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

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.