\eta }_b)=9391.8\pm 6.6\pm 2.0\mathrm{MeV}/c^2$, which corresponds to the hyperfine splitting $\Delta M_{\mathrm{hf}}(1S{)}_b=68.5\pm 6.6\pm 2.0\mathrm{MeV}/c^2$. Using $9\times {10}^6$ ${\rm Y}(2S)$ decays, we place an upper limit on the corresponding ${\rm Y}(2S)$ decay, $\mathcal{B}({\rm Y}(2S)\to \gamma {\eta }_b)<8.4\times {10}^{-4}$ at 90% confidence level.

Figure 1

(a) Distribution of $|\cos {\theta }_T|$ for ${\eta }_b$ signal MC events (dotted) and background dominated ${\rm Y}(3S)$ data (shaded) in three regions, I, II, and III defined in the text. The histogram of the Monte Carlo simulation of the ${\rm Y}(3S)\to \gamma {\eta }_b$ signal has been multiplied by a factor of 3000 to make it visible. (b) The $E_{\gamma }$ distribution from ${\rm Y}(3S)$ data in the three regions of $|\cos {\theta }_T|$. Only the ${\chi }_{bJ}(2P)\to \gamma {\rm Y}(1S)$ lines at around 770 MeV are visible above the background.

Figure 2

Background- and ${\chi }_{bJ}(2P)$- subtracted distributions of $E_{\gamma }$ from ${\rm Y}(3S)$ decays in three $|\cos {\theta }_T|$ regions, I, II, and III defined in the text. The curves are the results of the joint fit, with a CL of 18.5%. The ${\chi }_{bJ}(2P)$ peaks are indicated by the dotted lines and the ${\eta }_b$ signals by the dashed lines, which join the solid line.

Figure 3

Background- and ${\chi }_{bJ}(2P)$- subtracted distributions of $E_{\gamma }$ from ${\rm Y}(2S)$ decays in three $|\cos {\theta }_T|$ regions, I, II, and III defined in the text. The curves are the joint fit results. The ${\chi }_{bJ}(1P)$ peaks are indicated by the dotted lines and the 90% ${\eta }_b$ upper limits by the dashed lines.