Emergence of the exotic bottomoniumlike state $Y(10650)$ and support from Belle and Belle II data

Abstract

Near-threshold exotic hadrons are usually associated with $S$-wave hadron-hadron dynamics, while higher partial waves are expected to be strongly suppressed by the centrifugal barrier. We show that this expectation can be overturned in the bottomonium sector. In a coupled-channel meson exchange framework combined with the complex scaling method, we find a $J^{PC}=1^{--}$ pole, denoted as $Y(10650)$, generated dominantly by the $P$-wave $B^*\bar B^*$ interaction and located close to the $B^*\bar B^*$ threshold. This pole naturally accounts for the anomalous enhancement observed just above the opening of the $B^*\bar B^*$ threshold in $e^+e^-\to B^*\bar B^*$. Once its production strength is fixed by this threshold enhancement, the corresponding cross sections of $\sigma[e^+e^-\to Y(10650)\to B\bar B^*]$ are predicted by the pole residues and phase-space factors, giving a characteristic dip-or-peak structure consistent with the available Belle (II) data. We further study the hidden-bottom transition $Y(10650)\to \Upsilon(2S)\eta$ through a near-threshold $B^*\bar B^*$ loop mechanism. The resulting $\mathcal{O}(10\sim100~\mathrm{keV})$ width for $Y(10650)\to \Upsilon(2S)\eta$ is sufficient to account for the corresponding cross sections measured by Belle II. The simultaneous appearance of this state in open- and hidden-bottom channels provides a direct experimental path to test a $P$-wave near-threshold mechanism and makes $Y(10650)$ a strong candidate for the first neutral isoscalar exotic bottomoniumlike state in the spectral gap between $\Upsilon(4S)$ and $\Upsilon(5S)$.