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

TL;DR

This study searches for D-wave bottomonium states via the process $e^+e^- o \pi^+\pi^-\Upsilon(1D)$ at Belle II, setting upper limits on production cross sections due to no significant signals observed.

Contribution

First search for D-wave bottomonium states in this decay channel using Belle II data, providing upper limits where no signals are detected.

Findings

No significant signals observed for D-wave bottomonium states.

Upper limits set on cross sections times branching fractions at various energies.

Results constrain models of bottomonium spectrum and decay mechanisms.

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 $\Upsilon(10753)$ in the reaction $e^+e^- \to \pi^+\pi^- \Upsilon(1D)$, 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 $\Upsilon(10753)$ 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, $\sigma[e^+e^- \to \pi^+\pi^- \Upsilon_2(1D)] \times \mathcal{B}[\Upsilon_2(1D) \to \gamma \chi_{b1}]$ and $\sigma[e^+e^- \to \pi^+\pi^- \Upsilon_3(1D)] \times \mathcal{B}[\Upsilon_3(1D) \to \gamma \chi_{b2}]$, at each center-of-mass energy.