We study the transition widths of $\mathrm{\Upsilon }(10753)$ and $\mathrm{\Upsilon }(11020)$ into standard bottomonium under the hypothesis that they correspond to the two lowest laying $1^{--}$ hybrid bottomonium states. We employ weakly coupled potential NRQCD an effective field theory incorporating the heavy-quark and multipole expansions. We consider the transitions generated by the leading order and next-to-leading order singlet-octet operators. In the multipole expansion the heavy-quark matrix elements factorize from the production of light-quark mesons by gluonic operators. For the leading order operator we compute the widths with a single ${\pi }^0$, $\eta$ or ${\eta }^{\prime }$ in the final state and for the next-to-leading operator for ${\pi }^{+}{\pi }^{-}$ or $K^{+}{K}^{-}$. The hadronization of the gluonic operators is obtained, in the first case, from the axial anomaly and a standard ${\pi }^0-\eta -{\eta }^{\prime }$ mixing scheme and, in the second case, we employ a coupled-channel dispersive representation matched to chiral perturbation theory for both the $S$- and $D$-wave pieces of the gluonic operator. We compare with experimental values and semi-inclusive widths. Our results strongly suggest that $\mathrm{\Upsilon }(11020)$ is indeed a hybrid bottomonium state.

• Received 26 April 2021
• Accepted 22 June 2021

DOI:https://doi.org/10.1103/PhysRevD.104.034019

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Published by the American Physical Society