Study of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\mathrm{{\rm Y}}(1D)$ 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 $\mathrm{{\rm Y}}(10753)$ in the reaction $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\mathrm{{\rm Y}}(1D)$, using $19.6{\mathrm{f}\mathrm{b}}^{-1}$ 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 $\mathrm{{\rm Y}}(10753)$ 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, $\sigma [e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\mathrm{{\rm Y}}}_2(1D)]\times \mathcal{B}[{\mathrm{{\rm Y}}}_2(1D)\to \gamma {\chi }_{b1}]$ and $\sigma [e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\mathrm{{\rm Y}}}_3(1D)]\times \mathcal{B}[{\mathrm{{\rm Y}}}_3(1D)\to \gamma {\chi }_{b2}]$, at each center-of-mass energy.