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

TL;DR

This study presents an improved measurement of Born cross sections for $e^+e^-\to\chi_{bJ}\,\omega$ and $e^+e^-\to\chi_{bJ}\,(\pi^+\pi^-\pi^0)_{\rm non-\omega}$ (with $J=0,1,2$) using Belle and Belle II data across $\sqrt{s}=10.73$–11.02 GeV and around 10.75 GeV, respectively. A key result is that $\Upsilon(10753)$ decays to $\chi_{bJ}\,\omega$ but not to the non-$\omega$ final state, while $\Upsilon(10860)$ decays to $\chi_{bJ}\,(\pi^+\pi^-\pi^0)_{\rm non-\omega}$ but not to $\chi_{bJ}\,\omega$, indicating different internal structures for these resonances. The mass and width of $\Upsilon(10753)$ are measured as $M=(10756.1\pm3.4\,({\rm stat})\pm2.7\,({\rm syst}))$ MeV/$c^2$ and $\Gamma=(32.2\pm11.3\,({\rm stat})\pm14.9\,({\rm syst}))$ MeV, with the products $\Gamma_{ee}{\cal B}(\Upsilon(10753)\to\chi_{b1}\,\omega)=1.46\pm0.25\,({\rm stat})\pm0.20\,({\rm syst})$ eV and $\Gamma_{ee}{\cal B}(\Upsilon(10753)\to\chi_{b2}\,\omega)=1.29\pm0.38\,({\rm stat})\pm0.31\,({\rm syst})$ eV. The results, including an energy-dependent fit with a three-resonance model, support a complex coupling pattern and motivate future studies of $Z_b$-mediated mechanisms in the non-ω channel; they also provide tighter constraints on bottomonium-like structures in the 10.7–11.0 GeV region.

Abstract

We study the processes $χ_{bJ}\,ω$ and $χ_{bJ}\,(π^+π^-π^0)_{\rm non-ω}$ ($J$ = 0, 1, 2) at center-of-mass energies $\sqrt{s}$ from 10.73--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 $Υ(10753)$ state decays into $χ_{bJ}\,ω$ but not into $χ_{bJ}\,(π^+π^-π^0)_{\rm non-ω}$, while the $Υ(10860)$ state, in contrast, decays into $χ_{bJ}\,(π^+π^-π^0)_{\rm non-ω}$ but not into $χ_{bJ}\,ω$. The mass and width of the $Υ(10753)$ 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 $Υ(10753)\toχ_{b1}\,ω$ and $Υ(10753)\toχ_{b2}\,ω$ are ($1.46\pm0.25({\rm stat.})\pm 0.20({\rm syst.})$) eV and ($1.29\pm0.38({\rm stat.})\pm 0.31({\rm syst.})$) eV.

Figures (9)

• Figure 1: Scatter plots of $M(\pi^+\pi^-\pi^0)$ versus $M(\Upsilon(1S)\gamma)$ for selected events in Belle and Belle II data with all energies combined. The red boxes show the $\omega$ and $\chi_{bJ}$ signal regions.
• Figure 2: Distributions of $M(\Upsilon(1S)\gamma)$ and $M(\pi^+\pi^-\pi^0)$ in Belle data at $\sqrt{s}$ = 10.7712 and 10.8658 GeV, and Belle II data at $\sqrt{s}$ = 10.745 and 10.805 GeV with 2D fit results overlaid.
• Figure 3: The $M(\Upsilon(1S)\gamma)$ distributions after requiring events within the $\omega$ signal region in data at each energy point for the Belle and Belle II data samples. The vertical dashed lines (left to right) show the $\chi_{b0}$, $\chi_{b1}$, and $\chi_{b2}$ signal regions.
• Figure 4: The 2D fits to $M(\Upsilon(1S)\gamma)$ and $M(\pi^+\pi^-\pi^0)$ distributions from the data sample that combines all energies at Belle (left) and Belle II (right).
• Figure 5: The dependence of $\Delta(-2\ln\mathcal{L})$ on $\sigma_{\rm Born}(e^+e^- \to \chi_{b1}\,\omega)$ (red dots) at $\sqrt{s}$ = 10882.8 MeV (left) with $N^{\rm obs}=0$ and $N^{\rm bg}=0.3$ and at $\sqrt{s}$ = 10829.5 MeV (right) with $N^{\rm obs}=1$ and $N^{\rm bg}=0.3$. The red curves show the results of the fit discussed in the text. The blue curve in (b) shows the approximation using asymmetric Gaussian uncertainties.