Study of $e^+e^- \to π^+π^-Υ(1D)$ at Belle II

TL;DR

This study searches for dipion transitions from the vector resonance Υ(10753) to the D-wave bottomonia Υ_J(1D) with J = 2,3 by reconstructing Υ_J(1D) → γ χ_{b1,2} decays in e^+e^- collisions. Using 19.6 fb^-1 of Belle II data near 10.75 GeV and a π^+π^- recoil-mass analysis, the authors perform unbinned fits to extract potential signals but observe no significant contribution, setting 90% credibility level upper limits on σ[e^+e^- → π^+π^- Υ_2(1D)] × B(Υ_2(1D) → γ χ_{b1}) and σ[e^+e^- → π^+π^- Υ_3(1D)] × B(Υ_3(1D) → γ χ_{b2}) across several center-of-mass energies. The analysis carefully accounts for backgrounds (notably ωχ_{b1,b2} and ηΥ(2S)), ISR effects, and systematic uncertainties, and compares results under Υ(10753) vs Υ(5S) line-shapes. The findings suggest suppressed coupling of Υ(10753) to Υ_J(1D) via dipion transitions, providing constraints on bottomonium spectroscopy and potential exotic interpretations of Υ(10753). These measurements refine our understanding of radiative transitions in heavy quarkonia and inform future searches for D-wave states.

Abstract

The bottomonium spectrum, consisting of bound states of a $b$ quark and an anti-$b$ quark, provides an excellent laboratory for probing quantum chromodynamics in the non-perturbative regime. While $S$ and $P$-wave bottomonium states are well studied experimentally, information on $D$-wave states remains scarce. We search for $D$-wave bottomonium state via the decay of a vector bottomonium-like state $Υ(10753)$ in the reaction $e^+e^- \to π^+π^- Υ(1D)$, using $19.6~\mathrm{fb}^{-1}$ of data collected with the Belle II detector at center-of-mass energies $\sqrt{s} = 10.653, 10.701, 10.745$, and $10.805$~GeV, in the vicinity of the $Υ(10753)$ resonance. No significant signals are observed. Upper limits at the 90% credibility level are set on the products of the cross sections and branching fractions, $σ[e^+e^- \to π^+π^- Υ_2(1D)] \times \mathcal{B}[Υ_2(1D) \to γχ_{b1}]$ and $σ[e^+e^- \to π^+π^- Υ_3(1D)] \times \mathcal{B}[Υ_3(1D) \to γχ_{b2}]$, at each center-of-mass energy.

Figures (4)

• Figure 1: Normalized $M(\pi^+\pi^-)^{\text{recoil}}$ distributions for signal MC events. The dot-dashed blue line represents the $\Upsilon(2S)$ signal, the dashed violet line is the $\Upsilon_2(1D)$ signal, and the solid cyan line is the $\Upsilon_3(1D)$ signal.
• Figure 2: Fits to the $M(\pi^+\pi^-)^{\text{recoil}}$ distributions for data events in the $\chi_{b1}$ channel. Dots with error bars represent the data, the solid red line is the total fit, the dashed violet line is the $\Upsilon_2(1D)$ signal component, the dot-dashed blue line is the $\Upsilon(2S)$ signal component, the double-dot-dashed green line represents the $\omega \chi_{b1,b2}$ background, and the dotted blue line is the constant background component. Note that the $\sqrt{s} = 10.701~\mathrm{GeV}$ sample contains zero events.
• Figure 3: Fits to the $M(\pi^+\pi^-)^{\text{recoil}}$ distributions for data events in the $\chi_{b2}$ channel. Dots with error bars represent the data, the solid red line is the total fit, the long-dashed cyan line is the $\Upsilon_3(1D)$ signal component, the dot-dashed blue line is the $\Upsilon(2S)$ signal component, the double-dot-dashed green line represents the $\omega \chi_{b1,b2}$ background, and the dotted blue line is the constant background component. Note that the $\sqrt{s} = 10.701~\mathrm{GeV}$ sample contains zero events.
• Figure 4: Measured 90% credible upper limits on the product $\sigma[e^+e^- \to \pi^+\pi^- \Upsilon_2(1D)] \times \mathcal{B}(\Upsilon_2(1D) \to \gamma \chi_{b1})$ as a function of center-of-mass energy, evaluated under the $\Upsilon(10753)$ resonance hypothesis (left) and the $\Upsilon(5S)$ resonance hypothesis (right). Inverted triangles denote the measured upper limits. The dark dots with error bars indicate the estimated value at 10.866 GeV, derived from Belle results y5s-pipiInclusive-belle. The solid curves represent the extrapolated cross sections under the respective resonance hypotheses, with the filled bands illustrating the uncertainties associated with these extrapolations.