Observation of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0{\chi }_{bJ}$ and Search for $X_b\to \omega \mathrm{\Upsilon }(1S)$ at $\sqrt{s}=10.867\mathrm{GeV}$

The $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0{\chi }_{bJ}$ ($J=0,1,2$) processes are studied using a $118{\mathrm{fb}}^{-1}$ data sample acquired with the Belle detector at a center-of-mass energy of 10.867 GeV. Unambiguous ${\pi }^{+}{\pi }^{-}{\pi }^0{\chi }_{bJ}$ ($J=1,2$), $\omega {\chi }_{b1}$ signals are observed, and indication for $\omega {\chi }_{b2}$ is seen, both for the first time, and the corresponding cross section measurements are presented. No significant ${\pi }^{+}{\pi }^{-}{\pi }^0{\chi }_{b0}$ or $\omega {\chi }_{b0}$ signals are observed, and 90% confidence level upper limits on the cross sections for these two processes are obtained. In the ${\pi }^{+}{\pi }^{-}{\pi }^0$ invariant mass spectrum, significant non-$\omega$ signals are also observed. We search for the $X(3872)$-like state (named $X_b$) decaying into $\omega \mathrm{\Upsilon }(1S)$; no significant signal is observed with a mass between 10.55 and $10.65\mathrm{GeV}/c^2$.

Figure 1

The $\gamma \mathrm{\Upsilon }(1S)$ invariant mass distribution for selected $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0\gamma \mathrm{\Upsilon }(1S)$ candidate events. The shaded histogram is from normalized ${\pi }^0$-sideband events. The fit to the $\gamma \mathrm{\Upsilon }(1S)$ invariant mass spectrum is described in the text. The solid curves are the best fit for the total fit and background shape; the dash-dotted, dashed, and dotted curves represent the ${\chi }_{b0}$, ${\chi }_{b1}$, and ${\chi }_{b2}$ signals, respectively.

Figure 2

(a) The scatter plot of $M({\pi }^{+}{\pi }^{-}{\pi }^0)$ versus $M\mathbf{(}\gamma \mathrm{\Upsilon }(1S)\mathbf{)}$ for selected $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0\gamma \mathrm{\Upsilon }(1S)$ candidate events, and (b) the projections to $M({\pi }^{+}{\pi }^{-}{\pi }^0)$ for $9.8\mathrm{GeV}/c^2<M\mathbf{(}\gamma \mathrm{\Upsilon }(1S)\mathbf{)}<10\mathrm{GeV}/c^2$, where the dashed and dash-dotted curves represent the $\omega$ and $({\pi }^{+}{\pi }^{-}{\pi }^0{)}_{\mathrm{non}\text{−}\omega }$ events; the dotted curve shows the efficiency dependence on $M({\pi }^{+}{\pi }^{-}{\pi }^0)$. Projections of $M\mathbf{(}\gamma \mathrm{\Upsilon }(1S)\mathbf{)}$ (c) in the $\omega$ signal region and (d) outside of the $\omega$ signal region, where the dash-dotted, dashed, and dotted curves represent the ${\chi }_{b0}$, ${\chi }_{b1}$, and ${\chi }_{b2}$ signals, respectively. The solid curves are the best fit for the total signal and background shapes. The shaded histograms are from the normalized ${\pi }^0$-sideband events.

Figure 3

The $\omega \mathrm{\Upsilon }(1S)$ invariant mass distribution. The dots with error bars are from the data, the solid histogram is from the normalized contribution of $e^{+}{e}^{-}\to \omega {\chi }_{bJ}$ ($J=0,1,2$) from MC simulation, and the shaded histogram is from normalized $\omega$ mass sideband events. The dashed histogram is from the MC signal sample $e^{+}{e}^{-}\to \gamma X_b\to \gamma \omega \mathrm{\Upsilon }(1S)\to \gamma {\pi }^{+}{\pi }^{-}{\pi }^0{\ell }^{+}{\ell }^{-}$ at $\sqrt{s}=10.867\mathrm{GeV}$ with $X_b$ mass fixed at $10.6\mathrm{GeV}/c^2$ and yield fixed at the upper limit at 90% C.L.