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 $B^{\ast }{\bar{B}}^{\ast }$ interaction and located close to the $B^{\ast }{\bar{B}}^{\ast }$ threshold. This pole naturally accounts for the anomalous enhancement observed just above the opening of the $B^{\ast }{\bar{B}}^{\ast }$ threshold in $e^{+}{e}^{-}\to B^{\ast }{\bar{B}}^{\ast }$. Once its production strength is fixed by this threshold enhancement, the corresponding cross sections of $\sigma [e^{+}{e}^{-}\to Y(10650)\to B{\bar{B}}^{\ast }]$ 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 $Y(10650)\to {\rm Y}(2S)\eta$ through a near-threshold $B^{\ast }{\bar{B}}^{\ast }$ loop mechanism. The resulting $\mathcal{O}(10\sim 100\mathrm{keV})$ width for $Y(10650)\to {\rm Y}(2S)\eta$ 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 ${\rm Y}(4S)$ and ${\rm Y}(5S)$.

8+6 pages, 5 figures; v2 is a substantially revised version correcting errors in the coupled-channel pole calculations of v1, with all results updated; this version further presents a correlated analysis of Belle II open-bottom cross sections and the hidden-bottom ${\rm Y}(2S)\eta$ transition under theoretical constraints, yielding consistent experimental evidence for the predicted Y(10650)