Computation of the quarkonium and meson-meson composition of the ${\rm Y}(nS)$ states and of the new ${\rm Y}(10753)$ Belle resonance from lattice QCD static potentials

Abstract

We compute the composition of the bottomonium ${\rm Y}(nS)$ states (including ${\rm Y}(10860)$) and the new ${\rm Y}(10753)$ resonance reported by Belle in terms of quarkonium and meson-meson components. We use a recently developed novel approach utilizing lattice QCD string breaking potentials for the study of resonances. This approach is based on the Born Oppenheimer approximation and the unitary emergent wave method and allows to compute the poles of the $\text{mbox}S$ matrix. We focus on $I=0$ bottomonium $S$ wave bound states and resonances, where the Schrödinger equation is a set of coupled differential equations. One of the channels corresponds to a confined heavy quark-antiquark pair $\bar{b}b$, the others to pairs of heavy-light mesons. In a previous study only one meson-meson channel ${\bar{B}}^{(\ast )}{B}^{(\ast )}$ was considered. Now we also include the closed strangeness channel ${\bar{B}}_s^{(\ast )}{B}_s^{(\ast )}$ extending our formalism significantly to have a more realistic description of bottomonium. We confirm the new Belle resonance ${\rm Y}(10753)$ as a dynamical meson-meson resonance with around $85\%$ meson-meson content. Moreover, we identify ${\rm Y}(4S)$ and ${\rm Y}(10860)$ as states with both sizable quarkonium and meson-meson contents. With these results we contribute to the clarification of ongoing controversies in the vector bottomonium spectrum.

Comments: 14 pages, 5 figures; removed $k$ and $k_s$ prefactors in the Schroedinger equation (11) and in the boundary conditions (16) and (17)