Exotic to standard bottomonium transitions

Abstract

We study the transition widths of $\mathrm{\ensuremath{\Upsilon}}(10753)$ and $\mathrm{\ensuremath{\Upsilon}}(11020)$ into standard bottomonium under the hypothesis that they correspond to the two lowest laying ${1}^{\ensuremath{-}\ensuremath{-}}$ 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 ${\ensuremath{\pi}}^{0}$, $\ensuremath{\eta}$ or ${\ensuremath{\eta}}^{\ensuremath{'}}$ in the final state and for the next-to-leading operator for ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ or ${K}^{+}{K}^{\ensuremath{-}}$. The hadronization of the gluonic operators is obtained, in the first case, from the axial anomaly and a standard ${\ensuremath{\pi}}^{0}\ensuremath{-}\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{\ensuremath{'}}$ 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 $\mathrm{\ensuremath{\Upsilon}}(11020)$ is indeed a hybrid bottomonium state.

Topics & Concepts