Exotic to standard bottomonium transitions

Abstract

We study the transition widths of $\Upsilon(10753)$ and $\Upsilon(11020)$ 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 filed 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 $\eta'$ 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 $\pi^0-\eta-\eta'$ 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 $\Upsilon(11020)$ is indeed a hybrid bottomonium state.