Bottomonium resonances with $I=0$ from lattice QCD correlation functions with static and light quarks

Abstract

We discuss, how to study $I=0$ quarkonium resonances decaying into pairs of heavy-light mesons using static potentials from lattice QCD. These static potentials can be obtained from a set of correlation functions containing both static and light quarks. As a proof of concept we focus on bottomonium with relative orbital angular momentum $L=0$ of the $\bar{b}b$ pair corresponding to $J^{PC}=0^{-+}$ and $J^{PC}=1^{--}$. We use static potentials from an existing lattice QCD string breaking study and compute phase shifts and $\text{mbox}T$ matrix poles for the lightest heavy-light meson-meson decay channel. We discuss our results in the context of corresponding experimental results, in particular for ${\rm Y}(10860)$ and ${\rm Y}(11020)$.

Comments: 23 pages, 9 figures; version accepted for publication in PRD