Improved measurement of Born cross sections for $\chi_{bJ}\,\omega$ and $\chi_{bJ}\,(\pi^+\pi^-\pi^0)_{\rm non-\omega}$ ($J$ = 0, 1, 2) at Belle and Belle II

Abstract

We study the processes $\chi_{bJ}\,\omega$ and $\chi_{bJ}\,(\pi^+\pi^-\pi^0)_{\rm non-\omega}$ ($J$ = 0, 1, 2) at center-of-mass energies $\sqrt{s}$ from 10.73 to 11.02 GeV using a $142.5\,\mathrm{fb}^{-1}$ data sample collected with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider; and at $\sqrt{s}\sim10.75$ GeV using a $19.8\,\mathrm{fb}^{-1}$ sample collected with Belle II at SuperKEKB. We find that the $\Upsilon(10753)$ state decays into $\chi_{bJ}\,\omega$ but not into $\chi_{bJ}\,(\pi^+\pi^-\pi^0)_{\rm non-\omega}$, while the $\Upsilon(10860)$ state, in contrast, decays into $\chi_{bJ}\,(\pi^+\pi^-\pi^0)_{\rm non-\omega}$ but not into $\chi_{bJ}\,\omega$. The mass and width of the $\Upsilon(10753)$ state are measured to be $(10756.1\pm3.4({\rm stat.})\pm2.7({\rm syst.}))$ MeV/$c^2$ and $(32.2\pm11.3({\rm stat.})\pm14.9({\rm syst.}))$ MeV. The products of the partial width to $e^+e^-$ and branching fractions for $\Upsilon(10753)\to\chi_{b1}\,\omega$ and $\Upsilon(10753)\to\chi_{b2}\,\omega$ are ($1.57\pm0.27({\rm stat.})\pm 0.22({\rm syst.})$) eV and ($1.39\pm0.41({\rm stat.})\pm 0.33({\rm syst.})$) eV.