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 $\mbox{S}$ 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.

arXiv comment14 pages, 5 figures; removed $k$ and $k_s$ prefactors in the Schroedinger equation (11) and in the boundary conditions (16) and (17)

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• Heavy hybrid decays to quarkonia
• Heavy-Quark spin symmetry breaking in the Born-Oppenheimer approximation
• Diabatic description of bottomoniumlike mesons
• Study of $I=0$ bottomonium bound states and resonances in $S$, $P$, $D$ and $F$ waves with lattice QCD static-static-light-light potentials
• Heavy meson thresholds in Born-Oppenheimer Effective field theory
• Why quarkonium hybrid coupling to two S-wave heavy-light mesons is not suppressed
• Hidden-bottom hadronic transitions of ${\rm Y}(10753)$
• The unreasonable effectiveness of effective string theory: the case of the 3d SU(2) Higgs model
• Status and Prospects of Exotic Hadrons at Belle II
• Constructing static quark-anti-quark creation operators from Laplacian eigenmodes
• Bottomonia in an unquenched quark model
• Effect of continuum states on the double-heavy hadron spectra
• ${\chi }_{c1}(2p)$: an overshadowed charmoniumlike resonance
• Prediction of an $I(J^P)=0(1^{-})$ $\bar{b}\bar{b}ud$ Tetraquark Resonance Close to the $B^{\ast }{B}^{\ast }$ Threshold Using Lattice QCD Potentials
• Hidden-bottom hadronic decays of ${\rm Y}(10753)$ with a ${\eta }^{(\prime )}$ or $\omega$ emission
• Coupled-channel meson-meson scattering in the diabatic framework
• Search for $e^{+}{e}^{-}\to \gamma {\chi }_{bJ}$ ($J$ = 0, 1, 2) near $\sqrt{s}=10.746$ GeV at Belle II
• Improved measurement of Born cross sections for ${\chi }_{bJ}\omega$ and ${\chi }_{bJ}({\pi }^{+}{\pi }^{-}{\pi }^0{)}_{\mathrm{non}-\omega }$ ($J$ = 0, 1, 2) at Belle and Belle II
• Exotic hadrons associated with $b$-quark